ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8

  • 24,564 views
Uploaded on

This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building …

This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building structure in the South Europe. It id offers a detail view of the design of steel framed buildings to the structural Eurocodes and includes a set of worked examples showing the design of structural elements with using software (CSI ETABS). It is intended to be of particular to the people who want to become acquainted with design to the Eurocodes. Rules from EN 1998-1-1 for global analysis, type of analysis and verification checks are presented. Detail design rules for steel composite beam, steel column, steel bracing and composite slab with steel sheeting from EN 1998-1-1, EN1993-1-1 and EN1994-1-1 are presented. This guide covers the design of orthodox members in steel frames. It does not cover design rules for regularities. Certain practical limitations are given to the scope.

More in: Design , Technology , Business
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
No Downloads

Views

Total Views
24,564
On Slideshare
0
From Embeds
0
Number of Embeds
2

Actions

Shares
Downloads
4,834
Comments
0
Likes
13

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1.       Seismic  design  of  steel   building  accordance  to       Eurocode  3  and  8         Valentinos  Neophytou  BEng,  MSc           JULY  2013   -­‐Worked  examples  –  Hand  calculations   ETABS  manual
  • 2. Page 2 ABOUT THIS DOCUMENT This publication provides a concise compilation of selected rules in the Eurocode 8, together with relevant Cyprus National Annex, that relate to the design of common forms of concrete building structure in the South Europe. It id offers a detail view of the design of steel framed buildings to the structural Eurocodes and includes a set of worked examples showing the design of structural elements with using software (CSI ETABS). It is intended to be of particular to the people who want to become acquainted with design to the Eurocodes. Rules from EN 1998-1-1 for global analysis, type of analysis and verification checks are presented. Detail design rules for steel composite beam, steel column, steel bracing and composite slab with steel sheeting from EN 1998-1-1, EN1993-1-1 and EN1994-1-1 are presented. This guide covers the design of orthodox members in steel frames. It does not cover design rules for regularities. Certain practical limitations are given to the scope. Due to time constraints and knowledge, I may not be able to address the whole issues. Please send me your suggestions for improvement. Anyone interested to share his/her knowledge or willing to contribute either totally a new section about Eurocode 8 or within this section is encouraged. For further details: My LinkedIn Profile: http://www.linkedin.com/profile/view?id=125833097&trk=hb_tab_pro_top Email: valentinos_n@hotmail.com Slideshare Account: http://www.slideshare.net/ValentinosNeophytou
  • 3. Page 3 List of contents 1.1 DESIGN AND ANALYSIS EXAMPLE OF STEEL FRAME WITH CONCENTRIC BRACING .................................................................................................................................7 1.1 LAYOUT OF STRUCTURE...............................................................................................7 1.2 PRELIMINARY DESIGN...................................................................................................9 1.2.1 PRELIMINARY DESIGN OF COLUMNS AND BEAMS ............................................9 1.3 MATERIAL PROPERTIES ..............................................................................................11 1.3.1 MATERIAL PROPERTIES OF CONCRETE...............................................................11 1.3.2 MATERIAL PROPERTIES OF STEEL ........................................................................12 1.3.3 MATERIAL PROPERTIES OF STEEL AND CONCRETE AS DEFINE IN ETABS 13 1.3.4.1 MODELING REQUIREMENTS OF EC8 FOR CONCRETE MEMBERS...............15 1.3.4.2 MODELING REQUIREMENTS OF EC8 FOR FLOOR DIAPHRAGMS................15 1.3.4.3 MESHING OF SLABS................................................................................................16 1.4 JOINT MODELING (EN1993-1-1,CL.5.1.2) ...................................................................17 2.0 MODAL RESPONSE SPECTRUM ANALYSIS.............................................................20 2.1 STRUCTURAL TYPES AND BEHAVIOR FACTOR ACCORDING TO EN1998-1- 1,CL.6.3 ...................................................................................................................................20 2.2 DEFINE DESIGN HORIZONTAL RESPONSE SPECTRUM........................................24 2.2.1 VERTICAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.3)................................24 2.2.2 HORIZONTAL RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5)..........................24 2.2.3 PARAMETERS OF ELASTIC RESPONSE SPECTRUM (EN1998-1-1,CL.3.2.2.5)..25 2.2.3.1 GROUND INVESTIGATION CONDITIONS...........................................................29 2.2.3.2 IMPORTANCE FACTOR...........................................................................................29 2.2.3.3 DUCTILITY CLASS...................................................................................................30 2.3 ANALYSIS TYPES ..........................................................................................................31 2.3.1 MODAL RESPONSE SPECTRUM ANALYSIS..........................................................31 2.3.1.1 ACCIDENTAL ECCENTRICITY..............................................................................32 2.3.2 LATERAL FORCE ANALYSIS REQUIREMENTS....................................................34 2.3.4 ESTIMATION OF FUNDAMENTAL PERIOD T1 ......................................................35 2.3.5 AUTOMATIC LATERAL FORCE ANALYSIS USING ETABS................................36 2.3.6 USER LOADS - LATERAL FORCE ANALYSIS USING ETABS.............................38
  • 4. Page 4 2.3.7 TORSIONAL EFFECTS ................................................................................................45 2.3.8 SUMMARY OF ANALYSIS PROCESS IN SEISMIC DESIGN SITUATION...........46 3.0 DEFINE STATIC LOADS................................................................................................47 4.0 SEISMIC MASS REQUIREMENTS ACCORDING TO EC8.........................................48 4.1 MASS SOURCE OPTION ................................................................................................49 5.0 WIND LOADING ON STRUCTURE (EN1991-1-4:2004)..............................................51 5.1 CALCULATION OF WIND LOAD ACCORDING TO EN1991-1-4:2004....................51 5.2 APPLICATION OF WIND LOADING USING ETABS .................................................54 6.0 LOAD COMBINATION...................................................................................................59 7.0 DESIGN PREFERENCES ................................................................................................61 8.0 ANALYSIS AND DESIGN REQUIREMENTS FOR CONCENTRICALLY BRACED FRAMES ACCORDING TO EN1998-1-1,CL.6.7.2 ..............................................................64 8.1 STEPS OF THE DESIGN DETAIL OF CONCENTRIC STEEL FRAMES ...................65 8.2 CLASSIFICATION OF STEEL SECTIONS....................................................................66 8.3 DESIGN OF COMPOSITE SLAB UNDER GRAVITY LOADS....................................68 8.4 DESIGN OF COMPOSITE BEAM (WITH STEEL SHEETING) UNDER GRAVITY LOADS ....................................................................................................................................72 8.5 DETAIL DESIGN OF STEEL COLUMNS UNDER GRAVITY LOADS......................79 8.6 DETAIL DESIGN RULES OF STEEL CONCENTRIC BRACED FRAMES (CBF) ACCORDING TO EUROCODE 8..........................................................................................87 8.6.1 DETAIL DESIGN RULES OF STEEL BRACING ACCORDING TO EUROCODE 8 ..................................................................................................................................................87 8.7 DETAIL DESIGN RULES OF STEEL COLUMNS AND BEAMS ACCORDING TO EUROCODE 8.........................................................................................................................88 8.8 DETAIL DESIGN RULES OF STEEL COMPOSITE MEMBERS ACCORDING TO EUROCODE 8.........................................................................................................................89 8.9 DETAIL DESIGN RULES OF STEEL MOMENT RESISTANCE FRAMES (MRF) ACCORDING TO EUROCODE 8..........................................................................................90 8.9.1 DETAIL DESIGN RULES FOR MRF - DESIGN CRITERIA....................................90 8.9.2 DETAIL DESIGN RULES OF STEEL BEAM FOR MRF...........................................90 8.9.3 DETAIL DESIGN RULES OF STEEL COLUMN FOR MRF.....................................91 9.0 DESIGN OF STEEL FRAMES.........................................................................................92 9.1 DESIGN OF STEEL MEMBER OVERWRITES DATA.................................................92
  • 5. Page 5 9.2 DESIGN OF COLUMNS / BEAMS USING ETABS – GRAVITY LOAD ANALYSIS ONLY ......................................................................................................................................97 9.3 DESIGN OF STEEL COLUMN (GRAVITY DESIGN SITUATION) – HAND CALCULATIONS.................................................................................................................105 9.4 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATIONN).........................118 9.4.1 DESIGN OF STEEL COLUMN (SEISMIC DESIGN SITUATION – HAND CALCULATION)..................................................................................................................124 9.5 DESIGN OF COMPOSITE BEAMS - HAND CALCULATIONS................................128 9.5 DESIGN OF STEEL BRACING.....................................................................................145 9.5.1 MAIN CONFIGURATION OF DESIGN OF STEEL BRACING..............................145 9.5.2 SIMPLIFIED DESIGN OF FRAMES WITH X BRACING (EXTRACT FROM DESIGN GUIDANCE TO EC8) ...........................................................................................147 9.5.3 MODEL IN ETABS .....................................................................................................148 9.5.4 DESIGN OF STEEL BRACING (GRAVITY/SEISMIC DESIGN SITUATION) – HAND CALCULATION.......................................................................................................156 10.0 MODAL RESPONSE SPECTRUM ANALYSIS.........................................................170 10.1 SET THE ANALYSIS OPTIONS.................................................................................170 10.2 EVALUATE THE ANALYSIS RESULTS OF THE STRUCTURE ACCORDING TO THE MODAL ANALYSIS REQUIREMENTS ...................................................................171 10.2.1 ASSESS THE MODAL ANALYSIS RESULTS BASED ON THE EN1998...........172 11.0 SECOND ORDER EFFECTS (P – Δ EFFECTS) ACCORDING TO EN1998-1- 1,CL.4.4.2.2 ...........................................................................................................................173 11.1 DISPLACEMENT CALCULATION ACCORDING TO EN1998-1-1,CL.4.4.2.2 .....174 11.2 INTERSTOREY DRIFT................................................................................................174 11.3 CALCULATION OF SECOND ORDER EFFECT USING ETABS...........................175 11.3.1 INTERSTOREY DRIFT DISPLACEMENT .............................................................176 11.3.2 TOTAL GRAVITY LOAD PTOT................................................................................178 11.3.2 TOTAL SEISMIC STOREY SHEAR VTOT...............................................................180 12.0 DAMAGE LIMITATION ACCORDING TO EN1998-1-1,CL.4.4.3 ..........................184 12.1 CALCULATION OF DAMAGE LIMITATION..........................................................185 ANNEX - A ..........................................................................................................................186 ANNEX A.1 - ASSUMPTIONS MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3 & EC8) ..........................................................................................................186
  • 6. Page 6 A1.1:LIMITATION MADE IN THE DESIGN ALGORITHM (MANUAL OF ETABS – EC3&EC8).............................................................................................................................187 ANNEX –B: STEEL DESIGN FLOWCHARTS..................................................................188
  • 7. Page 7 1.1 Design and analysis example of steel frame with concentric bracing 1.1 Layout of structure Figure 1.1: Plan view Figure 1.2: Side Elevation (4) & (1)
  • 8. Page 8 Figure 1.3: Side Elevation (A) & (D) Table 1.1: Dimensions of the building Dimensions Symbol Value Units Storey height h 3.0 m Total height of the building H 9.0 m Beam length in X-direction lx 5.0 m Beam length in Y-direction ly 5.0 m Building width in X-direction Lx 15.0 m Building width in Y-direction Ly 15.0 m
  • 9. Page 9 1.2 Preliminary design Table 1.2: Seismic design data Data Symbol Value Units Seismic zone - 3 - Reference peak ground acceleration on type A ground, agR. agR 0.25 m/s2 Importance class γI 1.0 - Design ground acceleration on type A ground ag 0.25 m/s2 Design spectrum - Type 1 - Ground type - B - Structural system Steel frame with concentric bracing Behavior factor q 4.0 - 1.2.1 Preliminary design of columns and beams Preliminary design of steel beam Design data: Span of beam Bay width Overall depth of slab Loading data: Density of concrete Loads of floor per meter Live load Live load per meter Partial factor for actions: Safety factor are obtain from Table A.1(2)B EN1990 Permanent actions, γ G Variable actions, γ Q Total load Lx 5000mm:= wbay 5000mm:= h 130mm:= γ c 25kN m 3− ⋅:= gfloor γ c h⋅ Lx⋅ 16.25 kN m 1− ⋅⋅=:= qoffice 2kN m 2− ⋅:= qservice qoffice Lx⋅ 10 kN m 1− ⋅⋅=:= γ G 1.35:= γ Q 1.5:= Ed γ G gfloor⋅ γ Q qservice⋅+ 36.94 kN m 1− ⋅⋅=:=
  • 10. Page 10 Material properties: Young Modulus of Elasticity Structural steel (clause 6.1(1) EN 1993 1-1) Structural steel properties: Yield strength, fy Ultimate strength, fu Yield strength of reinforcement, fyk Deflection limitation: Deflection limit - General purpose Second moment area required Second moment area provided (IPE240) Moment resistance check: Design moment (Fixed end) Plastic modulus required Plastic modulus provided (IPE240) Weak Beam - Strong column -Capacity design: Plastic modulus of column required Plastic modulus of column provided (HE220A) Es 210kN mm 2− ⋅:= γ M0 1.0:= fy 355N mm 2− ⋅:= fu 450N mm 2− ⋅:= fyk 500N mm 2− ⋅:= F Lx 300 := Ireq 300 Ed⋅ Lx 3 ⋅ 384 Es⋅ 1.718 10 3 × cm 4 ⋅=:= Iprov 3892cm 4 := Check_1 if Iprov Ireq> "OK", "NOT OK",( ):= Check_1 "OK"= MEd Ed Lx 2 ⋅ 12 76.953kN m⋅⋅=:= Wpl.y.req MEd fy 216.769cm 3 ⋅=:= Wpl.y 324.4cm 3 := Check_2 if Wpl.y Wpl.y.req> "OK", "NOT OK",( ):= Check_2 "OK"= Wpl.y.c.req 1.3 Wpl.y⋅ 421.72cm 3 =:= Wpl.y.c 515cm 3 := Check_3 if Wpl.y.c Wpl.y.c.req> "OK", "NOT OK",( ):= Check_3 "OK"=
  • 11. Page 11 1.3 Material properties ETABS: Define > Material properties 1.3.1 Material properties of concrete Design requirement Poisson ratio is equal to v = 0 (cracked concrete) and v = 0.2 (un-cracked concrete) as (EN1992-1-1,cl.3.1.3). Table 1.3: Concrete properties (EN 1992, Table 3.1) Property Data for concrete C16/20 (N/mm2 ) C20/25 (N/mm2 ) C25/30 (N/mm2 ) C30/37 (N/mm2 ) Mass per unit Volume 2,5E-09 2,5E-09 2,5E-09 2,5E-09 Weight per unit volume 2,5E-05 2,5E-05 2,5E-05 2,5E-05 Modulus of Elasticity 29000 30000 31000 33000 Poisson’s Ratio (cracked concrete) 0 0 0 0 Coeff. of thermal expansion 10E-06 10E-06 10E-06 10E-06 Charact. ConcCyl. Strength, fck 16 20 25 30 Bending Reinf. Yield stress, fyk 500 500 500 500 Shear Reinf. Yield stress, fyk 500 500 500 500
  • 12. Page 12 1.3.2 Material properties of steel Table 1.4: Material properties of steel Material Properties Symbol Value Units References Mass per unit Volume γs 7.85E-09 kg/mm3 EN1991-1-1,table A.4 Weight per unit Volume γs 7.70E-05 N/mm3 EN1991-1-1,table A.4 Modulus of Elasticity Es 210,000 N/mm2 EN1993-1-1,cl.3.2.6(1) Poisson’s ratio ν 0.3 - EN1993-1-1,cl.3.2.6(1) Coeff of Thermal Expansion (Steel structures) α 1.2x10-5 per K (for T ≤ 100o C) K EN1993-1-1,cl.3.2.6(1) Coeff of Thermal Expansion (Composite Concrete- Steel structures) α 1.2x10-5 per K (for T ≤ 100o C) K EN1993-1-1,cl.3.2.6(1) Shear Modulus G ≈81,000 N/mm2 EN1993-1-1,cl.3.2.6(1) Characteristic yield strength of steel profile fy 275 N/mm2 EN1993-1-1,table 3.1 Ultimate strength fu 430 N/mm2 EN1993-1-1,table 3.1 Table 1.5: Strength vales of steel sections (EN1993-1-1,table 3.1) Steel grade Nominal thickness of the element t (mm) t ≤ 40mm 40mm < t ≤ 80mm Grade referencefy (N/mm2 ) fu (N/mm2 ) fy (N/mm2 ) fu (N/mm2 ) S235 235 360 215 360 EN 10025-2 S275 275 430 255 410 EN 10025-2 S355 355 510 335 470 EN 10025-2 S450 440 550 410 550 EN 10025-2 Note: You may use the product standard instead of those given in EN1993-1-1
  • 13. Page 13 1.3.3 Material properties of steel and concrete as define in ETABS Figure 1.4: Material properties of concrete (C25/30) Figure 1.5: Material properties of steel (S275) 1.3.4 Slab modeling
  • 14. Page 14 Table 1.6: Slab properties Data Symbol Value Units Slab depth hs 170 mm Diameter of stud d 19 mm Height of stud haw 152 mm Tensile strength of stud fu 430 N/mm2 ETABS: Define > Wall/Slab/Deck Sections/Add new deck Figure 1.6: Deck section properties Press “Set Modifier” in order to modify the slab properties
  • 15. Page 15 1.3.4.1 Modeling requirements of EC8 for concrete members 1. Unless a more accurate analysis of the cracked elements is performed, the elastic flexural and shear stiffness properties of concrete and masonry elements may be taken to be equal to one-half of the corresponding stiffness of the un-cracked elements (EN1998-1-1,cl.4.3.1(7)). Figure 1.7: Modified “Stiffness Modifiers” 1.3.4.2 Modeling requirements of EC8 for floor diaphragms ETABS: Select > Wall/Slab/Deck section > Select Deck ETABS: Define > Diaphragms ETABS: Select “D1” (Rigid diaphragms) 2. When the floor diaphragms of the building may be taken as being rigid in their planes, the masses and the moments of inertia of each floor may be lumped at the centre of gravity (EN1998-1-1,cl.4.3.1(4)).
  • 16. Page 16 1.3.4.3 Meshing of slabs ETABS: Select > Wall/Slab/Deck section > Select Deck ETABS: Assign > Shell area > Auto Object Auto mesh option When you have a composite beam floor system, ETABS, by default, automatically meshes (divides) the deck at every beam and girder. This allows ETABS to automatically distribute the loading on the deck to each beam or girder in an appropriate manner. Figure 1.8: Meshing of composite slab Figure 1.9: Meshing of normal slab
  • 17. Page 17 1.4 Joint modeling (EN1993-1-1,cl.5.1.2) (1) The effects of the behavior of the joints on the distribution of internal forces and moments within a structure, and on the overall deformations of the structure, may generally be neglected, but where such effects are significant (such as in the case of semi-continuous joints) they should be taken into account, see EN 1993-1-8. (2) (2) To identify whether the effects of joint behavior on the analysis need be taken into account, a distinction may be made between three joint models as follows, see EN 1993-1-8, 5.1.1: – simple, in which the joint may be assumed not to transmit bending moments. – continuous, in which the behavior of the joint may be assumed to have no effect on the analysis. – semi-continuous, in which the behavior of the joint needs to be taken into account in the analysis.
  • 18. Page 18 Table 1.7: Example of joint types Simple joint Continuous Fixed joint Semi- continuous joint ETABS: Pin joint in ETABS The pin-joint in ETABS can be achieved by selecting the members that you assumed to be pinned in the analysis process. This can be done as follow: Select member > Assign > Frame/Line > Frame Releases Partial Fixity Figure 1.10: Pinned joint (both ends)
  • 19. Page 19 ETABS: Fixed joint in ETABS The fixed-joint in ETABS can be achieved by selecting the members that you assumed to be fixed in the analysis process. This can be done as follow: Select member > Assign > Frame/Line > Frame Releases Partial Fixity Figure 1.11: Fixed joint
  • 20. Page 20 2.0 Modal Response Spectrum Analysis 2.1 Structural types and behavior factor according to EN1998-1-1,cl.6.3 Table 2.1: Structural types and behavior factor Structural Type q-factor DCM DCH Moment resisting frames (MRF) αu/ α1 =1.1 αu/ α1 =1.2 (1 bay) αu/ α1 =1.3 (multi-bay) dissipative zones in beams and column bases 4 5αu/ α1 Concentrically braced frames (CBF) Dissipative zones in tension diagonals 4 4 V-braced frames (CBF) 2 2.5
  • 21. Page 21 Dissipative zones in tension and compression diagonals Frames with K-bracing (CBF) Not allowed in dissipative design Eccentrically braced frame (EBF) αu/ α1 =1.2 dissipative zones in bending or shear links 4 5αu/ α1 Inverted pendulum system αu/ α1 =1.0 αu/ α1 =1.1 dissipative zones in column base, or column ends (NEd/Npl,Rd < 0.3) 2 2αu/ α1 Moment-resisting frames with concentric bracing (MRF) + (CBF) 4 4αu/ α1
  • 22. Page 22 αu/ α1 =1.2 dissipative zones in moment frame and tension diagonals Moment frames with infills Unconnected concrete or masonry infills, in contact with the frame 2 2 Connected reinforced concrete Infills See EN1998-1-1,table 5.1 Infills isolated from moment frame 4 5αu/ α1 Structures with concrete cores or walls See EN1998-1-1,table 5.1 Note: If the building is non-regular in elevation (see EN1998-1-1,cl.4.2.3.3) the upper limit values of q listed above should be reduced by 20 %
  • 23. Page 23 Table 2.2: Values of behavior factor for regular and irregular structure Structural type Regular in plan and elevation Irregular in plan / Regular in elevation Regular in plan / Irregular in elevation Irregular in plan & elevation Irregular in plan / Regular in elevation Regular in plan / Irregular in elevation Irregular in plan & elevation DCM DCH DCM DCM DCM DCH DCH DCH Moment resisting frame Single storey portal 4.0 5.5 3.2 3.2 3.2 5.25 4.4 4.2 One bay multi-storey 4.0 6.0 3.2 3.2 3.2 5.5 4.8 4.4 Multi-bay, multi-storey 4.0 6.5 3.2 3.2 3.2 5.75 5.2 4.6 Concentrically braced frame Diagonal bracing 4.0 4.0 3.2 4.0 4.0 4.0 3.2 3.2 V-bracing 2.0 2.5 1.6 2.5 2.5 2.5 2.0 2.0 Frame with masonry infill panels 2.0 2.0 1.6 2.0 2.0 2.0 1.6 1.6
  • 24. Page 24 2.2 Define design horizontal response spectrum 2.2.1 Vertical response spectrum (EN1998-1-1,cl.3.2.2.3) The vertical component of the seismic action should be taken into account if the avg>0.25g (2.5m/s2) in the cases listed below: • for horizontal structural member spanning 20m or more, • for horizontal cantilever components longer than 5m, • for horizontal pre-stressed components, • for beams supporting columns, • in based-isolated structures. 2.2.2 Horizontal response spectrum (EN1998-1-1,cl.3.2.2.5) For the horizontal components of the seismic action the design spectrum, Sd(T), shall be defined by the following expressions: 0 ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙ ! ! + ! !! ∙ !.! ! − ! ! (ΕΝ1998-1-1,Eq. 3.13) 𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙ !.! ! (ΕΝ1998-1-1,Eq. 3.14) 𝑇! ≤ 𝑇 ≤ 𝑇!: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙ 2.5 𝑞 𝑇! 𝑇                                                                                      ≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.15) 𝑇! ≤ 𝑇 ≤ 4𝑠: 𝑆! 𝑇 = 𝑎! ∙ 𝑆 ∙ !.! ! !!!! !! ≥ 𝛽 ∙ 𝑎! (ΕΝ1998-1-1,Eq. 3.5) Design ground acceleration on type A ground: ag=γIagR Lower bound factor for the horizontal spectrum: β=0.2 Note: the value of q are already incorporate with an appropriation value of damping viscous, however the symbol η is not present in the above expressions.
  • 25. Page 25 2.2.3 Parameters of elastic response spectrum (EN1998-1-1,cl.3.2.2.5) Table 2.3: Parameters of Type 1 elastic response spectrum (CYS NA EN1998-1-1,table 3.2) Ground Type S TB (s) TC (s) TD (s) A 1.0 0.15 0.4 2.0 B 1.2 0.15 0.5 2.0 C 1.15 0.20 0.6 2.0 D 1.35 0.20 0.8 2.0 E 1.4 0.15 0.5 2.0 Note: For important structures (γI>1.0), topographic amplification effects should be taken into account (see Annex A EN1998-5:2004 provides information for topographic amplification effects). ETABS: Define > Response spectrum function 1. Peak ground acceleration agR=0,25g, 2. Type C or D for building within category of importance I and II, 3. Define two response spectrum cases if the factor q is different in each direction, Select EUROCODE8 Spectrum Add New Function
  • 26. Page 26 4. Modify the existing values of elastic response spectrum case in order to change it into the design response spectrum. Figure 2.1: Response Spectrum to EC8 PERIOD   ACCELERATION   g  =   9.81   m/sec2     T   Sd(T)   β  =   0.2   -­‐   0.0000   0.2000   SoilType  =   B   -­‐   0.1000   0.1917   q  =   4.00   -­‐   0.1500   0.1875   αgR   =   0.25   -­‐   0.2000   0.1875   S  =   1.20   -­‐   0.4000   0.1875   TB   =   0.15   sec   0.6000   0.1563   TC   =   0.50   sec   0.8000   0.1172   TD   =   2.00   sec   1.0000   0.0938   T  =   0.50   sec   1.5000   0.0625                 2.0000   0.0469     Data  for  soil  type  -­‐  Type  Spectrum  1     2.5000   0.0300     index   Soil  Type   S   TB   TC   TD   3.0000   0.0500     1   A   1   0.15   0.4   2   4.0000   0.0500     2   B   1.2   0.15   0.5   2   5.0000   0.0500     3   C   1.15   0.2   0.6   2   6.0000   0.0500     4   D   1.35   0.2   0.8   2   8.0000   0.0500     5   E   1.4   0.15   0.5   2   10.0000   0.0500                 Convert the existing elastic response spectrum case to design response spectrum case
  • 27. Page 27
  • 28. Page 28 Figure 2.2: Amendment Response spectrum (q = 4)
  • 29. Page 29 2.2.3.1 Ground investigation conditions Table 2.4: Geological studies depend on the importance class (CYS NA EN1998-1-1, NA 2.3 / cl.3.1.1 (4)) Importance class of buildings Ground Type I II III IV A NRGS NRGS RGS RGS B NRGS NRGS RGS RGS C NRGS NRGS RGS RGS D NRGS NRGS RGS RGS E NRGS NRGS RGS RGS NRGS: Not required geological studies RGS: required geological studies if there is not adequate information 2.2.3.2 Importance factor Table 2.5: Importance classes for buildings (ΕΝ1998-1-1,table.4.3 and CYS NA EN1998- 1-1,cl NA2.12) Importance class Buildings Important factor γI Consequences Class I Buildings of minor importance for public safety, e.g. argricultural buildings, etc. 0.8 CC1 II Ordinary buildings, not belonging in the other categories. 1.0 CC2 III Buildings whose seismic resistance is of importance in view of the consequences associated with a collapse, e.g. schools, assembly halls, cultural institutions etc. 1.2 CC3 IV Buildings whose integrity during earthquakes is of vital importance for civil protection, e.g. hospitals, fire stations, power plants, etc. 1.4 CC3
  • 30. Page 30 CC1: Low consequence for loss of human life, and economic, social or environmental consequences small or negligible. CC2: Medium consequence for loss of human life, economic, social or environmental consequences considerable. CC3: High consequence for loss of human life, or economic, social or environmental consequences very great 2.2.3.3 Ductility class Table 2.6: Requirement for importance class relate to ductility class (CYS NA EN1998- 1-1,cl NA2.16 & cl.5.2.1(5)) Importance class Zone 1 Zone 2 Zone 3 I DCL DCL DCL II DCM/DCH DCM/DCH DCM/DCH III DCM/DCH DCM/DCH DCM/DCH IV DCH DCH DCH DCL: Ductility class low. DCM: Ductility class medium. DCH: Ductility class high.
  • 31. Page 31 2.3 Analysis types 2.3.1 Modal Response spectrum analysis Table 2.7: Requirements of modal response spectrum analysis according to Eurocode 8 Requirements Values References Regular in plan YES / NO ΕΝ1998-1-1,table 4.1 Regular in elevation NO ΕΝ1998-1-1,table 4.1 Sum of the effective modal masses ≥ 90% EN1998-1-1,cl.4.3.3.1(3) ≥ 5% of total mass Minimum number of modes k ≥3.√n k: is the number of modes n: is the number of storey EN1998-1-1,cl.4.3.3.1(5) Behaviour factor q Tk ≤ 0.20sec Tk: is the period of vibration of mode k. EN1998-1-1,cl.4.3.3.1(5) Fundamental period Tj ≤ 0.9 Ti SRSS EN1998-1-1,cl.4.3.3.2.1(2) Tj ≥ 0.9 Ti CQC Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2 1. Independently in X and Y direction, 2. Define design spectrum, 3. Use CQC rule for the combination of different modes (EN1998-1-1,cl.4.3.3.3.2(3)) 4. Use SRS rule for combined the results of modal analysis for both horizontal directions (EN1998-1-1,cl.4.3.3.5.1(21)). 5. Modal Combination: “Complete Quadratic Combination” (CQC) can be used if the Tj ≤ 0,9 Ti (EN1998-1-1,cl.4.3.3.3.2(3)P).
  • 32. Page 32 2.3.1.1 Accidental eccentricity Accidental eccentricity of each storey cause of uncertainties location of masses have been taken into account 5% (EN1998-1-1,cl.4.3.2). Moreover, if there are masonry infills with a moderately irregular and asymmetric distribution in plan, is doubled further in Eurocode 8 (i.e., to 10% of the storey orthogonal dimension in the baseline case, or 20% if accidental torsional effects are evaluated in a simplified way when using two separate 2D models). Table 2.8: Summary of accidental eccentricity Percentage of accidental eccentricity Geometry of model (3D/2D) Asymmetric distribution of mass (Regular/Irregular) Masonry infills (Regular/Irregular) 5% 3D Regular Regular 10% 3D Irregular Irregular 20% 2D - - Note: Accidental eccentricity is automatically included during response-spectrum analysis in ETABS, though equivalent static-load procedures are also available for manual evaluation. Note that floor diaphragms must be rigid, otherwise torsional effects are not substantial. ETABS implements an efficient and practical approach while formulating dynamic response from accidental eccentricity. After the response-spectrum load case is run, the X and Y acceleration at each joint location is determined, then multiplied by the tributary mass and the diaphragm eccentricity along either Y or X. The larger absolute value of these resultant moments (m*Xacc*dY or m*Yacc*dX) is then applied as torsion about the joint location. Static response is then added to response-spectrum output to account for the additional design forces caused by accidental eccentricity.
  • 33. Page 33 Define > Response spectrum cases Note: Add two response spectrum cases: EQX and EQY as showing below (figure 9). Figure 2.3: Response Spectrum case Data for EQY& EQX
  • 34. Page 34 2.3.2 Lateral force analysis requirements Table 2.9: Requirements of lateral force analysis according to Eurocode 8 Requirements Values References Regular in plan YES / NO ΕΝ1998-1-1,table 4.1 Regular in elevation YES ΕΝ1998-1-1,table 4.1 Ground acceleration 0.10-0.25g CYS NA EN1998-1- 1:Seismic zonation map Spectrum type 1 EN1998-1-1,cl.3.2.2.2(2)P Ground type A,B,C,D,E Normally type B or C can be used normal condition EN1998-1-1,cl.3.1.2(1) Lower bound factor for the horizontal design spectrum λ = 0.85 if T1 ≤ 2TC and more than 2 storey λ=1.0 in all other case EN1998-1-1,cl.4.3.3.2.2(1Ρ) Behaviour factor q Concrete DCM q= 1.5 – 3.90 EN1998-1-1,cl.5.2.2.2(2) Concrete DCH q= 1.6 – 5.85 EN1998-1-1,cl.5.2.2.2(2) Steel DCM q= 2.0 – 4.00 EN1998-1-1,cl.6.3.2(1) Steel DCH q= 2.0 – 5.85 EN1998-1-1,cl.6.3.2(1) Fundamental period T1≤4Tc T1≤2,0s EN1998-1-1,cl.4.3.3.2.1(2) Accidental eccentricity See section 2.1.1.1 EN1998-1-1,cl.4.3.2 Table 2.10: Equivalent Static Force Case Load case name Direction and Eccentricity % Eccentricity EQXA X Dir + Eccen. Y 0.05 EQYA X Dir – Eccen. Y 0.05 EQXB Y Dir + Eccen. X 0.05 EQYB Y Dir – Eccen. X 0.05
  • 35. Page 35 2.3.4 Estimation of fundamental period T1 Table 2.11: Estimation of fundamental period T1 Reference structure Period T1 Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at top of a vertical cantilever of height H. Cantilever mass MB = 0. 𝑇! = 2𝜋 𝑀𝐻! 3𝐸𝐼 Exact formula for Single Degree of Freedom Oscillator. Vertical cantilever of height H and of total mass MB. 𝑇! = 2𝜋 0.24𝑀! 𝐻! 3𝐸𝐼 Exact formula for Single Degree of Freedom Oscillator. Mass M lumped at top of a vertical cantilever of height H and of total mass MB. 𝑇! = 2𝜋 𝑀 + 0.24𝑀! 𝐻! 3𝐸𝐼 Approximate Relationship (Eurocode 8). Ct = 0,085 for moment resisting steel space frames Ct = 0,075 for eccentrically braced steel frames Ct = 0,050 for all other structures 𝑇! = 𝐶! 𝐻!/! H building height in m measured from foundation or top of rigid basement. Approximate Relationship (Eurocode 8). d : elastic horizontal displacement of top of building in m under gravity loads applied horizontally. 𝑇! = 2 𝑑
  • 36. Page 36 2.3.5 Automatic Lateral force analysis using ETABS ETABS: Define > Static load cases Figure 2.4: Apply the Equivalent Static Force Case Figure 2.5: Modify the Equivalent Static Force Case Note: The seismic forces should be applied only above the top of the basement
  • 37. Page 37 Fundamental period (EN1998-1-1,Eq.4.6) T1=CtH3/4 (For heights up to 40m) Value of Ct(EN1998-1-1,cl.4.3.3.2.2(3)) Ct = 0.085 (for moment resisting steel frames) Ct= 0.075 (for moment resisting concrete frames) Ct= 0.05 (for all other structures) (EN 1998-1-1:2004, cl. 4.3.3.2.2(3)) Ct= 0.075/√ΣAc(for concrete/masonry shear wall structures) (EN 1998-1-1:2004, Eq. 4.7) Ac= Σ[Ai·(0,2+(lwi/H2 ))] (EN 1998-1-1:2004, Eq. 4.8) Fundamental period requirements (EN1998-1-1,Eq.4.6) T1≤4TCT1≤2sec IF this YES LATERAL FORCE ANALYSIS RESPONSE SPECTRUM ANALYSIS Correction factor λ(EN1998-1- 1,cl.4.3.3.2.2(1Ρ)) λ=0.85 if T1≤2TC and more than 2 storey λ=1.0 in all other case Design spectrum Sd(T)(EN1998-1- 1,cl.3.2.2.5) 0≤T≤TB TB≤T≤TcTC≤T≤TD TD≤T Seismic mass(EN1998-1- 1,cl.3.2.4) ΣGk,j/g”+”ΣψE,i.Qk,i/g (EN 1998-1-1:2004, Eq.3.17) Base shear(EN1998-1- 1,cl.4.3.3.2.2) Fb=Sd(T1).m.λ (EN 1998-1-1:2004, Eq. 4.5) Horizontal seismic forces (according to displacement of the masses) F! = F! ∙ s! ∙ m! s! ∙ m! (EN 1998-1-1:2004, Eq. 4.10) Horizontal seismic forces (according to height of the masses) F! = F! ∙ z! ∙ m! z! ∙ m! (EN 1998-1-1:2004, Eq. 4.11) NO
  • 38. Page 38 2.3.6 User loads - Lateral force analysis using ETABS Geometrical data Span of the longitutinal direction Span of the transverse direction Span of each beam Span of each bracing Height of each column Total heigh of building Area of floor for each storey Number of floors Number of beams IPE240 at each floor Number of beams IPE180 at each floor Number of columns HE280A at each floor Number of TUBE sections D127-4 at each floor Lx 15m:= Ly 15m:= Lb 5m:= Lt 5.831m:= hc 3m:= H 9m:= Af Ly Lx⋅ 225m 2 =:= Nf 3:= Nb 24:= Ns 9:= Nc 16:= Nt 8:=
  • 39. Page 39 Dead load Weight of steel column HE280A Weight of primary beams IPE240 Weight of secondary beams IPE180 Weight of steel beams TUBE-D127-4 Slab thickness Weigth of concrete Weight of slab Weigth of finishes Total dead load Total dead load Live load Combination coefficient for variable action Live load Total live load Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P) Total gravity load per storey (EN1998-1-1,cl.3.2.4(2)P) Seismic mass gc 76.4kg m 1− ⋅:= gp 30.7kg m 1− ⋅:= gs 18.8kg m 1− ⋅:= gt 12.38kg m 1− ⋅:= hs 170mm:= γ c 25kN m 3− ⋅:= gslab γ c hs⋅ 4.25 kN m 2− ⋅⋅=:= gfin 1kN m 2− ⋅:= Gk.storey gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ 1.267 10 3 × kN⋅=:= Gk gc Nc⋅ hc⋅ gp Nb⋅ Lb⋅+ gs Ns⋅ Lb⋅+ gt Nt⋅ Lt⋅+( )g gslab Af⋅+ gfin Af⋅+⎡⎣ ⎤⎦ Nf⋅ 3.802 10 3 × kN⋅=:= ψEi 0.3:= qk 2kN m 2− ⋅:= Qk qk Af⋅ 450 kN⋅=:= FEd.storey Gk.storey ψEi Qk⋅( )+ 1.402 10 3 × kN⋅=:= FEd Gk ψEi Qk⋅( ) Nf⋅+ 4.207 10 3 × kN⋅=:= S_mass FEd g 4.29 10 5 × kg=:=
  • 40. Page 40 Horizontal design response Spectrum (EN1998-1-1,cl.3.2.2.5) Behaviour factor q (EN1998-1-1,cl.6.3) Lower bound factor (EN1998-1-1,cl.3.2.2.5(4)P) Seismic zone (CYS NA EN1998-1-1, zonation map) Importance factor (CYS NA EN1998-1-1,cl. NA2.12) Design ground acceleration on type A (EN1998-1-1,cl.3.2.1(3)) Value of Ct (EN1998-1-1,cl.4.3.3.2.2(3)) Fundamental period of vibration (EN1998-1-1,cl.4.3.3.2.2(3)) Type of soil (EN1998-1-1,cl.3.1.2(1)) Value of parameters describing the Type 1 elastic response spectrum (EN1998-1-1,table 3.2) Soil factor, S q 1.5:= β 0.2:= Seismic_zone "3":= agR 0.15g Seismic_zone "1"if 0.2g Seismic_zone "2"if 0.25g Seismic_zone "3"if 2.452 m s 2 =:= Importance_factor "II":= γ I 0.8 Importance_factor "I"if 1.0 Importance_factor "II"if 1.2 Importance_factor "III"if 1.4 Importance_factor "IV"if 1=:= ag γ I agR⋅ 2.452 m s 2 =:= Value_Ct "OTHER":= Ct 0.085 Value_Ct "MRSF"if 0.075 Value_Ct "MRCF"if 0.05 Value_Ct "OTHER"if 0.05=:= T1 Ct H m ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 3 4 ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ s 0.26s=:= Soil_type "B":= S 1.0 Soil_type "A"if 1.2 Soil_type "B"if 1.15 Soil_type "C"if 1.35 Soil_type "D"if 1.2=:=
  • 41. Page 41 Lower limit of the period, TB Upper limit of the period, TC Constant displacement value, TD Corection factor λ (EN1998-1-1,cl.4.3.3.2.2(1)P) Check the fundamental period of vibration requirements (EN1998-1-1,cl.4.3.3.2.1(2)) Design spectrum for elastic analysis (EN1998-1-1,cl.3.2.2.5(4)P) TB 0.15s Soil_type "A"if 0.15s Soil_type "B"if 0.20s Soil_type "C"if 0.20s Soil_type "D"if 0.15s=:= TC 0.40s Soil_type "A"if 0.50s Soil_type "B"if 0.60s Soil_type "C"if 0.80s Soil_type "D"if 0.5s=:= TD 2.0s Soil_type "A"if 2.0s Soil_type "B"if 2.0s Soil_type "C"if 2.0s Soil_type "D"if 2s=:= λ 0.85 T1 2TC≤ Nf 2>∧if 1 otherwise 0.85=:= Check_1 if T1 4TC≤ T1 2s≤∧ "Lateral force analysis", "Response spectrumanalysis",( ):= Check_1 "Lateral force analysis"= S1e T1( ) ag S⋅ 2 3 T1 TB 2.5 q 2 3 −⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅+ ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ ⋅:= S1e 0( ) 1.961 m s 2− ⋅⋅= S2e T1( ) ag S⋅ 2.5 q ⋅:= S2e TB( ) 4.903 m s 2− ⋅⋅= S3e T1( ) ag S⋅ 2.5 q ⋅ TC T1 ⋅ ag S⋅ 2.5 q ⋅ TC T1 ⋅ β ag⋅≥if β ag⋅( ) β ag⋅ ag S⋅ 2.5 q ⋅ TC T1 ⋅≥if := S3e TC( ) 4.903 m s 2− ⋅⋅= S4e T1( ) ag S⋅ 2.5 q ⋅ TC TD⋅ T1 2 ⋅ ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ ag S⋅ 2.5 q ⋅ TC TD⋅ T1 2 ⋅ β ag⋅≥if β ag⋅( ) ag S⋅ 2.5 q ⋅ TC TD⋅ T1( )2 ⋅ β ag⋅≤if :=
  • 42. Page 42 Design spectrum acceleration Seismic base shear (EN1998-1-1,cl.4.3.3.2.2(1)) Seismic base shear on each bracing Note: 2 bracing on each direction S4e T1( ) 72.642 m s 2 = Se T( ) if T TB< S1e T( ), if T TC< S2e T( ), if T TD< S3e T( ), S4e T( ),( ),( ),( ):= T 0.01sec 0.02sec, 4sec..:= 0 1 2 3 4 0 2 4 6 8 Se T( ) T Se S1e 0( ) 0 T1≤ TB≤if S2e TB( ) TB T1≤ TC≤if S3e TC( ) TC T1≤ TD≤if S4e T1( ) TD T1≤ 4s≤if 4.903 m s 2 =:= Fb S_mass Se⋅ T1 s ⋅ λ⋅ 464.519kN⋅=:= Fb.bracing Fb 2 232.259kN⋅=:=
  • 43. Page 43 Table 2.12: Summary table of the lateral force results Story Heigth                                 zi                                         (m) Mass                                   mi                                     (kN) zi*mi Fb                                   (kN) F=Fb(zi*mi)/ Σzi*mi Moment   M=F*zi   (kNm) Length  of   floor  Lx=Ly Accidental   eccentricity   ei=0.05L Torsional   moment   M=F*ei     (kNm) Moment  due  to   SRSS   MSRS=√Mx^2+My^2   (kNm) STORY1 9 1402 12618 464.52 232.26 2090.34 15 0.75 174.195 246.3489315 STORY2 6 1402 8412 464.52 154.84 929.04 15 0.75 116.13 164.232621 STORY3 3 1402 4206 464.52 77.42 232.26 15 0.75 58.065 82.1163105 TOTAL 4206 25236 464.52 3251.64 Mass per storey Heigth at roof level Heigth at level 2 Heigth at level 1 Total mass: Lateral force at roof level (EN1998-1-1,Eq.4.11) Lateral force at level 2 (EN1998-1-1,Eq.4.11) Lateral force at level 1 (EN1998-1-1,Eq.4.11) Check lateral force per storey mi FEd.storey 1.402 10 3 × kN=:= z3 9m:= z2 6m:= z1 3m:= Σmi_zi FEd.storey z3⋅ FEd.storey z2⋅+ FEd.storey z1⋅+ 2.524 10 4 × kN m⋅=:= F3 mi z3⋅ Σmi_zi Fb⋅ 232.259kN⋅=:= F2 mi z2⋅ Σmi_zi Fb⋅ 154.84kN⋅=:= F1 mi z1⋅ Σmi_zi Fb⋅ 77.42kN⋅=:= F F3 F2+ F1+ 464.519kN=:= Check_2 if F Fb≠ "OK", "NOT OK",( ):= Check_2 "OK"=
  • 44. Page 44 ETABS: Define > Static load case > Figure 2.6: Define manually the lateral forces Figure 2.7: Define manually the lateral forces/moments per storey
  • 45. Page 45 2.3.7 Torsional effects FLOW CHART OF TORSIONAL EFFECTS Carry out Lateral force analysis/ Response spectrum analysis 𝑀! = 𝑒! 𝐹! 𝑀! = 𝑒! 𝐹! 𝑒! = −0.05 ∗ 𝐿!𝑒! = +0.05 ∗ 𝐿! 𝑒! = +0.05 ∗ 𝐿!𝑒! = −0.05 ∗ 𝐿! SRSS rule 𝑀!"!! = 𝑀! ! + 𝑀! !
  • 46. Page 46 2.3.8 Summary of analysis process in seismic design situation Importance class/Ductility class I II III IV DCL DCM DCH DCM DCH DCH Ignore “topographic amplification effects” Consider “topographic amplification effects” IF Slopes <15o Cliffs height <30m Slopes <15o Cliffs height <30m Ignore Consider Regular in plan: YES Regular in elevation YES Regular in plan: NO Regular in elevation YES Regular in plan: YES Regular in elevation NO Regular in plan: NO Regular in elevation NO Type of soil: A , B ,C ,D, E, S1, S2 Type 1 elastic response spectrum 0≤T≤TB TB≤T≤TC TC≤T≤TD TD≤T≤4s LATERAL FORCE MODAL ANALYSIS Displacement ds=qd·de P-Δ effects θ≤0.1 – Ignore 0.1≤θ≤0.2 Consider 0.2≤θ≤0.3 Consider θ≥0.3 Not Permitted Interstorey drift drv≤0.005h - Brittle drv≤0.0075h - Ductile drv≤0.010h - Other Frame joint ΣMRC≥1.3ΣMRB Storey ≥ 2
  • 47. Page 47 3.0 Define static loads Here define as many load cases for your model as you need e.g. dead loads, live loads, wind loads, seismic loads, thermal loads etc. To be simple define only one dead load with self weight multiplier 1(including finishes, dead, walls etc) and one live load. Figure 3.1: Static load cases
  • 48. Page 48 4.0 Seismic mass requirements according to EC8 Combination of the seismic action with other actions (EN 1998-1-1,cl.3.2.4): 1. Define the category of building (EN 1991,Table 6.1), 2. Define the reduce factor (EN 1991, Table A.1.1). Combination of seismic mass 𝐆 𝐤,𝐣 + 𝛙 𝐄𝐢 𝐐 𝐤,𝐢 (ΕΝ1998-1-1,Eq. 3.17) Combination coefficient for variable action is: ψ!" = ϕ ∙ ψ!" (ΕΝ1998-1-1,Eq. 4.2) Table 4.1: Values of φ for calculating 𝛙 𝐄𝐢 (CYS NA EN1998-1-1:2004) Type of Variable action Storey φ Categories A-C1 Roof Storeys with correlated occupancies Independently occupied storeys 1,0 0,8 0,5 Categories A-F1 1.0 Table 4.2: Values of ψ coefficients Category Specific Use ψο ψ1 ψ2 A Domestic and residential 0.7 0.5 0.3 B Office 0.7 0.5 0.3 C Areas for Congregation 0.7 0.7 0.6 D Shopping 0.7 0.7 0.6 E Storage 1.0 0.9 0.8 F Traffic < 30 kN vehicle 0.7 0.7 0.6 G Traffic < 160 kN vehicle 0.7 0.5 0.3 H Roofs 0.7 0 0 Snow, altitude < 1000 m 0.5 0.2 0 Wind 0.5 0.2 0
  • 49. Page 49 4.1 Mass Source Option In ETABS, the user has the option of choosing one of three options for defining the source of the mass of a structure. Click the Define menu > Mass Source command to bring up the Define Mass Source form. The following options appear on the form: 1. From Self and Specified Mass: Each structural element has a material property associated with it; one of the items specified in the material properties is a mass per unit volume. When the ‘From Self and Specified Mass’ box is checked, ETABS determines the building mass associated with the element mass by multiplying the volume of each structural element times it’s specified mass per unit volume. This is the default. It is also possible to assign additional mass to account for partitions and cladding, etc. ETABS adds any additional mass assignments to the element mass to derive a total mass. You cannot have a negative mass in ETABS. 2. From Loads: This specifies a load combination that defines the mass of the structure. The mass is equal to the weight defined by the load combination divided by the gravitational multiplier, g. This mass is applied to each joint in the structure on a tributary area basis in all three translational directions. 3. From Self and Specified Mass and Loads: This option combines the first two options, allowing you to consider self- weight, specified mass, and loads in the same analysis. It is important to remember when using the ‘From Self and Specified Mass and Loads’ option, NOT to include the Dead Load Case in the ‘Define Mass Multiplier for Loads’ box. This will account for the dead load of the structure TWICE.
  • 50. Page 50 Figure 4.1: Seismic source
  • 51. Page 51 5.0 Wind loading on structure (EN1991-1-4:2004) 5.1 Calculation of Wind load according to EN1991-1-4:2004 Step by step procedure Figure 5.1: Fundamental Basic wind velocity, vb,0 (CYS NA EN1991-1-4,Fig.1) Season factor (CYS EN1991-1-4,NA 2.4) cseason=1.0 Directional factor (CYSEN1991-1-4,NA 2.4) cdir=1.0 (Conservative value for all direction) Basic wind velocity (EN1991-1-4, Eq. 4.1) vb=cdir.cseasonvb,0 Figure 1 Isotach contours of the fundamental value of the basic wind velocity v c z v z c z c
  • 52. Page 52 Table 5.1: Terrain category and terrain parameters (EN1991-1-4, Tab.:4.1) Terrain category Description z0 (m) zmin(m) 0 Sea, costal area exposed to the open sea. SEA 0.003 1 I Lakes or area with negligible vegetation and without obstacles. COUNTRY 0.01 1 II Area with low vegetation such as grass and isolated obstacles trees, buildings) with separations of at least 20 obstacle height. 0.05 2 III Area with regular cover of vegetation or buildings or woth isolatd obstacles with seperations of maximum 20 obstacle height (such as villages, suburban terrain, permanent forest). TOWN 0.3 5 IV* Area in which at least 15% of the surface is covered with building and their average height exceeds 15m. 1.0 10 * For buildings in terrain category IV, displacement height hdis should be consider and information can be found in Aneex A.5 of EN1991-1-4:2005. Roughness factor, cr(z) (EN1991-1-4,Eq.4.3-4.5) cr(z)=kr . ln(z/z0) for zmin≤z≤zmax cr(z)=cr . (zmin) for z≤zmin z0: is the roughness length Maximum height, zmax (EN1991-1-4, cl. 4.3.2) zmax=200m Orography factor co(z) co(z)=1 Terrain factor, (EN1991-1-4,cl.4.4) kr=0.19(z0/z0,II)0.07 Mean wind velocity, vm(z) (EN1991-1-4 cl.4.3.1 ) vm(z)=cr(z).co(z).vb Wind turbulence, Iv(z) (EN1991-1-4,Eq.4.7) Iv(z)=σv/vm(z)=kl/co(z)ln(z/z0) for zmin≤z≤zmax Iv(z)=Iv(zmin) for z≤zmin Turbulence factor: kl=1.0 (NA CYS EN1991-1-4, cl. NA 2.10) Note: for co(z)=1 Iv(z) is not important Peak velocity pressure, qpeak(z) (EN1991-1-4 Eq.4.8 ) qpeak(z)=[1+7 Iv(z)]0.5ρ vm 2 (z)=ce(z)·0.5·ρ·vb 2 Air density:ρ=1.25kg/m3
  • 53. Page 53 Table 5.3: Values of external pressure coefficient for vertical walls of rectangular plan building (EN1991-1-4, Tab.:4.1) ZONE A B C D E h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.7 1 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.5 ≤0.25 -1.2 -1.4 -0.8 -1.1 -0.5 +0.7 +1.0 -0.3 Note: Values for cpe,1 are intended for the design of small elements and fixings with an element of 1m2 or less such as cladding elements and roofing elements. Values for cpe,10 may be used for the design of the overall load bearing structure of buildings. The external pressure coeffiecient cpe,1 and cpe,10 is using for loadaded area of 1m2 and 10m2 respectively. Key for vertical walls – Flat Roof (EN1991-1-4, Fig.7.5) Key for vertical walls –Mono&dual pitch Roof (EN1991-1-4, Fig.7.5) Pressure on surface &Wind force (EN1991-1-4, Eq. 5.1&5.5) we=qp(ze).(cpe +cpi) & Fw=cscd·Σwe·Aref Table 5.2: Reference height ze, depending on h and b, and corresponding velocity pressure profile (EN1991-1-4, Fig. 7.4)
  • 54. Page 54 5.2 Application of wind loading using ETABS Table 5.4: Wind load assumptions Data Symbol Value Units Basic wind velocity vb,0 24 m/s Terrain category - II - Structural factor cscd 1 - Turbulence factor kl 1 - Orography factor co(z) 1 - ETABS: Clink on ETABS: Select from first drop-down menu ETABS: Click on select “NONE” and draw rectangular cover all side of plan view Draw walls in plan
  • 55. Page 55 ETABS: Select the area of elevation A-A ETABS: Assign > Shell/Area loads > Wind pressure coefficients Figure 5.2: Wind load areas Table 5.5: Wind pressure coefficient applied on walls Wind pressure coefficient for load case WINDX Windward load “Area D” Leeward load “Area E” Side load “Area A & B” Side load “Area A & B”
  • 56. Page 56 Wind pressure coefficient for load case WINDY Windward load “Area D” Leeward load “Area E” Side load “Area A & B” Side load “Area A & B”
  • 57. Page 57                   WIND LOADING ACCORDING TO EN1991-1-4:2005 Job No.:                       Sheet No.:                       Date: December 2012 Check by: CALCULATION OF WIND LOADING TO EN 1991-1-4:2005. Loading available for rectangular, clad buildings with flat roofs only. Obstruction height, have = 7.5 m Distance to nearest adjacent building, x = 50 m Height of building, h = 9 m Longitudinal length of the building , d = 15 m Transverse length of the building, b = 15 m Edge distance, (Wind direction - θ=90°) e = 15 Basic Wind Velocity, Vbo = 24 m/s ( Figure1) Season Factor, Cseason = 1.0 (cl.NA2.4) Directional Factor, Cdir = 1.0 (cl.NA2.4) Basic Wind Velocity, Vb0=CdirCseasonVb,o Vb = 24 m/s (Eq.4.1) Structural factor, CsCd = 1.0 (cl.6.2) Orography factor, Co(z) = 1.0 cl.4.3.1(1)) Turbulence factor, kI = 1.0 (cl.NA2.10) z0 zmin (Τable 4.1) Terrain Category Define terrain category II 0.05 2 Max heigh, zmax = 200 m (cl. 4.3.2) Height above ground, z = 100 m Dispacement height, hdis = 4.5 m (Annex A.5) Clear height of building, h-hdis = 4.5 Define height z 5
  • 58. Page 58 External  Pressure  Coefficients  Walls  Cpe                                     Wind  direction   θ=0°                                             Width                              b      =       15   m     Height                              h      =       9   m     Depth                              d      =       15   m     Edge distance, (Wind direction - θ=0°)       e    = 15 m   Actual  h/b  (For  zone  D  -­‐  windward  face)                  h/b      =       0.60                                                         Length  in   Zone  A                         Zones  A  &  B   exist             3   m     Length  in   Zone  B                                         12   m     Length  in   Zone  C                                         0   m                                                       Wind  direction   θ=90°                                             Width                              b      =       15   m     Height                              h      =       9   m     Depth                              d      =       15   m     Edge distance, (Wind direction - θ=90°)       e    = 15 m   Actual  h/b  (For  zone  D  -­‐  windward  face)                  h/b      =       0.60                                                         Length  in   Zone  A                         Zones    A  &  B   exist             3   m     Length  in   Zone  B                                         12   m     Length  in   Zone  C                                         0   m                                                                                                         Table  7.1  values  of  Cpe  for   wind  on                                             Front  (θ=90°)     Front  (θ=0°)             Zones  (θ=90°)     Zones  (θ=0°)           D       0.747         0.747              A     3   m   A   -­‐1.2   m         E       -­‐0.567         -­‐0.567              B     12   m   B   -­‐0.8   m         A       -­‐1.2         -­‐1.2              C     0   m   C   0   m         B       -­‐0.8         -­‐0.8                                     C       0         0                                    
  • 59. Page 59 6.0 Load combination Table 6.1: Load combination factors and coefficients Data Symbol Value Reference Permanent action γG 1.35 EN1990,cl.6.4.3.2 Variable action γQ 1.5 EN1990,cl.6.4.3.2 Office areas (Type B), ψ0 0.7 CYS NA EN1990:2002, Table A1.1 Roofs ψ0 0.7 CYS NA EN1990:2002, Table A1.1 Wind loads ψ0 0.5 CYS NA EN1990:2002, Table A1.1 Persistent and transient design situation – STR/GEO Equation 6.10 Ed=ΣγG Gk +γQ Qk1 + γQ ψ0,2 Qk2 Ultimate limit state (ULS) Static load combination STATIC 2. 1.35DL + 1.5LL STATIC 3. 1.35DL + 1.5LL + 0.75WINDX STATIC 4. 1.35DL + 1.5LL - 0.75WINDX STATIC 5. 1.35DL + 1.5LL + 0.75WINDY STATIC 6. 1.35DL + 1.5LL - 0.75WINDY STATIC 7. 1.35DL + 1.5WINDX + 1.05LL STATIC 8. 1.35DL - 1.5WINDX – 1.05LL STATIC 9. 1.35DL + 1.5WINDY + 1.05LL STATIC 10. 1.35DL - 1.5WINDY – 1.05LL Seismic load combination for “Modal Analysis” SEISMIC 2. DL + 0.3LL + EQX + 0.3EQY SEISMIC 3. DL + 0.3LL + EQX – 0.3EQY SEISMIC 4. DL + 0.3LL - EQX + 0.3EQY SEISMIC 5. DL + 0.3LL - EQX – 0.3EQY SEISMIC 6. DL + 0.3LL + EQY + 0.3EQX SEISMIC 7. DL + 0.3LL + EQY – 0.3EQX SEISMIC 8. DL + 0.3LL - EQY + 0.3EQX SEISMIC 9. DL + 0.3LL - EQY – 0.3EQX
  • 60. Page 60 Seismic load combination for “Lateral force Analysis” SEISMIC 10. DL + 0.3LL + EQXA + 0.3EQYA SEISMIC 11. DL + 0.3LL + EQXA – 0.3EQYA SEISMIC 12. DL + 0.3LL - EQXA + 0.3EQYA SEISMIC 13. DL + 0.3LL - EQXA – 0.3EQYA SEISMIC 14. DL + 0.3LL + EQYA + 0.3EQXA SEISMIC 15. DL + 0.3LL + EQYA – 0.3EQXA SEISMIC 16. DL + 0.3LL - EQYA + 0.3EQXA SEISMIC 17. DL + 0.3LL - EQYA – 0.3EQXA SEISMIC 18. DL + 0.3LL + EQXB + 0.3EQYB SEISMIC 19. DL + 0.3LL + EQXB – 0.3EQYB SEISMIC 20. DL + 0.3LL - EQXB + 0.3EQYB SEISMIC 21. DL + 0.3LL - EQXB – 0.3EQYB SEISMIC 22. DL + 0.3LL + EQYB + 0.3EQXB SEISMIC 23. DL + 0.3LL + EQYB – 0.3EQXB SEISMIC 24. DL + 0.3LL - EQYB + 0.3EQXB SEISMIC 25. DL + 0.3LL - EQYB – 0.3EQXB Serviceability limit state (SLS) STATIC 1. DL + LL
  • 61. Page 61 7.0 Design preferences ETABS: Options > Preferences > Steel frame design Figure 7.1: Steel frame design preferences 2 3 4 1 5 6
  • 62. Page 62 Table 7.1: Steel frame design parameters Note 1: Reliability class Class section classification according to EN1998-1-1,cl.6.5.3(2) 1. Depending on the ductility class and the behavior factor q used in the design, the requirements regarding the cross-sectional classes of the steel elements which dissipate energy are indicated in table below (EN1998-1-1,cl.6.5.3(2). Ductility class Reference q factor Cross-Section Class Lower limit q factor Upper limit DCM 1.5< q ≤ 2 Class 1, 2 or 3 2.0< q ≤ 4 Class 1 or 2 DCH 4.0< q Class 1 Note 2: Frame type See section 2.0 of this manual Note 3: Gamma factors Partial factors Values Reference Resistance of cross-sections whatever the class γΜ0=1.00 EN1993-1-1,cl.6.1(1) Resistance of members to instability assessed by member checks γΜ1=1.00 EN1993-1-1,cl.6.1(1) Resistance of cross-sections in tension to fracture γΜ1=1.25 EN1993-1-1,cl.6.1(1) Note 4: Behavior factor See section 2.0 of this manual Note 5: System Omega Omega Factor (System Overstrength Factor) axial load member: (𝛀 = 𝑵 𝒑𝒍,𝑹𝒅/𝑵 𝑬𝒅) Omega factor may different for each diagonal member.
  • 63. Page 63 1. Run the design analysis with the Ω=1 2. Find the Npl,Rd and NEd of the bracing member and then overwrite the omega factor for each diagonal member separately and then re-run the analysis.(Ω=1). Note: Omega factor should be limited to the following for all diagonal members Note 6: Vertical deflection limits STEEL MEMBERS (CYS NA EN1993-1-1,table NA.1) Vertical deflection Limits wmax Cantilevers L/180 Beams carrying plaster or other brittle finish L/360 Other beams (except purlin and sheeting rails) L/250 Purlins and sheeting rails To suit cladding General use L/300 ETABS deflection limits DL limit, L/ 360 Super DL+LL Limit, L/ 360 Live load Limit, L/ 360 Total Limit, L/ 360 Total Camper Limit, L/ 360 Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK",( ):=
  • 64. Page 64 8.0 Analysis and design requirements for Concentrically braced frames according to EN1998-1-1,cl.6.7.2 Analysis requirements according to EN1998-1-1,cl.6.7.2 Beams & Columns 1. Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1- 1,cl6.7.2(1)P). Diagonal members 2. The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action: a) in frames with diagonal bracings, only the tension diagonals shall be taken into account, b) in frames with V bracings, both the tension and compression diagonals shall be taken into account (EN1998-1-1,cl6.7.2(2). 3. Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied: a) a non-linear static (pushover) global analysis or non-linear time history analysis is used, b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and, c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).
  • 65. Page 65 8.1 Steps of the design detail of Concentric steel frames Table 8.1: Detail steel frame design Design step number Description Step 1 Design of slab under gravity loads (without CBF bracings) considering columns as fixed supports Step 2 Design columns under gravity loads (without CBF bracings) Step 3 Design beams under gravity loads (without CBF bracings) Step 4 Check concentric bracings under gravity loads combination Step 5 Accidental torsional effects Step 6 Second order effects (P-Δ) (P loads are those taken in the definition of the seismic mass “m”) Step 7 Check of beams and of concentric bracings under gravity loads combination Step 8 Design of concentric bracing under seismic combination of loads with the accidental torsional effects and P-Δ effects taken into account Step 9 Check of beams and columns under seismic combination of loads with bracings overstrength factors Ω and with second order effects taken into account Step 10 Re-run the analysis with the modified overstrength factors Ω
  • 66. Page 66 8.2 Classification of steel sections Table 8.2: Section classification (EN1993-1-1,cl.5.5) Classes Analysis type Description Class 1 Plastic analysis Section can form a plastic hinge with the rotation capacity required from plastic analysis, without reduction of the resistance Class 2 Plastic/ Elastic analysis Section can develop its plastic moment capacity, but has limited rotation capacity. Class 3 Elastic analysis Section in which the stress in the extreme compression fiber of the section, assuming an elastic distribution of stresses, can reach the yield strength, but local buckling is likely to prevent the development of the plastic moment capacity. Description of detail requirements Equations References Reduction of yield and ultimate strength of sections EN10025-2 ε - Factor EN1993-1-1,Table 5.2 Depth of a part of section for internal compression (I-sections) EN1993-1-1,Table 5.2 Section classification for web element EN1993-1-1,Table 5.2 fy. fy t 16mm<if fy 10N mm 2− ⋅− 16mm t< 40mm<if fy 20N mm 2− ⋅− 40mm t< 80mm<if := fu. fu t 16mm≤if fu 10N mm 2− ⋅− 16mm t< 40mm≤if fu 20N mm 2− ⋅− 40mm t< 80mm≤if := ε 235 fy := cw h 2 tf⋅− 2 r⋅−:= Class_type web "CLASS 1" cw tw 72 ε⋅≤if "CLASS 2" 84 ε⋅ cw tw < 83 ε⋅≤if "CLASS 3" 105 ε⋅ cw tw < 124 ε⋅≤if :=
  • 67. Page 67 Depth of a part of section for oustand flange (I-sections) EN1993-1-1,Table 5.2 Section classification for flange element EN1993-1-1,Table 5.2 cf b tw− 2.r−( ) 2 := Class_type flange "CLASS 1" cf tf 9 ε⋅≤if "CLASS 2" 9 ε⋅ cf tf < 10 ε⋅≤if "CLASS 3" 10 ε⋅ cf tf < 14 ε⋅≤if :=
  • 68. Page 68 8.3 Design of composite slab under gravity loads Table 8.3: Detail design of composite slab (with steel sheeting) Partial factor Value References Partial factor of longitudinal shear in composite slabs γvs = 1.25 CYS EN1994-1- 1cl.2.4.1.2(6)P Partial factor for shear connector γv = 1.25 CYS EN1994-1- 1cl.2.4.1.2(5)P Partial factor for steel reinforcement γs = 1.15 CYS EN1992-1-1,table 2.1 Partial factor of concrete γc = 1.5 CYS EN1992-1-1,table 2.1 Partial factor of structural steel γM0 = 1.0 CYS EN1993-1-1,cl 6.1(1) Description of detail requirements Equations References Minimum nominal thickness of profile steel sheets t ≥ 0.70mm CYS EN1994-1-1,cl.3.5(2) Minimum depth of slab h ≥ 90mm EN1994-1-1,cl.9.2.1(2) Depth of concrete slab above steel sheeting hc ≥ 50mm EN1994-1-1,cl.9.2.1(2) Minimum steel reinforcement in both direction As.prov ≥80mm2 /m EN1994-1-1,cl.9.2.1(4) Spacing of the reinforcement bars s = min{2h,350mm} EN1994-1-1,cl.9.2.1(5) Maximum height of steel decking hp ≤ 85mm EN1994-1-1,cl.6.6.4.2(3) Minimum width per ribs b0 ≥ hp EN1994-1-1,cl.6.6.4.2(3) Diameter of stud that welded in the sheeting d ≤ 20mm EN1994-1-1,cl.6.6.4.2(3)
  • 69. Page 69 For holes provided in the sheeting, the diameter of the stud d ≤ 22mm EN1994-1-1,cl.6.6.4.2(3) Maximum overall height of stud hsc ≤ hp +75mm EN1994-1-1,cl.6.6.4.1(2) Design stage Description of checks Equations References Resistance verifications of metal decking at the construction stage Construction Stage Moment resistance of steel sheeting From manufacture data - Concrete compressive strength fcd = fck / γc EN1994-1-1,cl.2.4.1.2(2)P Design yield strength fyo,d = fyp / γM0 - Bending resistance of metal decking MEd / MRd <1.0 EN1993-1-3,cl.6.1.1 Shear resistance of metal decking 𝑉!,!" = !! !"#$ 𝑡  𝑓!" 𝛾!! EN1993-1-3,cl.6.1.5(1) Deflection of metal decking 𝛿!"# = !"! !"#!"    (W in kN/m2 ) - δmax ≤ min {L/ 180,20mm) EN1994-1-1,cl.9.6(2) Resistance verifications of composite slab at the composite stage Composite Stage Area of concrete Ac = b hc (b=1m) - Compression design force of concrete Nc = 0.85 fcd Ac EN1994-1-1,cl.6.2.1.2 Tensile resistance of profiles steel sheeting Np = fyp,d Ap EN1994-1-1,cl.6.2.1.2
  • 70. Page 70 Location of neutral axis Neutral axis=if{Np < Nc “Lie above steel sheeting”, “Lie below steel sheeting”} EN1994-1-1,9.7.2(5) & (6) Depth of concrete in compression xpl = Ape fyp,d / 0.85 b fcd EN1994-1-1,fig.9.6 Moment resistance (full shear connection) Mpl, Rd = Ap fyd (dp – 0.5 xpl) - Bending resistance of slab MEd / Mpl,Rd <1.0 - The design values of m and k Should be obtain from the manufacture - Shear span (for UDL load) Ls = L / 4 EN1994-1-1,cl.9.7.3(5) Shear span (for UDL & point load) Ls = 3L/8 EN1994-1-1,cl.9.7.3(5) Shear resistance (in longitudinal direction) Vl,Rd = bdp /γvs [(mAp / bLs ) + k] EN1994-1-1,Eq. 9.7 Longitudinal shear resistance of slab VEd / Vl,Rd - Coefficient factor k k = 1+(200 / dp)1/2 EN1992-1-1,cl.6.2.2(1) Value of vmin vmin = 0.035k3/2 fck 1/2 CYS EN1992-1-1,Eq.6.3 Design vertical shear resistance Vv,Rd = vmin bs dp 1 EN1992-1-1,Eq.6.2b Vertical shear resistance check VEd / Vv,Rd < 1.0 - Serviceability limit state (SLS) - Deflection Calculation of deflection (simply supported slab) 𝛿!"# = !"! !"#!"    (W in kN/m2 ) - Deflection limits (imposed load) L / 350 (not greater than 20mm) Deflection limits (total load) L / 250 (not greater than 30mm) EN1992-1-1,cl.7.4.1(4) Serviceability limit state (SLS) - Cracking Minimum amount of steel ratio (un-propped) As = 0.2% Ac EN1994-1-1,cl.9.8.1(2) Minimum amount of steel ratio (propped) As = 0.4% Ac EN1994-1-1,cl.9.8.1(2)
  • 71. Page 71 Serviceability limit state (SLS) – Floor vibration Floor vibration limits f = 18 / √δa SCI-P-076 : Design guide on the vibration of floors Note 1: Although in reality the slab is continuous, it is normally convenient to design it as simply supported. As a consequence of this, the beneficial effect of compression from the hogging moment at the support is neglected, such that σcp = 0.
  • 72. Page 72 8.4 Design of composite beam (with steel sheeting) under gravity loads Table 8.4: Detail design of composite beam Minimum height of stud EN1994-1-1,cl.6.6.1.2(1) Nominal diameter of stud EN1994-1-1,cl.6.6.1.2(1) Ultimate strength of shear connector EN1994-1-1,cl.6.6.4.2(1) Check the minimum spacing of studs EN1994-1-1,cl.6.6.5.5(3) Preliminary depth of beams EN1994-1-1,cl.6.4.3(1) Ultimate limit state Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5) Moment resistance of steel section Y-Y axis Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2) Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6) Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g) Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a) Shear resistance of steel Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2) hmin if hsc 4d≥ "OK", "NOT OK",( ):= dlim if 16mm d< 25mm< "OK", "NOT OK",( ):= fus 450N mm 2− ⋅:= slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK",( ):= hmax 600mm fy 235N mm 2− ⋅≤if 550mm 235N mm 2− ⋅ fy< 275N mm 2− ⋅≤if 400mm 275 N⋅ mm 2− ⋅ fy< 355N mm 2− ⋅≤if 270mm 355 N⋅ mm 2− ⋅ fy< 460N mm 2− ⋅≤if :=
  • 73. Page 73 Construction Stage section Y-Y axis Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6)) Bending and shear interaction check (cl.6.2.2.4) Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5) Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5) Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3) Reduced design plastic resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5) Lateral torsional buckling of the steel beam It is assumed that the steel beam is laterally restrained by the steel sheeting during construction. In order to provide restraint, the sheeting is fixed to the beam either by the action of through-deck welding or by short-fired pins Effective width of composite beam (cl.5.4.1.2(5)) Effective width of composite beam (EN1994-1-1cl. 5.4.1.2(5)) Plastic resistance moment of composite section with full shear connection (cl.6.2) hw tw 72 ε η ⋅< Ma.pl.Rd. Wpl.y ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vy 0.5>if Ma.pl.Rd vy 0.5<if := beff bo 2 min L1 2 L2 2 + Le 8 , ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ +:=
  • 74. Page 74 Composite Stage Tensile resistance of steel section (EN1993-1-1,cl.6.2.3(2)) Compression resistance of concrete slab (EN1994-1-1,cl.6.2.1.2(1d) Tensile resistance in web of steel section - Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1)) Bending resistance with full shear connection (EN1994-1-1,cl.6.1.2) Bending resistance check checks (EN1993-1-1,cl.6.2.5(1)) Vertical Shear resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6) Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P) Check if the verification of shear buckling resistance (EN1993-1-1,cl.6.2.6(6)) Npl.a fy A⋅ γ M0 := Nc.f 0.85 fcd⋅ beff⋅ hc⋅:= Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:= Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if "Lies in the top flange of the beam" Nc.f Npl.a≤if "Lies in the web of the beam" Nc.f Npl.w<if := Mpl.Rd Npl.a ha 2 h+ Npl.a Nc.f hc 2 ⋅− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ Location_neutral axis "Lies in the concrete slab"if Npl.a ha 2 ⋅ Nc.f hc 2 hp+ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅+ Location_neutral axis "Lies in the top flange of the beam"if Ma.pl.Rd Nc.f hc ha+ 2hp+ 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅+ Nc.f 2 Npl.w ha 4 ⋅− Location_neutral axis "Lies in the top flange of the beam"if := Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK",( ):= Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK",( ):= Check_9 if hw tw 72 ε η ⋅< "Not required shear buckling resistance", "Required shearbuckling resistance", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ :=
  • 75. Page 75 Composite Stage required or not Design resistance of shear stud connector (cl.6.6.3.1(1)) Upper limit of reduction factor kt (EN1994-1-1,Table:6.2) Reduction factor kt Ribs transverse to the supporting beams (EN1994-1-1,cl.6.6.4.2) Limitation of kt (EN1994-1-1,cl.6.6.4.2(2)) Reduction factor kt Ribs parallel to the supporting beams (EN1994-1-1,cl.6.6.4.1) Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1)) Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1)) Factor α (EN1994-1-1,cl.6.6.3.1(1)) kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if 1.0 nr 1 1mm ts<∧ d 20mm<∧if 0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if 0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if 0.70 nr 2 1mm ts≥∧ d 20mm<∧if 0.80 nr 2 1mm ts<∧ d 20mm<∧if 0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if 0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if := kt 0.7 nr bo hp ⋅ hsc hp 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅:= Check_10 if kt kt.max< "OK", "NOT OK",( ):= kt 0.6 bo hp ⋅ hsc hp 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ 1.0≤:= hmin if hsc 4d≥ "Ductile", "Not Ductile",( ):= dlim if 16mm d< 25mm< "Ductile", "Not ductile",( ):= α 0.2 hsc d 1+ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ 3 hsc d ≤ 4≤if 1 hsc d 4>if 1=:=
  • 76. Page 76 Composite Stage Design shear resistance of a headed stud (EN1994-1-1,cl.6.6.3.1(1)) Degree of shear connection (cl.6.6.1.2(1)) Ratio of the degree shear connection (EN1994-1-1,cl.6.2.1.3(3)) Minimum degree of shear connection for equal flange (EN1994-1-1,cl.6.6.1.2(1)) Check the degree of shear interaction within the limits (EN1994-1-1,cl.6.6.1.2(1)) Number of shear connector required - Stud spacing - Check the minimum spacing of studs (EN1994-1-1,cl.6.6.5.7(4)) Adequacy of the shear connection (EN1994-1-1,cl.6.6.1.3(3)) Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4) Length under consideration - PRd kt min 0.8 fus⋅ π⋅ d 2 4 ⋅ γ v 0.29 α⋅ d 2 ⋅ fck Ecm⋅⋅ γ v , ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅:= η Nc.f Npl.a := ηmin 1 355 fy N mm 2− ⋅ ⎛⎜ ⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎟ ⎠ 0.75 0.03 Le m ⋅− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅− Le 25m<if 1.0 Le 25m>if := Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK",( ):= n 2 Npl.a⋅ PRd := sprov Le Nstud := slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK",( ):= Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing",( ):= Δ x Le 2 :=
  • 77. Page 77 Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3)) Strength reduction factor (EN1992-1-1,Eq.6.6N) Area of transverse reinforcement required (EN1992-1-1,cl.6.2.4(4)) Check the crushing compression in the flange (EN1992-1-1cl.6.2.4(4)) Serviceability limit state Vertical deflection Construction Stage Maximum deflection at construction stage - Vertical deflection limit (CYS NA EN1993-1-1,table NA.1) Composite Stage Short term elastic modular ration (EN1994-1-1,cl.7.2.1) Second moment of area of the composite section - Deflection with full shear connection - Vibration of floor (Simplified analysis) (EN1990 A1.4.4) vEd Npl.a 2 hc⋅ Δ x⋅ := v 0.6 1 fck 250 N⋅ mm 2− ⋅ − ⎛⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎠ ⋅:= As.req vEd hc⋅ sf⋅ fyd sin θf( ) cos θf( ) ⋅ := Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK",( ):= δc 5 Gk.c Qk.c+( )⋅ Le 4 ⋅ 384 Es⋅ Iyy⋅ := Check_15 if δc Le 250 < "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := no Es Ecm := r A beff hc⋅ := Ic A h 2 hp⋅+ hc+( )2 ⋅ 4 1 no r⋅+( )⋅ beff hc 3 ⋅ 12 no⋅ + Iyy+:= δcom 5 Gk Qk+( )⋅ Le( )4 ⋅ 384 Es⋅ Ic⋅ :=
  • 78. Page 78 Total load on beam is EN1990,A1.4.4 Increase the inertia, Ic by 10% to allow for the increased dynamic stiffness of the composite beam - Instantaneous deflection caused by re-application of the self weigth of the floor and the beam to the composite beam - Natural frequency SCI P354 Check natural frequency limitation - Fv Gk ψ1 Qk⋅+:= Icl Iy Iy 0.1⋅( )+:= δα 5 Fv Le⋅( )⋅ Le 3 ⋅ 384 Es⋅ Icl⋅ := f 18 Hz⋅ δα mm := Check_17 if f 4Hz< "OK", "NOT OK",( ):=
  • 79. Page 79 8.5 Detail design of steel columns under gravity loads Table 8.5: Detail design of composite beam Partial factor Value References Partial factor of cross-sections whatever the class is γM0 = 1.0 CYS EN1993-1-1,cl 6.1(1) Partial factor of member to instability assessed by member checks γM1 = 1.0 CYS EN1993-1-1,cl 6.1(1) Description of detail requirements Equations References Design plastic resistance of the gross cross-section Npl,Rd = A fy / γM0 EN1993-1-1,cl.6.2.3(2) Compression resistance of steel section Nc,Rd =A fy / γM0 EN1993-1-1,cl.6.2.4(1) Bending interaction check Moment resistance of steel section Y-Y axis Mc,Rd,y =Mpl,Rd,y = Wpl,y fy / γM0 EN1993-1-1,cl.6.2.5(2) Moment resistance of steel section Z-Z axis Mc,Rd,z= Mpl,Rd,z = Wpl,z fy / γM0 EN1993-1-1,cl.6.2.5(2) Shear interaction check Factor for shear area η = 1.0 (conservative value) EN1993-1-1,cl.6.2.6(3g) Shear area 1 Av = A -2 b tf + (tw + 2r) tf ≥ η hw tw EN1993-1-1,cl.6.2.6(3a) Shear resistance of steel section Y-Y axis Vpl,Rd y = Av (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2) Shear resistance of steel section Z-Z axis Vpl,Rd,z = 2b tf (fy / √3) / γM0 EN1993-1-1,cl.6.2.6(2) Bending and shear interaction check Area of web Aw = hw tw EN1993-1-1,cl.6.2.8(5)
  • 80. Page 80 Coefficient of interaction vy=VEd / Vpl.Rd,y EN1993-1-1,cl.6.2.8(5) Reduced yield strength ρ = [(2VEd / Vpl.Rd,y) – 1] 2 EN1993-1-1,cl.6.2.8(3) Reduced design plastic resistance moment Y-Y axis EN1993-1-1,cl.6.2.8(5) Coefficient of interaction vz=VEd / VRd,y EN1993-1-1,cl.6.2.8(5) Reduced yield strength ρ = [(2VEd / Vpl.Rd,z) – 1] 2 EN1993-1-1,cl.6.2.8(3) Reduced design plastic resistance moment Z-Z axis EN1993-1-1,cl.6.2.8(5) Check combination of axial and bending EN1993-1-1,cl.6.2.1(7) Bending and axial interaction check Criteria 1 – Y-Y axis c1=NEd ≤ Npl,Rd EN1993-1-1,cl.6.2.9.1(4) Criteria 2 – Y-Y axis c2=NEd ≤ (0.5 hw tw fy )/ γM0 EN1993-1-1,cl.6.2.9.1(4) Check criteria c= max(cy1, cy2) Factor a a = min {(A-2 b tf) / A) ,0.5} EN1993-1-1,cl.6.2.9.1(5) Factor n n = NEd / Npl,Rd EN1993-1-1,cl.6.2.9.1(5) Factor β EN1993-1-1,cl.6.2.9.1(6) Reduced design value of the resistance to bending MN,y,Rd = Mpl,y,Rd (1-n)/(1-0,5a) if c>1.0 and EN1993-1-1,cl.6.2.9.1(5) Mc.Rd.y Wpl.y ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vy 0.5>if Mc.Rd.y vy 0.5<if := Mc.Rd.z Wpl.z ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vz 0.5>if Mc.Rd.z vz 0.5<if := Check_1 if NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := β 5n 5n 1≥if 1 otherwise 1=:=
  • 81. Page 81 moments making allowance for the presence of axial forces (Y-Y axis) MN,y,Rd = Mpl,y,Rd if 0 ≤ c ≤ 1.0 Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (Z-Z axis) MN,z,Rd = Mpl,z,Rd for n<a and MN,z,Rd = Mpl,z,Rd [1-(n-a/1-a)2 ] for n>a EN1993-1-1,cl.6.2.9.1(5) Check combination of bi-axial bending EN1993-1-1,cl.6.2.9.1(6) Buckling interaction check Buckling length See: Figure 1: Effective length columns Design Guidance of EC3) Elastic critical force for the relevant buckling mode based on the gross cross sectional properties 𝑁!".! = 𝐸! 𝐼! 𝜋! 𝐿!".! ! - Non dimensional slenderness λ! = 𝐴𝑓! 𝑁!".! EN1993-1-1,cl.6.3.1.2(1) Buckling curve EN1993-1-1,table 6.2 Imperfection factor a EN1993-1-1,table 6.1 Check_1 if MEd.y MN.y.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ a MEd.z MN.z.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ β + ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 1.0≤ "OK", "NOT OK", ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ := Buckling_class_Y "a" tf 40mm<if "b" 40mm tf< 100mm<if h b 1.2>if "b" tf 100mm≤if "d" tf 100mm>if h b 1.2≤if :=
  • 82. Page 82 Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1) Reduction factor χ χ = 1 Φ + Φ! − λ! ≤ 1,0 EN1993-1-1,cl.6.3.1.2(1) Design buckling resistance of a compression member 𝑁!,!" = 𝜒𝐴𝑓! 𝛾!!) EN1993-1-1,cl.6.3.1.1(3) Buckling length See: Figure 1: Effective length columns Design Guidance of EC3) Elastic critical force for the relevant buckling mode based on the gross cross sectional properties 𝑁!".! = 𝐸! 𝐼! 𝜋! 𝐿!".! ! - Non dimensional slenderness λ! = 𝐴𝑓! 𝑁!".! EN1993-1-1,cl.6.3.1.2(1) Buckling curve EN1993-1-1,table 6.2 Imperfection factor a EN1993-1-1,table 6.1 αy 0.1 Buckling_class_Y "ao"if 0.21 Buckling_class_Y "a"if 0.34 Buckling_class_Y "b"if 0.49 Buckling_class_Y "c"if 0.76 Buckling_class_Y "d"if := Buckling_class_Y "a" tf 40mm<if "b" 40mm tf< 100mm<if h b 1.2>if "b" tf 100mm≤if "d" tf 100mm>if h b 1.2≤if :=
  • 83. Page 83 Value to determine the reduction factor χ Φ = 0.5 [1 + α (λ – 0.2) + λ2 EN1993-1-1,cl.6.3.1.2(1) Reduction factor χ χ = 1 Φ + Φ! − λ! ≤ 𝜒 ≤ 1,0 EN1993-1-1,cl.6.3.1.2(1) Design buckling resistance of a compression member 𝑁!,!",! = 𝜒𝐴𝑓! 𝛾!!) EN1993-1-1,cl.6.3.1.1(3) Non dimensional slenderness EN1993-1-1,cl.6.3.1.2(1) Check the bukling effects if can be ignored and only cross section check is adequate EN1993-1-1,cl.6.3.1.2(4) Lateral torsional buckling interaction check Elastic critical moment for lateral torsional buckling NCCI: SN003a-EN-EU Effective length factor (Pinned End) k = 1.0 NCCI: SN003a Factor for end warping kw = 1.0 NCCI: SN003a Coefficient factor C1 (Load condition: UDL) NCCI: SN003a Coefficient factor C2 C2 = 1.554 NCCI: SN003a Distance between the point of load application and the shear centre (load applied on centre) zg = 0m NCCI: SN003a αz 0.1 Buckling_class_Z "ao"if 0.21 Buckling_class_Z "a"if 0.34 Buckling_class_Z "b"if 0.49 Buckling_class_Z "c"if 0.76 Buckling_class_Z "d"if := λ max λy λz,( ):= Check if λ 0.2< "Ignored buckling effects", "Consider bucklingeffects",( ):= Mcr C1 π 2 Es⋅ Izz⋅ k Lcr⋅( )2 ⋅ k kw ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 Iw Izz ⋅ k Lcr⋅( )2 G It⋅ π 2 Es Izz⋅ + C2 zg⋅( )2 +⋅ C2 zg⋅−:= C1 1.88 1.40ψ− 0.52ψ 2 +:= Check_5 if C1 2.7≤ "OK", "NOT OK",( ):=
  • 84. Page 84 Lateral torsional buckling curves EN1993-1-1,table 6.4 Imperfection factors for lateral torsional buckling curves EN1993-1-1,table 6.3 Non dimensional slenderness for lateral torsional buckling EN1993-1-1,cl.6.3.2.2(1) Value to determine the reduction factor χLT EN1993-1-1,cl.6.3.2.2(1) Reduction factor for lateral-torsional buckling EN1993-1-1,cl.6.3.2.2(1) Check if the lateral torsional buckling can be ignored EN1993-1-1,cl.6.3.2.2(4) Moments due to the shift of the centroidal axis for class sections 1,2 & 3 EN1993-1- 1,cl.6.3.3(4)/table 6.7 Characteristic resistance to normal force of the critical cross-section EN1993-1- 1,cl.6.3.3(4)/table 6.7 Characteristic moment resistance of the critical cross-section E1993-1-1,cl.6.3.3(4)/table 6.7) Buckling_curve_Z "a" h b 2≤if "b" h b 2>if := αLT 0.21 Buckling_curve_Z "a"if 0.34 Buckling_curve_Z "b"if 0.49 Buckling_curve_Z "c"if 0.76 Buckling_curve_Z "d"if := λLT Wpl.y fy⋅ Mcr := φ LT 0.5 1 αLT λLT 0.2−( )⋅+ λLT 2 +⎡ ⎣ ⎤ ⎦⋅:= χLT 1 φ LT φ LT 2 λLT 2 −+ := Check_6 if λLT λLTO< "Ignored torsional buckling effects", "Consider torsional buckling effects",( ):= Check_7 if MEd.y Mcr λLTO 2 < "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := ΔM Ed.z 0:= ΔM Ed.y 0:= NRk fy A⋅:= My.Rk fy Wpl.y⋅:= Mz.Rk fy Wpl.z⋅:=
  • 85. Page 85 Ratio of end moments EN193-1-1,Table B2) Equivalent uniform moment factor EN1993-1-1,table B.1&B.2 Interaction factors EN1993-1-1,table B.1&B.2 Combined bending and axial compression EN1993-1-1,Eq.6.61 ψy MEd.y1 MEd.y2 1− MEd.y1 MEd.y2 ≤ 1≤if MEd.y2 MEd.y1 1− MEd.y2 MEd.y1 ≤ 1≤if := ψz MEd.z1 MEd.z2 1− MEd.z1 MEd.z2 ≤ 1≤if MEd.z2 MEd.z1 1− MEd.z2 MEd.z1 ≤ 1≤if := Cmy 0.6 0.4 ψy⋅+:= Cmz 0.6 0.4 ψz⋅+:= kyy min Cmy 1 λy 0.2−( ) NEd χy NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmy 1 0.8 NEd χy NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ := kzz min Cmz 1 2λz 0.6−( ) NEd χz NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmz 1 1.4 NEd χz NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ := kyz 0.6kzz:= kzy 0.6kyy:= NEd xy NRk⋅ γ M1 kyy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kyz Mz.Ed ΔM Ed.z+ Mz.Rk γ M1 ⋅+
  • 86. Page 86 Combined bending and axial compression EN1993-1-1,Eq.6.62 Note: This equations is applicable only for I and H sections with section class 1 and 2 Note 1: The shear area is for rolled I and H sections, load parallel to web NEd χz NRk⋅ γ M1 kzy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kzz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+
  • 87. Page 87 8.6 Detail design rules of steel Concentric Braced Frames (CBF) according to Eurocode 8 8.6.1 Detail design rules of steel bracing according to Eurocode 8 Description Value References Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P Non-dimensional slenderness (X bracing) EN1998-1-1,cl.6.7.3(1) Non-dimensional slenderness (one diagonal) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(2) Non-dimensional slenderness (V bracing) λ ≤ 2.0 EN1998-1-1,cl.6.7.3(3) Non-dimensional slenderness (V,X & one bracing) EN1998-1-1,cl.6.7.3(4) Yield resistance check EN1998-1-1,cl.6.7.3(5) Check Ω factor EN1998-1-1,cl.6.7.3(8) Check Ω factor EN1998-1-1,cl.6.7.3(8) Ductility class require for seismic design EN1998-1-1,cl.6.5.3(2) Check_6 if 1.3 λy< 2< "OK", "NOT OK",( ):= Check_5 if Ns 3≥ "Consider limitation (AsEC8)", "Ignorelimitation (As EC3)",( ):= Check_15 if NEd Npl.Rd≤ "OK", "NOT OK",( ):= Ω. Npl.Rd NEd := Check_16 if Ωmax 1.25Ωmin≤ "OK", "NOT OK",( ):= Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if "CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if "CLASS 1" q 4> Ductility_class "DCH"∧if :=
  • 88. Page 88 8.7 Detail design rules of steel columns and beams according to Eurocode 8 Description Value References Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P Yield resistance check EN1998-1-1,cl.6.7.3(5) Check Ω factor EN1998-1-1,cl.6.7.3(8) Minimum resistance requirement, NEd EN1998-1-1,cl.6.7.4(1) Ductility class require for seismic design EN1998-1-1,cl.6.5.3(2) Check_15 if NEd Npl.Rd≤ "OK", "NOT OK",( ):= Ω. Npl.Rd NEd := NEd. NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+:= Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if "CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if "CLASS 1" q 4> Ductility_class "DCH"∧if :=
  • 89. Page 89 8.8 Detail design rules of steel composite members according to Eurocode 8 Description Value References Minimum concrete strength C20/25 – C40/50 CYS EN1998-1-1cl.7.2.1(1) Steel reinforcement class B or C EN1998-1-1,cl.7.2.2(2) Minimum degree of connection η ≤ 0.8 EN1998-1-1,cl.7.6.2(3) Reduction factor kt = 0.75 EN1998-1-1,cl.7.6.2(4) Profiled steel sheeting with ribs transverse to the supporting beams is used, the reduction factor kt = kt * kr EN1998-1-1,cl.7.6.2(6) Yield strength of steel EN1998-1-1,cl.7.6.2(8) Ductility class require for seismic design EN1998-1-1,cl.6.5.3(2) fy "fy=355" 1.5 q< 4≤ Ductility_class "DCM"∧ x d 0.27≤∧if "fy=235" 1.5 q< 4≤ Ductility_class "DCM"∧ 0.27 x d < 0.36≤∧if "fy=355" q 4> Ductility_class "DCH"∧ x d 0.20≤∧if "fy=235" q 4> Ductility_class "DCH"∧ 0.20 x d < 0.27≤∧if := xx Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if "CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if "CLASS 1" q 4> Ductility_class "DCH"∧if :=
  • 90. Page 90 8.9 Detail design rules of steel moment resistance frames (MRF) according to Eurocode 8 8.9.1 Detail design rules for MRF - Design criteria Description Value References Below design criteria apply to (Bottom – Top) Single/Multi-story buildings EN1998-1-1cl.6.6.1(1) Moment capacity (where fixed support is provided) ∑MRc ≥ 1.3MRb EN1998-1-1,cl.4.4.2.3(4) 8.9.2 Detail design rules of steel beam for MRF Description Value References Moment capacity verification 𝑀!" 𝑀!".!"   ≤ 1.0 EN1998-1-1,cl.6.6.2.(2) Design shear force VEd = VEd.G + VEd.M Where VEd.M = (Mpl.Rd.A + Mpl.Rd.B)/L EN1998-1-1,cl.6.6.2.(2) Shear capacity verification 𝑉!" 𝑉!".!"   ≤ 0.5 EN1998-1-1,cl.6.6.2.(2) Axial capacity verification 𝑁!" 𝑁!".!"   ≤ 0.15 EN1998-1-1,cl.6.6.2.(2)
  • 91. Page 91 8.9.3 Detail design rules of steel column for MRF Description Value References Overstrength factor used in design γov = 1.25 CYS EN1998-1-1cl.6.2(3)P Check Ω factor (derivate from all beam with moment connection) Ω!"# = !!".!" !!".!   MEd.E : Lateral force EN1998-1-1cl.6.6.3(1P) Design axial compression force NEd = NEd.G +1.1γvoΩ NEd.E NEd.E : Lateral force EN1998-1-1cl.6.6.3(1P) Design bending moment MEd = MEd.G +1.1γvoΩ MEd.E MEd.E : Lateral force EN1998-1-1cl.6.6.3(1P) Design shear force VEd = VEd.G +1.1γvoΩ VEd. VEd.E : Lateral force EN1998-1-1cl.6.6.3(1P) Design shear force verification 𝑉!" 𝑉!".!"   ≤ 0.5 EN1998-1-1cl.6.6.3(4)
  • 92. Page 92 9.0 Design of steel frames 9.1 Design of steel member overwrites data Figure 9.1: Steel design result of the member Overwrites
  • 93. Page 93 Figure 9.2: Steel frame design overwrites for Eurocode 3 3 2 1 4 7 8 9 10 11 12 5 6
  • 94. Page 94 Table 9.1: Steel frame design overwrites for Eurocode 3 Explanation of Steel frame design overwrites for Eurocode 3 Note No. Parameter Values 1 Effective length factor 2 Moment coefficient kyy kzz
  • 95. Page 95 3 Bending Coefficient (C1) 4 Moment coefficient 5 Overstrength factor used in design1 6 Omega gamma factor γov = 1.25 7 Compressive/Tensile capacity 8 Major bending capacity, Mc3Rd 9 Minor bending capacity, Mc2Rd 10 Buckling resistance moment Ω. Npl.Rd NEd :=
  • 96. Page 96 11 Major shear capacity, Vc3Rd 12 Minor shear capacity, Vc2Rd Notes: 1 Ω is not calculated automatically by the program. Rather, its value can be overwritten by the user through design Preference and Overwrites.
  • 97. Page 97 9.2 Design of columns / beams using ETABS – Gravity load analysis only STEP 1: Analyze > Run Analysis STEP 2: Design > Steel frame design > Select design combo… Note: Under gravity load conditions, only beams and columns shall be considered to resist such loads, without taking into account the bracing members (EN1998-1-1,cl6.7.2(1)P). Design combination at ULS STATIC 1. 1.35DL + 1.5LL STATIC 10. 1.00DL + 0.3LL Figure 9.3: Gravity load combination at ULS Design combination at SLS DSTLD 1. DL + LL DSTLD 2. DL
  • 98. Page 98 Figure 9.4: Gravity load combination at SLS Figure 9.5: Steel design under gravity load ONLY Write click on each member in order to check it individually Column name: C2 Storey level: Storey 1
  • 99. Page 99 Figure 9.6: Steel design result of the member Figure 9.7: Ultimate moment results under worst case combination ETABS: Display > Show tables Worst case combination
  • 100. Page 100 Take the ultimate moment and shear force from the above table and place them into the Excel spreadsheet or Mathcad file in order to verify the steel design results of ETABS. Table 9.2: Summarize of design values required to carry out the design of steel member Design value Symbol Results (kN) Design axial force for gravity load combination (G+0.3Q) NEd.GV 344.75 Design moment at y-y at end 1 (seismic load combination) MEd.GV.y1 -1.293 Design moment at y-y at end 2 (seismic load combination) MEd.GV.y2 3.195 Design moment at z-z at end 1 (seismic load combination) MEd.GV.z1 -0.173 Design moment at z-z at end 2 (seismic load combination) MEd.GV.z2 -0.142 Shear forces at y-y at end (seismic load combination) VEd.GV.y -0.01 Shear force at z-z at end 1 (seismic load combination) VEd.GV.z -1.63 Press the button summary
  • 101. Page 101 Design results of ETABS ETABS/HAND Description of comparison Results ETABS Equation 6.62 in EC3 0.160 HAND (see section 9.3) 0.135
  • 102. Page 102 ETABS/HAND N.c.Rd N.t.Rd N.pl.Rd ETABS 2675.75 2675.75 2675.75 HAND (see section 9.3) 2675.75 2675.75 2675.75 ETABS/HAND Curve Alpha LambarBar Phi Chi Nb.Rd y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z y-y z-z ETABS “b” “c” 0.340 0.490 0.268 0.454 0.548 0.66 0.976 0.868 2610 2322 HAND (see section 9.3) “b” “b” 0.340 0.340 0.248 0.42 0.539 0.625 0.983 0.918 2630 2534
  • 103. Page 103 ETABS/HAND M.c.Rd M.v.Rd M.b.rd y-y z-z y-y z-z ETABS 305.8 142.45 305.8 142.45 302.05 HAND (see section 9.3) 305.8 142.45 305.8 142.45 305.80 ETABS/HAND Curve AlphaLT LambdaBarLT PhiLT ChiLT C1 Mcr ETABS a 0.21 0.255 0.538 0.988 2.532 4694 HAND (see section 9.3) b 0.34 0.24 0.535 0.986 2.532 4679 ETABS/HAND kyy kyz kzy kzz ETABS 0.442 0.582 0.964 0.970 HAND (see section 9.3) 0.441 0.576 0.265 0.96
  • 104. Page 104 ETABS/HAND V.c.Rd V.pl.Rd η y-y z-z ETABS 504 1234 504 1.2 HAND (see section 9.3) 504 1156 504 1.0
  • 105. Page 105 9.3 Design of steel column (Gravity design situation) – Hand calculations 1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations Length of column Total axial load on column, NEd Shear force y-y axis Shear force z-z axis Design moment y-y axis Design moment y-y axis Maximum moment Design moment z-z axis Design moment z-z axis Maximum moment Section properties: Depth of section,h: Width of section,b: Thickness of web, tw: Thickness of flange, tf : Thickness of element Second moment of area z-z: Second moment of area y-y: Cross section area, A: Radius of section: Heigth of web, hw hc 3m:= NEd 344.798kN:= VEd.y 0.011kN:= VEd.z 1.626kN:= MEd.y1 3.195kN m⋅:= MEd.y2 1.293− kN m⋅:= MEd.y max MEd.y1 MEd.y2,( ) 3.195kN m⋅⋅=:= MEd.z1 0.142− kN m⋅:= MEd.z2 0.173− kN m⋅:= MEd.z max MEd.z1 MEd.z2,( ) 0.142− kN m⋅⋅=:= h 270mm:= b 280mm:= tw 8mm:= tf 13mm:= t max tw tf,( ) 13 mm⋅=:= Izz 47630000mm 4 := Iyy 1.367 10 8 ⋅ mm 4 := A 9730mm 2 := r 24mm:= hw h 2tf− 2r− 196 mm⋅=:=
  • 106. Page 106 Area of the web Warping Constant, Iw: Torsional Constant, IT: Plastic Modulus, Wply Plastic Modulus, Wplz Elastic modulus, E: Yield strength of steel , fy: Ultimate strength, fu: Shear modulus Reduction of yield and ultimate strength of sections EN10025-2 Partial safety factor Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1)) Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1)) Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1)) Section classification For section classification the coefficient ε is: For a flange element: Aw hw tw⋅ 1.568 10 3 × mm 2 ⋅=:= Iw 753.7 10 9 ⋅ mm 6 ⋅:= It 635000mm 4 := Wpl.y 1112000mm 3 := Wpl.z 518000mm 3 := Es 210kN mm 2− ⋅:= fy 275N mm 2− ⋅:= fu 430N mm 2− ⋅:= G 81kN mm 2− ⋅:= fy fy t 16mm≤if fy 10N mm 2− ⋅− 16mm t< 40mm≤if fy 20N mm 2− ⋅− 40mm t< 80mm≤if := fy 275 N mm 2− ⋅⋅= fu fu t 16mm≤if fu 10N mm 2− ⋅− 16mm t< 40mm≤if fu 20N mm 2− ⋅− 40mm t< 80mm≤if := fu 430 N mm 2− ⋅⋅= γ M0 1:= γ M1 1:= γ M2 1.25:= ε 235 fy N mm 2− ⋅ 0.924=:=
  • 107. Page 107 For a web element: Tension resistance (cl.6.2.3) Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2) Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b)) Design tension resistance (EN1993-1-1,cl.6.2.3(2)) Check tension capacity cf b tw− 2.r−( ) 2 112 mm⋅=:= Class_type flange "CLASS 1" cf tf 9 ε⋅≤if "CLASS 2" 9 ε⋅ cf tf < 10 ε⋅≤if "CLASS 3" 10 ε⋅ cf tf < 14 ε⋅≤if := Class_type flange "CLASS 2"= cw h 2 tf⋅− 2 r⋅− 196 mm⋅=:= Class_type web "CLASS 1" cw tw 72 ε⋅≤if "CLASS 2" 84 ε⋅ cw tw < 83 ε⋅≤if "CLASS 3" 105 ε⋅ cw tw < 124 ε⋅≤if := Class_typeweb "CLASS 1"= Class_type if Class_typeflange Class_typeweb Class_typeflange, "ADD MANUALY",( ):= Class_type "ADD MANUALY"= Npl.Rd A fy⋅ γ M0 2.676 10 3 × kN⋅=:= Nu.Rd 0.9A fy⋅ γ M2 1.927 10 3 × kN⋅=:= Nt.Rd min Nu.Rd Npl.Rd,( ) 1.927 10 3 × kN⋅=:= Check1 if NEd Nt.Rd 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check1 "OK"=
  • 108. Page 108 Compression resistance (cl.6.2.4) Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1)) Check compression capacity (EN1993-1-1,cl.6.2.4(1)P) Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2) Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2) Shear resistance (cl.6.2.6) Factor for shear area (EN1993-1-1,cl.6.2.6(g)) Shear area of steel section (EN1993-1-1,cl.6.2.6(3)) Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2)) Shear area of steel section (EN1993-1-1,cl.6.2.6(3)) Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2)) Nc.Rd Npl.Rd 2.676 10 3 × kN⋅=:= Check2 if NEd Nc.Rd 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check2 "OK"= Mc.Rd.y Wpl.y fy⋅ γ M0 305.8kN m⋅⋅=:= Mc.Rd.z Wpl.z fy⋅ γ M0 142.45kN m⋅⋅=:= η 1:= Avy A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:= Av Avy Avy η tw⋅ hw⋅>if η tw⋅ hw⋅ Avy η tw⋅ hw⋅<if := Av 3.178 10 3 × mm 2 ⋅= Vpl.Rd.y Av fy 3( ) 1− ⋅ γ M0 ⋅ 504.575kN⋅=:= Avz 2 b⋅ tf⋅ 7.28 10 3 × mm 2 ⋅=:= Vpl.Rd.z 2 b⋅ tf⋅ fy 3( ) 1− ⋅ γ M0 ⋅ 1.156 10 3 × kN⋅=:=
  • 109. Page 109 Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6)) Bending and shear interaction check (cl.6.2.8) Strong axis Y-Y Interaction check 1 Reduced yield strength Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5)) Weak axis Z-Z Interaction check 1 Reduced yield strength Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5)) Check if hw tw 72 ε η ⋅< "Not required shear buckling resistance", "Required shearbuckling resistance", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check "Not required shear buckling resistance"= vy VEd.y Vpl.Rd.y 2.18 10 5− ×=:= ρ 2VEd.y Vpl.Rd.y 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 1=:= Mc.Rd.y Wpl.y ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vy 0.5>if Mc.Rd.y vy 0.5<if := Mc.Rd.y 305.8kN m⋅⋅= vz VEd.z Vpl.Rd.z 1.407 10 3− ×=:= ρ 2VEd.z Vpl.Rd.z 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 0.994=:= Mc.Rd.z Wpl.z ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vz 0.5>if Mc.Rd.z vz 0.5<if := Mc.Rd.z 142.45kN m⋅⋅=
  • 110. Page 110 Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7)) Unity factor Bending and axial force interaction check (cl.6.2.9) Factor a Factor n Factor β Coefficient 1 Coefficient 2 Coefficient check Strong axis Y-Y Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1- 1,cl.6.2.9.1(5)) Check_1 if NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 0.138= Check_1 "OK"= a min A 2b tf⋅−( ) A 0.5, ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 0.252=:= n NEd Npl.Rd 0.129=:= β 5n 5n 1≥if 1 otherwise 1=:= c1 NEd 0.25Npl.Rd 0.515=:= c2 NEd 0.5hw tw⋅ fy⋅ 1.599=:= c max c1 c2,( ) 1.599=:= MN.y.Rd Mc.Rd.y 1 n−( )⋅ 1 0.5a− c 1>if Mc.Rd.y 0 c≤ 1≤if := MN.y.Rd 304.764kN m⋅⋅=
  • 111. Page 111 Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1- 1,cl.6.2.9.1(5)) Check combination of bi-axial bending (EN1993-1-1,cl.6.2.9.1(6)) Unity factor Bucking interaction check (cl.6.3) Strong axis Y-Y Status of effective length Effective length factor (Guidance of EC3) Buckling length of column (fixed end) Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1) MN.z.Rd Mc.Rd.z n a≤if Mc.Rd.z 1 n a− 1 a− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 − ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ ⋅ n a≥if := MN.z.Rd 142.45kN m⋅⋅= Check_1 if MEd.y MN.y.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ a MEd.z MN.z.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ β + ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 1.0≤ "OK", "NOT OK", ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ := MEd.y MN.y.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ a MEd.z MN.z.Rd ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ β + 0.316= Check_1 "OK"= Effective_Length " Pinned Fixed":= k 0.7 Effective_Length "Fixed Fixed"if 0.85 Effective_Length "Partial restraint"if 0.85 Effective_Length " Pinned Fixed"if 1 Effective_Length "Pinned Pinned"if 0.85=:= Lcr k hc 2.55m=:= Ncry Es Iyy⋅ π 2 ⋅ Lcr 2 4.357 10 4 × kN⋅=:=
  • 112. Page 112 Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.2(1) Buckling curve (EN1993-1-1,table 6.2) Imperfection factor (EN1993-1-1,table 6.1) Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ check Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3)) Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1)) λy A fy⋅ Ncry 0.248=:= Buckling_class_Y "a" tf 40mm<if "b" 40mm tf< 100mm<if h b 1.2>if "b" tf 100mm≤if "d" tf 100mm>if h b 1.2≤if := Buckling_class_Y "b"= αy 0.1 Buckling_class_Y "ao"if 0.21 Buckling_class_Y "a"if 0.34 Buckling_class_Y "b"if 0.49 Buckling_class_Y "c"if 0.76 Buckling_class_Y "d"if := αy 0.34:= φ y 0.5 1 αy λy 0.2−( )⋅+ λy 2 +⎡ ⎣ ⎤ ⎦⋅ 0.539=:= χy 1 φ y φ y 2 λy 2 −+ 0.983=:= Check1 if χy 1.0≤ "OK", "NOT OK",( ):= Check1 "OK"= Nb.Rd.y χy A⋅ fy⋅ γ M1 2.63 10 3 × kN⋅=:= Check2 if NEd Nb.Rd.y "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check2 "OK"=
  • 113. Page 113 Weak axis Z-Z Buckling length of column (fixed end) Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1) Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.2(1) Check if the buckling may be ignored (EN1993-1-1,cl.6.3.1.2(4)) Slenderness parameter MinimumEuler Buckling Buckling curve (EN1993-1-1,table 6.2) Imperfection factor (EN1993-1-1,table 6.1) Lcr k hc⋅ 2.55m=:= Ncrz Es Izz⋅ π 2 ⋅ Lcr 2 1.518 10 4 × kN⋅=:= λz A fy⋅ Ncrz 0.42=:= λ max λy λz,( ):= Ncr min Ncry Ncrz,( ):= Check_2 if λ 0.2< NEd Ncr 0.04<∧ "Ignored buckling effects", "Consider buckling effects", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_2 "Consider buckling effects"= Buckling_class_Z "a" tf 40mm<if "b" 40mm tf< 100mm<if h b 1.2>if "b" tf 100mm≤if "d" tf 100mm>if h b 1.2≤if := Buckling_class_Z "b"= αz 0.1 Buckling_class_Z "ao"if 0.21 Buckling_class_Z "a"if 0.34 Buckling_class_Z "b"if 0.49 Buckling_class_Z "c"if 0.76 Buckling_class_Z "d"if := αz 0.34:=
  • 114. Page 114 Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ check Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3)) Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1)) Lateral torsional buckling check (cl.6.3.2) Effective length factor, k (SN003a-EN-EU) Factor for end warping, kw (SN003a-EN-EU) Ratio of the smaller and larger moment Coefficient factor C1 (SN003a-EN-EU) Coefficient factor C1 check (SN003a-EN-EU) Coefficient factor C2 (SN003a-EN-EU) Distance between the point of load application and the shear centre φ z 0.5 1 αz λz 0.2−( )⋅+ λz 2 +⎡ ⎣ ⎤ ⎦⋅ 0.625=:= χz 1 φ z φ z 2 λz 2 −+ 0.918=:= Check_3 if χz 1.0≤ "OK", "NOT OK",( ):= Check_3 "OK"= Nb.Rd.z χz A⋅ fy⋅ γ M1 2.457 10 3 × kN⋅=:= Check_4 if NEd Nb.Rd.z "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_4 "OK"= k 0.85= kw 1.0:= ψ MEd.y2 MEd.y1 0.405−=:= C1 1.88 1.40ψ− 0.52ψ 2 + 2.532=:= Check_5 if C1 2.7≤ "OK", "NOT OK",( ):= Check_5 "OK"= C2 1.554:= zg 0m:=
  • 115. Page 115 Elastic critical moment for lateral torsional buckling (SN003a-EN-EU) Lateral torsional buckling curve (EN1993-1-1,table 6.4) Imperfection factor for lateral torsional (EN1993-1-1,table 6.3) Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1)) Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1)) Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1)) Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1)) Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3)) Mcr C1 π 2 Es⋅ Izz⋅ Lcr( )2 ⋅ k kw ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 Iw Izz ⋅ Lcr( )2 G It⋅ π 2 Es Izz⋅ + C2 zg⋅( )2 +⋅ C2 zg⋅− 4.679 10 3 × kN m⋅⋅=:= Buckling_curve_Z "b" h b 2≤if "c" h b 2>if := Buckling_curve_Z "b"= αLT 0.21 Buckling_curve_Z "a"if 0.34 Buckling_curve_Z "b"if 0.49 Buckling_curve_Z "c"if 0.76 Buckling_curve_Z "d"if := αLT 0.34= λLT Wpl.y fy⋅ Mcr 0.256=:= φ LT 0.5 1 αLT λLT 0.2−( )⋅+ λLT 2 +⎡ ⎣ ⎤ ⎦⋅ 0.542=:= χLT 1 φ LT φ LT 2 λLT 2 −+ 0.98=:= Check_6 if χLT 1≤ χLT 1 λLT 2 ≤∧ "OK", "NOT OK",⎛⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎠ := Check_6 "OK"= λLTO 0.4:= Mb.Rd χLT Wpl.y⋅ fy γ M1 ⋅ 299.741kN m⋅⋅=:= Check_7 if MEd.y Mb.Rd 1≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ :=
  • 116. Page 116 Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4)) Combine bending and axial compression cl.6.3.3 Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7) Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7) Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7) Ratio of end moments (EN1993-1-1,Table B2) Equivalent uniform moment factor Equivalent uniform moment factor Check_7 "OK"= Check_8 if λLT λLTO< MEd.y Mcr λLTO 2 <∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_8 "Ignored torsional buckling effects"= ΔM Ed.z 0:= ΔM Ed.y 0:= NRk fy A⋅ 2.676 10 3 × kN⋅=:= My.Rk Mc.Rd.y 305.8kN m⋅⋅=:= Mz.Rk Mc.Rd.z 142.45kN m⋅⋅=:= ψy MEd.y1 MEd.y2 1− MEd.y1 MEd.y2 ≤ 1≤if MEd.y2 MEd.y1 1− MEd.y2 MEd.y1 ≤ 1≤if := ψz MEd.z1 MEd.z2 1− MEd.z1 MEd.z2 ≤ 1≤if MEd.z2 MEd.z1 1− MEd.z2 MEd.z1 ≤ 1≤if := Cmy 0.6 0.4 ψy⋅+ 0.438=:= Cmz 0.6 0.4 ψz⋅+ 0.928=:=
  • 117. Page 117 Interaction factors (EN1993-1-1,table B.1&B.2) EN1993-1-1,Equation 6.61 Unity factor EN1993-1-1,Equation 6.62 Unity factor kyy min Cmy 1 λy 0.2−( ) NEd χy NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmy 1 0.8 NEd χy NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ 0.441=:= kzz min Cmz 1 2λz 0.6−( ) NEd χz NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmz 1 1.4 NEd χz NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ 0.96=:= kyz 0.6kzz 0.576=:= kzy 0.6kyy 0.265=:= Check_9 if NEd χy NRk⋅ γ M1 kyy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kyz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ := NEd χy NRk⋅ γ M1 kyy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kyz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 0.135= Check_9 "OK"= Check_10 if NEd χz NRk⋅ γ M1 kzy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kzz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ := NEd χz NRk⋅ γ M1 kzy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kzz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 0.142= Check_10 "OK"=
  • 118. Page 118 9.4 Design of steel column (Seismic design situationn) Column name: C2 Storey level: Storey 1
  • 119. Page 119 Step 1: Option > Preferences > Steel frame design Step 2: Design > Steel frame design > Select design combo… Figure 9.7: Lateral/gravity load combination at ULS Modify the existing “System Omega”. The omega factor is equal to the minimum section overstrength factor of concentric bracing. See below: Note: the minimum value of Ω is calculate over all the diagonals of the braced frame system
  • 120. Page 120 Figure 9.8: Gravity load combination at SLS Ultimate limit state (ULS) Static load combination STATIC 1. 1.35DL + 1.5LL STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL
  • 121. Page 121 STATIC 9. 1.35DL - 1.5WINDY – 1.05LL STATIC 10. DL + 0.3LL Seismic load combination for “Modal Analysis” SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX Serviceability limit state (SLS) DSTLD 1. DL + LL DSTLD 2. LL ETABS: Display > Show Tables Table 9.3a: Analysis results of gravity load combination (STATIC 10: G + 0.3Q) Story   Column   Load   Loc   P   V2   V3   T   M2   M3   STORY1   C2   STATIC10   0   -­‐245.17   -­‐0.28   -­‐0.27   0   -­‐0.43   0.001   STORY1   C2   STATIC10   1.38   -­‐244.13   -­‐0.28   -­‐0.27   0   -­‐0.055   0.389   Select all combinations
  • 122. Page 122 STORY1   C2   STATIC10   2.76   -­‐243.1   -­‐0.28   -­‐0.27   0   0.321   0.776   Note:  P  =  NEd.G     Table 9.3b: Analysis results of seismic action (MODAL EQX / EQY) Story   Column   Load   Loc   P   V2   V3   T   M2   M3   STORY1   C2   EQX   0   38.99   29.66   0.49   -­‐0.001   0.884   58.02   STORY1   C2   EQX   1.38   38.99   29.66   0.49   -­‐0.001   0.202   17.094   STORY1   C2   EQX   2.76   38.99   29.66   0.49   -­‐0.001   -­‐0.48   -­‐23.833   STORY1   C2   EQX   0   33.61   26.3   1.15   0.001   1.917   51.189   STORY1   C2   EQX   1.38   33.61   26.3   1.15   0.001   0.332   14.928   STORY1   C2   EQX   2.76   33.61   26.3   1.15   0.001   1.256   21.431   STORY1   C2   EQY   0   3.55   2.72   8.97   0.003   14.692   5.227   STORY1   C2   EQY   1.38   3.55   2.72   8.97   0.003   2.313   1.468   STORY1   C2   EQY   2.76   3.55   2.72   8.97   0.003   10.076   2.297   STORY1   C2   EQY   0   2.6   1.89   10.93   0.002   17.899   3.709   STORY1   C2   EQY   1.38   2.6   1.89   10.93   0.002   2.813   1.097   STORY1   C2   EQY   2.76   2.6   1.89   10.93   0.002   -­‐12.273   -­‐1.516   Note:  P  =  NEd.E   Results of Seismic load combination (SEISMIC 1-8) Select all the seismic load combinations Sort out the highest values of P, V and M
  • 123. Page 123 Table 9.4: Analysis result of design values of V and M based on worst case seismic design combination Story   Column   Load   Loc   P   V2   V3   T   M2   M3   STORY1   C2   SEISMIC1  MIN   0   -­‐279.84   -­‐27.4   -­‐4.11   -­‐0.002   -­‐6.755   -­‐52.756   STORY1   C2   SEISMIC1  MIN   1.38   -­‐278.8   -­‐27.4   -­‐4.11   -­‐0.002   -­‐1.081   -­‐14.979   STORY1   C2   SEISMIC1  MIN   2.76   -­‐277.77   -­‐27.4   -­‐4.11   -­‐0.002   -­‐3.958   -­‐21.344   Table 9.5: Summarize of design values required to carry out the design of steel member Design value Symbol Results (kN/kNm) Design axial force for gravity load combination (G+0.3Q) NEd.G 245 Design axial force for the design seismic action alone NEd.E 39 Design moment at y-y at end 1 (seismic load combination) MEd.SC.y1 52.8 Design moment at y-y at end 2 (seismic load combination) MEd.SC.y2 21.3 Design moment at z-z at end 1 (seismic load combination) MEd.SC.z1 6.8 Design moment at z-z at end 2 (seismic load combination) MEd.SC.z2 4.0 Shear forces at y-y at end (seismic load combination) VEd.SC.y 27.4 Shear force at z-z at end 1 (seismic load combination) VEd.SC.z 4.1
  • 124. Page 124 9.4.1 Design of steel column (Seismic design situation – Hand calculation) Detail design of steel column using Eurocode 3 and Eurocode 8 1. Rolled I - section 2. Limit to class 1 and 2 section 3. Column not susceptible to torsional deformations Design data Length of column Overstrength factor (EN1998-1-1,cl.6.1.3(2)) Omega factor of bracing members at storey 1 Behavior factor q Ductlity class Total axial force due to the non-seismic actions (G+ψ EiQ) Total axial force due to the non-seismic actions (seismic) Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1)) Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1)) Design moment y-y axis (seismic combination) Design moment y-y axis (seismic combination) Design moment y-y axis (seismic combination) Design moment y-y axis (seismic combination) Maximum moment Maximum moment hc 3m:= γ ov 1.25:= Ω 2.5:= q 4:= Ductility_class "DCM":= NEd.G 245.17kN:= NEd.E 39kN:= VEd.y 4.11kN:= VEd.z 27.4kN:= MEd.y1 52.76kN m⋅:= MEd.y2 21.34kN m⋅:= MEd.z1 6.75kN m⋅:= MEd.z2 3.96kN m⋅:= MEd.y max MEd.y1 MEd.y2,( ) 52.76kN m⋅⋅=:= MEd.z max MEd.z1 MEd.z2,( ) 6.75 kN m⋅⋅=:=
  • 125. Page 125 Design shear force due to Eurocode requirement (EN1998-1-1,cl.6.7.4(1)) Section properties: Depth of section,h: Width of section,b: Thickness of web, tw: Thickness of flange, tf : Thickness of element Second moment of area z-z: Second moment of area y-y: Cross section area, A: Radius of section,r: Heigth of web, hw Area of the web Warping Constant, Iw: Torsional Constant, IT: Plastic Modulus, Wply Plastic Modulus, Wplz Elastic modulus, E: Yield strength of steel , fy: Ultimate strength, fu: Shear modulus NEd NEd.G 1.1 γ ov⋅ Ω⋅ NEd.E⋅+ 379.233kN⋅=:= h 270mm:= b 280mm:= tw 8mm:= tf 13mm:= t max tw tf,( ) 13 mm⋅=:= Izz 47630000mm 4 := Iyy 1.367 10 8 ⋅ mm 4 := A 9730mm 2 := r 24mm:= hw h 2tf− 2r− 196 mm⋅=:= Aw hw tw⋅ 1.568 10 3 × mm 2 ⋅=:= Iw 753.7 10 9 ⋅ mm 6 ⋅:= It 635000mm 4 := Wpl.y 1112000mm 3 := Wpl.z 518000mm 3 := Es 210kN mm 2− ⋅:= fy 275N mm 2− ⋅:= fu 430N mm 2− ⋅:= G 81kN mm 2− ⋅:=
  • 126. Page 126 Reduction of yield and ultimate strenght of sections EN10025-2 Partial safety factor Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1)) Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1)) Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1)) Section classification For section classification the coefficient ε is: For a flange element: fy fy t 16mm≤if fy 10N mm 2− ⋅− 16mm t< 40mm≤if fy 20N mm 2− ⋅− 40mm t< 80mm≤if := fy 275 N mm 2− ⋅⋅= fu fu t 16mm≤if fu 10N mm 2− ⋅− 16mm t< 40mm≤if fu 20N mm 2− ⋅− 40mm t< 80mm≤if := fu 430 N mm 2− ⋅⋅= γ M0 1:= γ M1 1:= γ M2 1.25:= ε 235 fy N mm 2− ⋅ 0.924=:= cf b tw− 2.r−( ) 2 112 mm⋅=:= Class_type flange "CLASS 1" cf tf 9 ε⋅≤if "CLASS 2" 9 ε⋅ cf tf < 10 ε⋅≤if "CLASS 3" 10 ε⋅ cf tf < 14 ε⋅≤if := Class_typeflange "CLASS 2"=
  • 127. Page 127 Note: The column now has to be check using the resistance verification checks of Eurocode 3 as shown in section 9.3 of this document. For a web element: Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2)) Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2)) cw h 2 tf⋅− 2 r⋅− 196 mm⋅=:= Class_type web "CLASS 1" cw tw 72 ε⋅≤if "CLASS 2" 84 ε⋅ cw tw < 83 ε⋅≤if "CLASS 3" 105 ε⋅ cw tw < 124 ε⋅≤if := Class_typeweb "CLASS 1"= Class_type if Class_typeflange Class_typeweb Class_typeflange, "ADD MANUALY",( ):= Class_type "ADD MANUALY"= Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if "CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if "CLASS 1" q 4> Ductility_class "DCH"∧if := Class_type_req "CLASS 1 or 2"=
  • 128. Page 128 9.5 Design of composite beams - Hand calculations ETABS: Define > Wall/Slab/Deck sections Figure 9.9: Define deck section Comflor60 -Corus Figure 9.10: Modified “Stiffness Modifiers” (crack-sections)
  • 129. Page 129 ETABS: Analyze > Run analysis ETABS: Display > Show Tables > Select all combinations
  • 130. Page 130 Assumptions - Design and analysis This design process is envisaging a analyzed to determine the forces and moments in the individual structural members. Simple design approach: This method applies to structures in which the connections between members will not develop any significant restraint moments. Members forces and moments are calculated on the basic of the following assumptions: 1. Simply supported beam. 2. The steel sheeting with ribs is placed transverse to the beam. 3. Limited only to I abd H rolled sections with equal flanges 4. Ignored any contribution of steel sheeting to the transverse reinforcements Length of beam Spacing of the secondary beams (LHS) Spacing of the secondary beams (RHS) Loading length Slab design data Comfloor 60 Overall depth of slab Steel sheeting deck profile (Comflor 60) Depth of concrete slab above steel sheeting Rib width at top Rib width at bottom Le 5m:= L1 5m:= L2 5m:= L L1 2 L2 2 + 5m=:= h 150mm:= hp 60mm:= hc h hp− 90 mm⋅=:= b1 131mm:= b2 180mm:=
  • 131. Page 131 Distance between shear connector (Assume single shear connector) Space of each troughs Thickness of steel sheeting Structural steel properties Depth of section, h: Width of section,b: Thickness of web, tw: Thickness of flange, tf : Thickness of element Radius of section,r: Heigth of web, hw Area of the web Radious of gyration Second moment of area z-z: Second moment of area y-y: Cross section area, A: Torsional Constant, IT: Warping Constant, Iw: Plastic Modulus, Wply Plastic Modulus, Wplz Yield strength Ultimate strength Modulus of Elasticity Shear modulus bo b1 b2+ 2 155.5mm⋅=:= e 300mm:= ts 1mm:= ha 240mm:= b 120mm:= tw 6.2mm:= tf 9.8mm:= t max tw tf,( ) 9.8 mm⋅=:= r 15mm:= hw ha 2tf− 2r− 190.4mm⋅=:= Aw hw tw⋅ 1.18 10 3 × mm 2 ⋅=:= iz 26.9507mm:= Izz 2840000mm 4 := Iyy 38920000mm 4 := A 3910mm 2 := It 130000mm 4 := Iw 753.7 10 9 ⋅ mm 6 ⋅:= Wpl.y 367000mm 3 := Wpl.z 73900mm 3 := fy 275N mm 2− ⋅:= fu 430N mm 2− ⋅:= Es 210kN mm 2− ⋅:= G 81kN mm 2− ⋅:=
  • 132. Page 132 Concrete properties Yield strength of reinforcement Cylinder strength Modulus of Elasticity Shear connector properties Diameter Overall height before welding Ultimate strength of shear connector Number of stud per in one rib Material partial factors for resistance Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1)) Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1)) Partial factor for concrete (EN 1992 1-1 Table 2.1N) Partial factor for reinforcing steel (EN 1992 1-1 Table 2.1N) Partial factor for design shear resistance of a headed stud (CYS EN1994-1-1,cl.2.4.1.2(5)P) Partial factor for design shear resistance of a composite slab (CYS EN1994-1-1,cl.2.4.1.2(6)P) Partial factor for permanent action Partial factor for variable action Design value of the cylinder compressive strength of concrete (EN1992-1-1,cl. fyk 500N mm 2− ⋅:= fck 25N mm 2− ⋅:= Ecm 31kN mm 2− ⋅:= d 19mm:= hsc 95mm:= fus 450N mm 2− ⋅:= nr 1:= γ M0 1.0:= γ M1 1.0:= γ c 1.5:= γ s 1.15:= γ v 1.25:= γ vs 1.25:= γ G 1.35:= γ Q 1.5:= fcd fck γ c 16.667N mm 2− ⋅⋅=:=
  • 133. Page 133 Design value of the yield strength of structural steel Loading at construction stage Dead load Weight of steel deck (Comfloor 60) Weight of wet concrete Weight of steel beam (IPE240) Live load Construction live load Total load at construction stage Moment at construction stage Shear force at construction stage Design moments and shear forces Shear force at composite stage Design moment at composite stage Shear force at composite stage Design moment at composite stage fyd fyk γ s 434.783N mm 2− ⋅⋅=:= gk.deck 0.114kN m 2− ⋅:= gk.c.wet 2.79kN m 2− ⋅:= gk.b 0.8kN m 1− ⋅:= qk 0.75kN m 2− ⋅:= FEd γ G gk.deck L⋅ gk.c.wet L⋅+ gk.b+( )⋅ γ Q qk⋅ L⋅+ 26.307kN m 1− ⋅⋅=:= MEd.c FEd L 2 ⋅ 8 82.209kN m⋅⋅=:= VEd.c FEd L⋅ 2 65.767kN⋅=:= VEd.c 65.767kN⋅= MEd.c 82.209kN m⋅⋅= VEd 55.5kN:= MEd 132kN m⋅:=
  • 134. Page 134 Ultimate limit state verification Construction stage Section classification (EN19931-1,cl.5.6(6)) Reduction of yield and ultimate strength of sections EN10025-2 For section classification the coefficient ε is: For a flange element: fy fy t 16mm≤if fy 10N mm 2− ⋅− 16mm t< 40mm≤if fy 20N mm 2− ⋅− 40mm t< 80mm≤if := fy 275 N mm 2− ⋅⋅= fu fu t 16mm≤if fu 10N mm 2− ⋅− 16mm t< 40mm≤if fu 20N mm 2− ⋅− 40mm t< 80mm≤if := fu 430 N mm 2− ⋅⋅= ε 235 fy N mm 2− ⋅ 0.924=:= cf b tw− 2.r−( ) 2 41.9 mm⋅=:= Class_type flange "CLASS 1" cf tf 9 ε⋅≤if "CLASS 2" 9 ε⋅ cf tf < 10 ε⋅≤if "CLASS 3" 10 ε⋅ cf tf < 14 ε⋅≤if := Class_type flange "CLASS 1"=
  • 135. Page 135 For a web element: Bending Resistance of the steel section (EN1993-1-1,cl.6.2.5) Design resistance for bending (EN1993-1-1,cl.6.2.5(2)) Bending resistance check checks (EN1993-1-1,cl.6.2.5(1)) Vertical Shear resistance of the steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6) Factor for shear area (EN1993-1-1,cl.6.2.6(g)) Shear area of steel section (EN1993-1-1,cl.6.2.6(3)) Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2)) cw ha 2 tf⋅− 2 r⋅− 190.4mm⋅=:= Class_type web "CLASS 1" cw tw 72 ε⋅≤if "CLASS 2" 84 ε⋅ cw tw < 83 ε⋅≤if "CLASS 3" 105 ε⋅ cw tw < 124 ε⋅≤if := Class_typeweb "CLASS 1"= Class_type if Class_typeflange Class_typeweb Class_typeflange, "ADD MANUALY",( ):= Class_type "CLASS 1"= Ma.pl.Rd Wpl.y fy⋅ γ M0 100.925kN m⋅⋅=:= Check_1 if MEd.c Ma.pl.Rd≤ "OK", "NOT OK",( ):= Check_1 "OK"= η 1:= Av1 A 2 b⋅ tf⋅− tw 2r+( ) tf⋅+:= Av Av1 Av1 η tw⋅ hw⋅>if η tw⋅ hw⋅ Av1 η tw⋅ hw⋅<if := Av 1.913 10 3 × mm 2 ⋅= Vpl.Rd Av fy 3( ) 1− ⋅ γ M0 ⋅ 303.691kN⋅=:=
  • 136. Page 136 Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P) Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6)) Bending and shear interaction check (cl.6.2.2.4) Strong axis Y-Y Interaction check 1 Reduced yield strength Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5)) Lateral torsional buckling resistance of steel beam (EN1993-1-1,cl.6.3.2) Status of effective length Effective length factor (Guidance of EC3) Check_2 if VEd Vpl.Rd≤ "OK", "NOT OK",( ):= Check_2 "OK"= Check_3 if hw tw 72 ε η ⋅< "Not required shear buckling resistance", "Required shearbuckling resistance", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_3 "Not required shear buckling resistance"= vy VEd Vpl.Rd 0.183=:= ρ 2VEd Vpl.Rd 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 0.403=:= Ma.pl.Rd. Wpl.y ρ Aw 2 ⋅ 4tw − ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ fy⋅ γ M0 vy 0.5>if Ma.pl.Rd vy 0.5<if := Ma.pl.Rd 100.925kN m⋅⋅= Effective_Length "Pinned Pinned":= k 0.7 Effective_Length "Fixed Fixed"if 0.85 Effective_Length "Partial restraint"if 0.85 Effective_Length " Pinned Fixed"if 1 Effective_Length "Pinned Pinned"if 1=:=
  • 137. Page 137 Effective length (pinned) Factor for end warping, kw (SN003a-EN-EU) Coefficient factor C1 (SN003a-EN-EU) Coefficient factor C2 (SN003a-EN-EU) Distance between the point of load application and the shear centre Elastic critical moment for lateral torsional buckling (SN003a-EN-EU) Lateral torsional buckling curve (EN1993-1-1,table 6.4) Imperfection factor for lateral torsional (EN1993-1-1,table 6.3) Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1)) Parameter introducing the effect of biaxial bending (EN1994-1-1,cl.6.3.2.3(1)) Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1)) Lcr k Le⋅ 5m=:= kw 1.0:= C1 1.348:= C2 0.454:= zg 0m:= Mcr C1 π 2 Es⋅ Izz⋅ Lcr( )2 ⋅ k kw ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 Iw Izz ⋅ Lcr( )2 G It⋅ π 2 Es Izz⋅ + C2 zg⋅( )2 +⋅ C2 zg⋅− 176.744kN m⋅⋅=:= Buckling_curve_Z "b" h b 2≤if "c" h b 2>if := Buckling_curve_Z "b"= αLT 0.21 Buckling_curve_Z "a"if 0.34 Buckling_curve_Z "b"if 0.49 Buckling_curve_Z "c"if 0.76 Buckling_curve_Z "d"if := αLT 0.34= λLT Wpl.y fy⋅ Mcr 0.756=:= β 0.75:= λLTO 0.4:=
  • 138. Page 138 Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1)) Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1)) Design plastic resistance (EN1993-1-1,cl.6.3.2.1) Section verification for lateral torsional buckling (EN1993-1-1,cl.6.3.2.1(1)) Composite stage Effective width of composite beam (cl.5.4.1.2(5)) Total effective width at mid-span (EN1994-1-1cl. 5.4.1.2(5)) Plastic resistance moment of composite section with full shear connection (cl.6.2) Tensile resistance of steel section (EN1993-1-1,cl.6.2.3(2)) Compression resistance of concrete slab (EN1994-1-1,cl.6.2.1.2(1d) Tensile resistance in web of steel section φ LT 0.5 1 αLT λLT λLTO−( )⋅+ β λLT 2 ⋅⎛ ⎝ ⎞ ⎠+⎡ ⎣ ⎤ ⎦⋅ 0.775=:= χLT 1 φ LT φ LT 2 β λLT 2 −+ 0.841=:= Check_5 if χLT 1≤ χLT 1 λLT 2 ≤∧ "OK", "NOT OK",⎛⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎠ := Check_5 "OK"= Mb.Rd χLT Wpl.y fy⋅ γ M1 ⋅ 84.882kN m⋅⋅=:= Check_6 if MEd.c Mb.Rd 1< "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_6 "OK"= beff bo 2 min L1 2 L2 2 + Le 8 , ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ +:= Npl.a fy A⋅ γ M0 1.075 10 3 × kN⋅=:= Nc.f 0.85 fcd⋅ beff⋅ hc⋅ 1.792 10 3 × kN⋅=:= Npl.w fy tw⋅ ha 2 tf⋅−( )⋅:=
  • 139. Page 139 Location of neutral axis (EN1994-1-1,cl.6.2.1.2(1)) Bending resistance with full shear connection (EN1994-1-1,cl.6.1.2) Bending resistance check checks (EN1993-1-1,cl.6.2.5(1)) Vertical Sheat resistance of the composite steel section (cl.6.2.2) & (EN1993-1-1,cl.6.2.6) Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2)) Design of shear resistance check (EN1993-1-1,cl.6.2.6(1)P) Location_neutral axis "Lies in the concrete slab" Nc.f Npl.a>if "Lies in the top flange of the beam" Nc.f Npl.a≤if "Lies in the web of the beam" Nc.f Npl.w<if := Location_neutral axis "Lies in theconcrete slab"= Mpl.Rd Npl.a ha 2 h+ Npl.a Nc.f hc 2 ⋅− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ Location_neutral axis "Lies in the concrete slab"if Npl.a ha 2 ⋅ Nc.f hc 2 hp+ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅+ Location_neutral axis "Lies in the top flange of the beam"if Ma.pl.Rd Nc.f hc ha+ 2hp+ 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅+ Nc.f 2 Npl.w ha 4 ⋅− Location_neutral axis "Lies in the top flange of the beam"if := Mpl.Rd 261.285kN m⋅⋅= Check_7 if MEd Mpl.Rd≤ "OK", "NOT OK",( ):= Check_7 "OK"= Vpl.Rd 303.691kN⋅= Check_8 if VEd Vpl.Rd≤ "OK", "NOT OK",( ):= Check_8 "OK"=
  • 140. Page 140 Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6)) Design resistance of shear stud connector (cl.6.6.3.1(1)) For sheeting with ribs transverse to the beam For sheeting parallel to the beam see Equation 6.22 of EC4 Upper limit of reduction factor kt (EN1994-1-1,Table:6.2) Reduction factor kt (EN1994-1-1,cl.6.6.4.2) Limitation of kt (EN1994-1-1,cl.6.6.4.2(2)) Minimum height of shear stud (EN1994-1-1,cl.6.6.1.2(1)) Check_9 if hw tw 72 ε η ⋅< "Not required shear buckling resistance", "Required shearbuckling resistance", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_9 "Not required shear buckling resistance"= kt.max 0.85 nr 1 1mm ts≥∧ d 20mm<∧if 1.0 nr 1 1mm ts<∧ d 20mm<∧if 0.75 nr 1 1mm ts≥∧ 19mm d≤ 22mm<∧if 0.75 nr 1 1mm ts<∧ 19mm d≤ 22mm<∧if 0.70 nr 2 1mm ts≥∧ d 20mm<∧if 0.80 nr 2 1mm ts<∧ d 20mm<∧if 0.60 nr 2 1mm ts≥∧ 19mm d≤ 22mm<∧if 0.60 nr 2 1mm ts<∧ 19mm d≤ 22mm<∧if := kt.max 0.75= kt 0.6 bo hp ⋅ hsc hp 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅:= kt kt kt kt.max<if kt.max otherwise 0.75=:= hmin if hsc 4d≥ "Ductile", "Not Ductile",( ):= hmin "Ductile"=
  • 141. Page 141 Limitation of stud diameter (EN1994-1-1,cl.6.6.1.2(1)) Factor α (EN1994-1-1,cl.6.6.3.1(1)) Design shear resistance of a headed stud (EN1994-1-1,cl.6.6.3.1(1)) Degree of shear connection (cl.6.6.1.2(1)) Ratio of the degree shear connection (EN1994-1-1,cl.6.2.1.3(3)) Minimum degree of shear connection for equal flange (EN1994-1-1,cl.6.6.1.2(1)) Check the degree of shear interaction within the limits (EN1994-1-1,cl.6.6.1.2(1)) Number of shear connector required Numper of stud provided Stud spacing dlim if 16mm d< 25mm< "Ductile", "Not ductile",( ):= dlim "Ductile"= α 0.2 hsc d 1+ ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅ 3 hsc d ≤ 4≤if 1 hsc d 4>if 1=:= PRd kt min 0.8 fus⋅ π⋅ d 2 4 ⋅ γ v 0.29 α⋅ d 2 ⋅ fck Ecm⋅⋅ γ v , ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅ 55.298kN⋅=:= η Nc.f Npl.a 1.667=:= ηmin 1 355 fy N mm 2− ⋅ ⎛⎜ ⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎟ ⎠ 0.75 0.03 Le m ⋅− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ ⋅− Le 25m<if 1.0 Le 25m>if := ηmin 0.225= Check_11 if η ηmin> η 0.4≥∧ "OK", "NOT OK",( ):= Check_11 "OK"= n 2 Npl.a⋅ PRd 38.889=:= Nstud 40:= sprov Le Nstud 0.125m=:=
  • 142. Page 142 Check the minimum spacing of studs (EN1994-1-1,cl.6.6.5.7(4)) Adequacy of the shear connection (EN1994-1-1,cl.6.6.1.3(3)) Design of transverse reinforcement (cl.6.6.6.2) & (EN1992-1-1,cl.6.2.4) Length under consideration Longitudinal shear stress (EN1992-1-1,cl.6.2.4(3)) Strength reduction factor (EN1992-1-1,Eq.6.6N) Angle between the diagonal strut (EN1992-1-1,cl.6.2.4(4)) Assume spacing of the bars Area of transverse reinforcement required (EN1992-1-1,cl.6.2.4(4)) Area of transverse reinforcement provided Check the crushing compression in the flange (EN1992-1-1cl.6.2.4(4)) slim if sprov 5 d⋅≥ sprov 6 h⋅<∧ "OK", "NOT OK",( ):= slim "OK"= Check_12 if Mpl.Rd 2.5 Ma.pl.Rd⋅< "Uniform spacing", "Not uniform spacing",(:= Check_12 "Not uniform spacing"= Δ x Le 2 2.5m=:= vEd Npl.a 2 hc⋅ Δ x⋅ := v 0.6 1 fck 250 N⋅ mm 2− ⋅ − ⎛⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎠ ⋅:= θf 45deg:= sf 200mm:= As.req vEd hc⋅ sf⋅ fyd sin θf( ) cos θf( ) ⋅ := As.prov 193mm 2 := Check_13 if As.req As.prov≤ "OK", "NOT OK",( ):= Check_13 "OK"= Check_14 if vEd v fcd⋅ sin θf( )⋅ cos cos θf( )( )⋅≤ "OK", "NOT OK",( ):= Check_14 "OK"=
  • 143. Page 143 Serviceability limit state verification Construction stage Dead load at composite stage Live load at composite stage Maximum deflection at construction stage Vertical deflection limit (CYS NA EN1993-1-1,table NA.1) Short term elastic modular ration (EN1994-1-1,cl.7.2.1) Second moment of area of the composite section, Ic Deflection with full shear connection Vertical deflection limit (CYS NA EN1993-1-1,table NA.1) Gk 10.88kN m 1− ⋅:= Qk 5.0kN m 1− ⋅:= δcon 5 Gk Qk+( )⋅ Le 4 ⋅ 384 Es⋅ Iyy⋅ 15.812mm⋅=:= Check_15 if δcon Le 250 < "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_15 "OK"= no Es Ecm := r A beff hc⋅ := Iy A h 2 hp⋅+ hc+( )2 ⋅ 4 1 no r⋅+( )⋅ beff hc 3 ⋅ 12 no⋅ + Iyy+ 1.563 10 4− × m 4 =:= δcom 5 Gk Qk+( )⋅ Le( )4 ⋅ 384 Es⋅ Iy⋅ 3.938mm⋅=:= Check_16 if δcom Le 200 < "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_16 "OK"=
  • 144. Page 144 Vibration (Simplified analysis): Loading: Permanent load Imposed load For category B building Total weigth floor, Fv Increase the inertia, Ic by 10% to allow for the increased dynamic stiffness of the composite beam, Icl Instantaneous deflection caused by re-application of the self weight of the floor and the beam to the composite beam, δ α Natural frequncy, f Check beam vibration (SCI-P-076) Gk 10.88 kN m 1− ⋅⋅= Qk 5 kN m 1− ⋅⋅= ψ1 0.5:= Fv Gk ψ1 Qk⋅+:= Icl Iy Iy 0.1⋅( )+:= δα 5 Fv Le⋅( )⋅ Le 3 ⋅ 384 Es⋅ Icl⋅ 3.016mm⋅=:= f 18 δα mm ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ Hz 10.364Hz⋅=:= Check_17 if f 4 Hz⋅> "OK", "NOT OK",( ):= Check_17 "OK"=
  • 145. Page 145 9.5 Design of steel bracing 9.5.1 Main configuration of design of steel bracing Basic theory: Tension only, utilises two members at each storey but only the tension element is assumed to resist wind load and seismic load, the compression element is assumed to buckle and offer no resistance to lateral movement. Eurocode 8 requirement: The diagonals shall be taken into account as follows in an elastic analysis of the structure for the seismic action: a) in frames with diagonal bracings, only the tension diagonals shall be taken into account, b) in frames with V bracings, both the tension and compression diagonals shall be taken into account (EN1998-1-1,cl6.7.2(2). Taking into account of both tension and compression diagonals in the analysis of any type of concentric bracing is allowed provided that all of the following conditions are satisfied: a) a non-linear static (pushover) global analysis or non-linear time history analysis is used, b) both pre-buckling and post-buckling situations are taken into account in the modeling of the behavior of diagonals and, c) background information justifying the model used to represent the behavior of diagonals is provided (EN1998-1-1,cl6.7.2(3).
  • 146. Page 146 Figure 9.11: Method of design bracing in this manual Steps for designing steel bracing member: 1. Delete the compression member. 2. Leave the tension members only. 3. Run the design of steel frame. 4. Find the suitable section and ensure that the section pass all the checks. 5. Ensure that the compression member has been placed at the construction drawings. Ignore compression members Compression members Tension members Direction of shear
  • 147. Page 147 9.5.2 Simplified design of frames with X bracing (Extract from Design guidance to EC8) In a standard design, the following simplified approach may be used: • The analysis of the structure is realized considering that only one diagonal in each X bracing is present, the other diagonal being considered as already buckled and unable to provide strength. This corresponds to an underestimation of both the stiffness and the strength of the structural system at the initial (pre-buckling) stage, but to a safe-side estimate at the post-buckling stage. • The beams and columns are capacity designed according to the real yield strength of the diagonals, for bending with increased axial force and bending moment from the analysis for the combination of the design seismic action with gravity loads. However, this simplified approach could be dangerous for the stability of the structure, if it does not take into account that action effects of compression in columns and beams at the pre-buckling stage are higher than in the post-buckling stage envisaged in the analysis. Indeed, if the buckling loads of the diagonal are closed to their yield load in tension, the initial shear resistance Vinit of the X bracing is underestimated by a model where only one diagonal is considered present. If low-slenderness diagonals are used, Vinit can be close to double the value of Vpl.Rd computed with the hypothesis of one active yielded diagonal. The only way to prevent this unsafe situation is to design slender diagonal having their buckling load at most around 0.5Npl.Rd. This condition is behind the prescribed lower bound limit value of 1.3 for the slenderness λ. The prescribed upper bound limit max λ=2, is justified by the aim to avoid shock effects during the load reversal in diagonals.
  • 148. Page 148 9.5.3 Model in ETABS Figure 9.12: Amendment model Assume that the steel bracing resist the lateral force at the +X direction Assume that the steel bracing resist the lateral force at the -X direction
  • 149. Page 149 Assume that the steel bracing resist the lateral force at the -Y direction Assume that the steel bracing resist the lateral force at the +Y direction
  • 150. Page 150 STEP 2: Design > Steel frame design > Select design combo… Figure 9.13: Lateral/gravity load combination at ULS Figure 9.14: Gravity load combination at SLS
  • 151. Page 151 Ultimate limit state (ULS) Static load combination STATIC 11. 1.35DL + 1.5LL + 0.75WINDX STATIC 12. 1.35DL + 1.5LL - 0.75WINDX STATIC 13. 1.35DL + 1.5LL + 0.75WINDY STATIC 14. 1.35DL + 1.5LL - 0.75WINDY STATIC 15. 1.35DL + 1.5WINDX + 1.05LL STATIC 16. 1.35DL - 1.5WINDX – 1.05LL STATIC 17. 1.35DL + 1.5WINDY + 1.05LL STATIC 18. 1.35DL - 1.5WINDY – 1.05LL Seismic load combination for “Modal Analysis” SEISMIC 9. DL + 0.3LL + EQX + 0.3EQY SEISMIC 10. DL + 0.3LL + EQX – 0.3EQY SEISMIC 11. DL + 0.3LL - EQX + 0.3EQY SEISMIC 12. DL + 0.3LL - EQX – 0.3EQY SEISMIC 13. DL + 0.3LL + EQY + 0.3EQX SEISMIC 14. DL + 0.3LL + EQY – 0.3EQX SEISMIC 15. DL + 0.3LL - EQY + 0.3EQX SEISMIC 16. DL + 0.3LL - EQY – 0.3EQX Serviceability limit state (SLS) DSTLD 3. DL + LL
  • 152. Page 152 Figure 9.15: Design steel bracing member Write click on member Brace name: D3 Storey level: Storey 1
  • 153. Page 153 Table 9.6: Design value of brace D3 Story   Brace   Load   Loc   P   V2   V3   T   M2   M3   STORY1   D3   SEISMIC1  MIN   0   -­‐361.83   -­‐1.41   -­‐0.05   -­‐0.044   -­‐0.173   -­‐1.792   STORY1   D3   SEISMIC2  MIN   0   -­‐361.83   -­‐1.41   -­‐0.05   -­‐0.044   -­‐0.173   -­‐1.792   STORY1   D3   SEISMIC3  MIN   0   -­‐361.83   -­‐1.41   -­‐0.05   -­‐0.044   -­‐0.173   -­‐1.792   STORY1   D3   SEISMIC4  MIN   0   -­‐361.83   -­‐1.41   -­‐0.05   -­‐0.044   -­‐0.173   -­‐1.792   STORY1   D3   SEISMIC1  MIN   2.915   -­‐361.06   -­‐0.13   -­‐0.05   -­‐0.044   -­‐0.054   0.443   STORY1   D3   SEISMIC2  MIN   2.915   -­‐361.06   -­‐0.13   -­‐0.05   -­‐0.044   -­‐0.054   0.443   STORY1   D3   SEISMIC3  MIN   2.915   -­‐361.06   -­‐0.13   -­‐0.05   -­‐0.044   -­‐0.054   0.443   STORY1   D3   SEISMIC4  MIN   2.915   -­‐361.06   -­‐0.13   -­‐0.05   -­‐0.044   -­‐0.054   0.443  
  • 154. Page 154 Worst case combination Modify the default steel design data if needed
  • 155. Page 155 Table 9.7: Summarize of design values required to carry out the design of steel member Design value Symbol Results (kN/kNm) Design axial force for the worse case design load combination NEd 361.83 Design moment at y-y at end 1 (worse case combination) MEd.y1 -1.792 Design moment at y-y at end 2 (worse case combination) MEd.y2 0.443 Design moment at z-z at end 1 (worse case combination) MEd.z1 -0.173 Design moment at z-z at end 2 (worse case combination) MEd.z2 -0.054 Shear forces at y-y at end (worse case combination) VEd.y -0.05 Shear force at z-z at end 1 (worse case combination) VEd.z -1.41 Modify the omega factors if needed Modify the effective length factor if needed
  • 156. Page 156 9.5.4 Design of steel bracing (Gravity/Seismic design situation) – Hand calculation 1. Rolled I - section 2. Limit to class 1 and 2 section Design data Overstrength factor (EN1998-1-1,cl.6.1.3(2)) Behavior factor q Ductlity class Number of storeys Length of bracing Total axial load on column, NEd Shear force y-y axis Shear force z-z axis Design moment y-y axis Design moment y-y axis Maximum moment Design moment z-z axis Design moment z-z axis Maximum moment Section properties: Depth of section,d: Width of section,b: Thickness of web, tw: Thickness of flange, tf : Thickness of element γ ov 1.25:= q 4:= Ductility_class "DCM":= Ns 3:= hc 5.831m:= NEd 361.83kN:= VEd.y 0.05kN:= VEd.z 1.41kN:= MEd.y1 1.792kN m⋅:= MEd.y2 0.443kN m⋅:= MEd.y max MEd.y1 MEd.y2,( ) 1.792kN m⋅⋅=:= MEd.z1 0.173− kN m⋅:= MEd.z2 0.054− kN m⋅:= MEd.z max MEd.z1 MEd.z2,( ) 0.054− kN m⋅⋅=:= d 120mm:= b 120mm:= tw 16mm:= tf 16mm:= t max tw tf,( ) 16 mm⋅=:=
  • 157. Page 157 Second moment of area z-z: Second moment of area y-y: Cross section area, A: Warping Constant, Iw: Torsional Constant, IT: Plastic Modulus, Wply Plastic Modulus, Wplz Elastic modulus, E: Yield strength of steel , fy: Ultimate strength, fu: Shear modulus Reduction of yield and ultimate strenght of sections EN10025-2 Partial safety factor Resistance of cross-sections whatever the class (CYS EN1993-1-1,cl 6.1(1)) Resistance of members to instability (CYS EN1993-1-1,cl 6.1(1)) Resistance of cross-section in tension (CYS EN1993-1-1,cl.6.1(1)) Izz 12280000mm 4 := Iyy 12280000mm 4 := A 6656mm 2 := Iw 0 mm 6 ⋅:= It 18000000mm 4 := Wpl.y 261600mm 3 := Wpl.z 261600mm 3 := Es 210kN mm 2− ⋅:= fy 275N mm 2− ⋅:= fu 430N mm 2− ⋅:= G 81kN mm 2− ⋅:= fy fy t 16mm≤if fy 10N mm 2− ⋅− 16mm t< 40mm≤if fy 20N mm 2− ⋅− 40mm t< 80mm≤if := fy 275 N mm 2− ⋅⋅= fu fu t 16mm≤if fu 10N mm 2− ⋅− 16mm t< 40mm≤if fu 20N mm 2− ⋅− 40mm t< 80mm≤if := fu 430 N mm 2− ⋅⋅= γ M0 1:= γ M1 1:= γ M2 1.25:=
  • 158. Page 158 Section classification For section classification the coefficient ε is: Requirements on cross-sectional class of dissipative elements depending on Ductility class (EN1998-1-1,cl.6.5.3(2)) Section classification rule for EC8 (EN1998-1-1,cl.6.5.3(2)) ε 235 fy N mm 2− ⋅ 0.924=:= cf d 2tf− 88 mm⋅=:= Class_type_flange "CLASS 1" cf t 33 ε⋅≤if "CLASS 2" 33 ε⋅ cf t < 38 ε⋅≤if "CLASS 3" 38 ε⋅ cf t < 42 ε⋅≤if := Class_type_flange "CLASS 1"= cw d 2tw− 88 mm⋅=:= Class_type_web "CLASS 1" cw t 72 ε⋅≤if "CLASS 2" 72 ε⋅ cw t < 83 ε⋅≤if "CLASS 3" 83 ε⋅ cw t < 124 ε⋅≤if := Class_type_web "CLASS 1"= Class_type if Class_type_flange Class_type_web Class_type_flange, "ADD MANUALY",( ):= Class_type "CLASS 1"= Class_type_req "CLASS 1 , 2 or 3" 1.5 q< 2≤ Ductility_class "DCM"∧if "CLASS 1 or 2" 2 q< 4≤ Ductility_class "DCM"∧if "CLASS 1" q 4> Ductility_class "DCH"∧if "CLASS 1 or 2"=:= Class_type_req "CLASS 1 or 2"=
  • 159. Page 159 Tension resistance (cl.6.2.2) Design plastic resistance of the cross section (EN1993-1-1,cl.6.2.3(2a)) Modified plastic resistance of cross section as described in "Design Guidance to EC8" (cl.6.10.2) Design ultimate resistance (EN1993-1-1,cl.6.2.3(2b)) Design tension resistance (EN1993-1-1,cl.6.2.3(2)) Check tension capacity (EN1993-1-1,cl.6.2.3(1)P) Compression resistance (cl.6.2.3) Compression resistance of steel section (EN1993-1-1,cl.6.2.4(1)) Check compression capacity (EN1993-1-1,cl.6.2.4(1)P) Bending resistance (cl.6.2.5) Moment resistance of steel section at Y-Y (EN1993-1-1,cl.6.2.5(2) Moment resistance of steel section at Z-Z (EN1993-1-1,cl.6.2.5(2) Sheat resistance (cl.6.2.6) Factor for shear area (EN1993-1-1,cl.6.2.6(g)) Shear area of steel section (EN1993-1-1,cl.6.2.6(3)) Shear area of steel section (EN1993-1-1,cl.6.2.6(3)) Shear resistance of steel section Y-Y (EN1993-1-1,cl.6.2.6(2)) Npl.Rd A fy⋅ γ M0 1.83 10 3 × kN⋅=:= Npl.Rd 0.5 Npl.Rd⋅ 915.2kN⋅=:= Nu.Rd 0.9A fy⋅ γ M2 1.318 10 3 × kN⋅=:= Nt.Rd min Nu.Rd Npl.Rd,( ) 915.2kN⋅=:= Check_1 if NEd Nt.Rd 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_1 "OK"= Nc.Rd Npl.Rd 915.2kN⋅=:= Check_2 if NEd Nc.Rd 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_2 "OK"= Mc.Rd.y Wpl.y fy⋅ γ M0 71.94kN m⋅⋅=:= Mc.Rd.z Wpl.z fy⋅ γ M0 71.94kN m⋅⋅=:= η 1:= Avy A b⋅ b d+ 3.328 10 3 × mm 2 ⋅=:= Avz A d⋅ b d+ 3.328 10 3 × mm 2 ⋅=:= Vpl.Rd.y Avy fy 3( ) 1− ⋅ γ M0 ⋅ 528.391kN⋅=:=
  • 160. Page 160 Shear resistance of steel section Z-Z (EN1993-1-1,cl.6.2.6(2)) Check if the verification of shear buckling resistance required or not (EN1993-1-1,cl.6.2.6(6)) Bending and shear interaction check (cl.6.2.8) Strong axis Y-Y Interaction check 1 Reduced yield strength Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5)) Weak axis Z-Z Interaction check 1 Reduced yield strength Vpl.Rd.z Avz fy 3( ) 1− ⋅ γ M0 ⋅ 528.391kN⋅=:= Check_3 if d t 72 ε η ⋅< "Not required shear buckling resistance", "Required shear buckling resistance",⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_3 "Not required shear buckling resistance"= vy VEd.y Vpl.Rd.y 9.463 10 5− ×=:= ρ 2VEd.y Vpl.Rd.y 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 1=:= Mc.Rd.y Wpl.y ρ A 2 ⋅ 4t − ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ fy⋅ γ M0 vy 0.5>if Mc.Rd.y vy 0.5<if := Mc.Rd.y 71.94kN m⋅⋅= vz VEd.z Vpl.Rd.z 2.668 10 3− ×=:= ρ 2VEd.z Vpl.Rd.z 1− ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 0.989=:=
  • 161. Page 161 Reduced design plastic resistance moment (EN1993-1-1,cl.6.2.8(5)) Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7)) Unity factor Bending and axial force interaction check (cl.6.2.9) Factor a Factor a Factor n Factor β Factor α Mc.Rd.z Wpl.z ρ A 2 ⋅ 4t − ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ fy⋅ γ M0 vz 0.5>if Mc.Rd.z vz 0.5<if := Mc.Rd.z 71.94kN m⋅⋅= Check_4 if NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 0.42= Check_4 "OK"= aw min A 2b tw⋅−( ) A 0.5, ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 0.423=:= af min A 2d tf⋅−( ) A 0.5, ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 0.423=:= n NEd Npl.Rd 0.395=:= β 1.66 1 1.13n 2 − 1.66 1 1.13n 2 − 6≤if 6 otherwise 2.016=:= a β 2.016=:=
  • 162. Page 162 Strong axis Y-Y Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5)) Weak axis Z-Z Reduced design value of the resistance to bending moments making allowance for the presence of axial forces (EN1993-1-1,cl.6.2.9.1(5)) Check combination of axial and bending (EN1993-1-1,cl.6.2.1(7)) Unity factor Bucking interaction check (cl.6.3) Strong axis Y-Y Status of effective length Effective length factor (Guidance of EC3) MN.y.Rd Mc.Rd.y 1 n−( )⋅ 1 0.5aw− := MN.y.Rd MN.y.Rd MN.y.Rd Mc.Rd.y≤if Mc.Rd.y MN.y.Rd Mc.Rd.y>if := MN.y.Rd 55.168kN m⋅⋅= MN.z.Rd Mc.Rd.z 1 n−( )⋅ 1 0.5af− := MN.z.Rd MN.z.Rd MN.z.Rd Mc.Rd.z≤if Mc.Rd.z MN.z.Rd Mc.Rd.z>if := MN.z.Rd 55.168kN m⋅⋅= Check_5 if NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := NEd Npl.Rd MEd.y Mc.Rd.y + MEd.z Mc.Rd.z + 0.42= Check_5 "OK"= Effective_Length "Pinned Pinned":= ky 0.7 Effective_Length "Fixed Fixed"if 0.85 Effective_Length "Partial restraint"if 0.85 Effective_Length " Pinned Fixed"if 1 Effective_Length "Pinned Pinned"if 1=:=
  • 163. Page 163 Buckling length of column (fixed end) Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1) Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.3(1) Check for X bracing (EN1998-1-1,cl.6.7.3(4)) Check for X bracing (EN1998-1-1,cl.6.7.3(1)) Type of the section Buckling curve (EN1993-1-1,table 6.2) Imperfection factor (EN1993-1-1,table 6.1) Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ check Lcry ky hc 5.831m=:= Ncry Es Iyy⋅ π 2 ⋅ Lcry 2 748.568kN⋅=:= λy A fy⋅ Ncry 1.564=:= Check_6 if Ns 3≥ "Consider limitation (AsEC8)", "Ignorelimitation (As EC3)",( ):= Check_6 "Consider limitation (As EC8)"= Check_7 if 1.3 λy< 2< "OK", "NOT OK",( ):= Check_7 "OK"= Section "Hot finished":= Buckling_curve "a" Section "Hot finished"if "c" Section "Cold formed"if := Buckling_curve "a"= αy 0.21 Buckling_curve "a"if 0.49 Buckling_curve "c"if := αy 0.21= φ y 0.5 1 αy λy 0.2−( )⋅+ λy 2 +⎡ ⎣ ⎤ ⎦⋅ 1.866=:= χy 1 φ y φ y 2 λy 2 −+ 0.347=:= Check_8 if χy 1.0≤ "OK", "NOT OK",( ):= Check_8 "OK"=
  • 164. Page 164 Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3)) Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1)) Weak axis Z-Z Status of effective length Effective length factor (Guidance of EC3) Buckling length of column (fixed end) Euler Buckling at y-y axis (EN1993-1-1,cl.6.3.1.2(1) Slenderness parameter at y-y axis (for class 1,2 and 3 cross-section) (EN1993-1-1,cl.6.3.1.3(1) Check for X bracing (EN1998-1-1,cl.6.7.3(4)) Check for X bracing (EN1998-1-1,cl.6.7.3(1)) Type of the section Nb.Rd.y χy A⋅ fy⋅ γ M1 634.758kN⋅=:= Check_9 if NEd Nb.Rd.y "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_9 "OK"= Effective_Length "Pinned Pinned":= kz 0.7 Effective_Length "Fixed Fixed"if 0.85 Effective_Length "Partial restraint"if 0.85 Effective_Length " Pinned Fixed"if 1 Effective_Length "Pinned Pinned"if 1=:= Lcrz kzhc 5.831m=:= Ncrz Es Izz⋅ π 2 ⋅ Lcrz 2 748.568kN⋅=:= λz A fy⋅ Ncrz 1.564=:= Check_10 if Ns 3≥ "Consider limitation (As EC8)", "Ignorelimitation (As EC3)",( ):= Check_10 "Consider limitation (As EC8)"= Check_11 if 1.3 λz< 2< "OK", "NOT OK",( ):= Check_11 "OK"= Section "Hot finished":=
  • 165. Page 165 Buckling curve (EN1993-1-1,table 6.2) Value to determine the reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ (EN1993-1-1,cl.6.3.1.2(1)) Reduction factor χ check Design buklcing resistance (EN1993-1-1,cl.6.3.1.1(3)) Buckling resistance of compression member check (EN1993-1-1,cl.6.3.1.1(1)) Lateral torsional buckling check (cl.6.3.2) Effective length factor, k (SN003a-EN-EU) Factor for end warping, kw (SN003a-EN-EU) Ratio of the smaller and larger moment Coefficient factor C1 (SN003a-EN-EU) Buckling_curve "a" Section "Hot finished"if "c" Section "Cold formed"if := Buckling_curve "a"= αz 0.21 Buckling_curve "a"if 0.49 Buckling_curve "c"if := αz 0.21= φ z 0.5 1 αz λz 0.2−( )⋅+ λz 2 +⎡ ⎣ ⎤ ⎦⋅ 1.866=:= χz 1 φ z φ z 2 λz 2 −+ 0.347=:= Check_12 if χz 1.0≤ "OK", "NOT OK",( ):= Check_12 "OK"= Nb.Rd.z χz A⋅ fy⋅ γ M1 634.758kN⋅=:= Check_13 if NEd Nb.Rd.z "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_13 "OK"= kz 1= kw 1.0:= ψ MEd.y2 MEd.y1 0.247=:= C1 1.88 1.40ψ− 0.52ψ 2 + 1.566=:=
  • 166. Page 166 Coefficient factor C1 check (SN003a-EN-EU) Coefficient factor C2 (SN003a-EN-EU) Distance between the point of load application and the shear centre Elastic critical moment for lateral torsional buckling (SN003a-EN-EU) Imperfection factor for lateral torsional CHS sections (EN1993-1-1,table 6.3) Non dimensional slenderness (EN1993-1-1,cl.6.3.2.2(1)) Value to determine the reduction factor (EN1993-1-1,cl.6.3.2.2(1)) Reduction factor for lateral-torsional buckling (EN1993-1-1,cl.6.3.2.2(1)) Parameter λ LTO (EN1993-1-1,cl.6.3.2.3(1)) Design buckling resistance moment (EN1993-1-1,cl.6.3.2.1(3)) Check_14 if C1 2.7≤ "OK", "NOT OK",( ):= Check_14 "OK"= C2 1.554:= zg 0m:= Mcr C1 π 2 Es⋅ Izz⋅ Lcrz( )2 ⋅ kz kw ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 Iw Izz ⋅ Lcrz( )2 G It⋅ π 2 Es Izz⋅ + C2 zg⋅( )2 +⋅ C2 zg⋅− 1.636 10 3 × kN m⋅⋅=:= αLT 0.76:= λLT Wpl.y fy⋅ Mcr 0.21=:= φ LT 0.5 1 αLT λLT 0.2−( )⋅+ λLT 2 +⎡ ⎣ ⎤ ⎦⋅ 0.526=:= χLT 1 φ LT φ LT 2 λLT 2 −+ 0.992=:= Check_15 if χLT 1≤ χLT 1 λLT 2 ≤∧ "OK", "NOT OK",⎛⎜ ⎜ ⎝ ⎞⎟ ⎟ ⎠ := Check_15 "OK"= λLTO 0.4:= Mb.Rd χLT Wpl.y⋅ fy γ M1 ⋅ 71.389kN m⋅⋅=:= Check_16 if MEd.y Mb.Rd 1≤ "OK", "NOT OK", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ :=
  • 167. Page 167 Check if the lateral torsional buckling be ignored (EN1993-1-1,cl.6.3.2.2(4)) Combine bending and axial compression cl.6.3.3 Moments due to the shift of the centroidal axis for class sections 1,2 & 3 (EN1993-1-1,cl.6.3.3(4)/table 6.7) Characteristic resistance to normal force of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7) Characteristic moment resistance of the critical cross-section (EN1993-1-1,cl.6.3.3(4)/table 6.7) Ratio of end moments (EN1993-1-1,Table B2) Equivalent uniform moment factor Equivalent uniform moment factor Check_16 "OK"= Check_17 if λLT λLTO< MEd.y Mcr λLTO 2 <∧ "Ignored torsional buckling effects", "Consider torsional buckling effects", ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ := Check_17 "Ignored torsional buckling effects"= ΔM Ed.z 0:= ΔM Ed.y 0:= NRk fy A⋅ 1.83 10 3 × kN⋅=:= My.Rk fy Wpl.y⋅ 71.94kN m⋅⋅=:= Mz.Rk fy Wpl.z⋅ 71.94kN m⋅⋅=:= ψy MEd.y1 MEd.y2 1− MEd.y1 MEd.y2 ≤ 1≤if MEd.y2 MEd.y1 1− MEd.y2 MEd.y1 ≤ 1≤if := ψz MEd.z1 MEd.z2 1− MEd.z1 MEd.z2 ≤ 1≤if MEd.z2 MEd.z1 1− MEd.z2 MEd.z1 ≤ 1≤if := Cmy 0.6 0.4 ψy⋅+ 0.699=:= Cmz 0.6 0.4 ψz⋅+ 0.725=:= kyy min Cmy 1 λy 0.2−( ) NEd χy NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmy 1 0.8 NEd χy NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ 1.018=:=
  • 168. Page 168 Interaction factors (EN1993-1-1,table B.1&B.2) EN1993-1-1,Equation 6.61 Unity factor EN1993-1-1,Equation 6.62 Unity factor kzz min Cmz 1 2λz 0.6−( ) NEd χz NRk γ M1 ⋅ ⋅+ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ ⋅ ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Cmz 1 1.4 NEd χz NRk γ M1 ⋅ ⋅+ ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ ⋅, ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ 1.303=:= kyz 0.6kzz 0.782=:= kzy 0.6kyy 0.611=:= Check_18 if NEd χy NRk⋅ γ M1 kyy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kyz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ := NEd χy NRk⋅ γ M1 kyy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kyz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 0.595= Check_18 "OK"= Check_19 if NEd χz NRk⋅ γ M1 kzy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kzz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 1.0≤ "OK", "NOT OK", ⎛ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎠ := NEd χz NRk⋅ γ M1 kzy MEd.y ΔM Ed.y+ χLT My.Rk γ M1 ⋅ ⋅+ kzz MEd.z ΔM Ed.z+ Mz.Rk γ M1 ⋅+ 0.584= Check_19 "OK"=
  • 169. Page 169 Eurocode 8 requirements Yield resistance (EN1998-1-1,cl.6.7.3(5)) Yield resistance check (EN1998-1-1,cl.6.7.3(5)) Check omega factor (EN1998-1-1,cl.6.7.3(8)) Axial force at storey 3 Axial force at storey 2 Area of steel section (RHS 100X100X10) Design plastic resistance of the cross section Storey 3: RHS 100X100X10 (EN1993-1-1,cl.6.2.3(2a)) Omega factor Omega factor Omega factor Minimum omega Minimum omega Check Ω factor (EN1998-1-1,cl.6.7.3(8)) Check_20 if NEd Npl.Rd≤ "OK", "NOT OK",( ):= Check_20 "OK"= NEd.3 162.34kN:= NEd.2 317.56kN:= A 3600mm 2 := Npl.Rd.3 0.5A fy⋅ γ M0 495 kN⋅=:= Ωstorey1 Npl.Rd NEd 2.529=:= Ωstorey2 Npl.Rd NEd.2 2.882=:= Ωstorey3 Npl.Rd.3 NEd.3 3.049=:= Ωmin min Ωstorey1 Ωstorey2, Ωstorey3,( ):= Ωmin 2.529= Ωmax max Ωstorey1 Ωstorey2, Ωstorey3,( ):= Ωmax 3.049= Check_21 if Ωmax 1.25Ωmin≤ "OK", "NOT OK",( ):= Check_21 "OK"=
  • 170. Page 170 10.0 Modal response spectrum analysis 10.1 Set the analysis options 1. ETABS: Analyze > Set analysis Options Calculate the number of modes: Figure 10.1: Set the modal analysis parameters
  • 171. Page 171 10.2 Evaluate the analysis results of the structure according to the modal analysis requirements 2. ETABS: Display > Show Tables Figure 10.2: Modal response spectrum results
  • 172. Page 172 10.2.1 Assess the modal analysis results based on the EN1998 The requirements of the sum of effective modal masses for the modes taken into account amounts to at least 90% of the total mass of the structure is satisfied (EN1998-1- 1,cl.4.3.3.3.1(3)).
  • 173. Page 173 Effective mass of mode 6 = 97% > 90% “OK” 11.0 Second order effects (P – Δ effects) according to EN1998-1-1,cl.4.4.2.2 The criterion for taking into account the second order effect is based on the interstorey drift sensitivity coefficient θ, which is define with equation (EN 1998-1-1,cl.4.4.2.2(2)). Θ = P!"! ∙ d! V!"! ∙ h dr: is the interstorey drift h: is the storey height. Vtot: is the total seismic storey shear. Ptot: is the total gravity load at and above storey considered in the seismic design situation (G+0.3Q). Table 11.1: Consequences of value of P-Δ coefficient θ on the analysis θ≤0,1 No need to consider P-Δ effects 0,1≤θ≤0,2 P-Δ effects may be taken into account approximately by amplifying the effects of the seismic actions by ! !!! 0,2≤θ≤0,3 P-Δ effects must be accounted for by an analysis including second order effects explicity θ≥0,3 Not permitted Important note: If the above expression is not satisfied, second order effects, should be enable in ETABS. ETABS: Analyze > Set analysis option > > Set the parameters
  • 174. Page 174 11.1 Displacement calculation according to EN1998-1-1,cl.4.4.2.2 d! = q ∗ d! ds : is the displacement of a point of the structural system induced by the design seismic action. qd : is the displacement behaviour factor, assumed equal to q unless otherwise specified. de : is the displacement of the same point of the structural system, as determined by a linear analysis based on the design response spectrum. 11.2 Interstorey drift Interstorey drift is the design interstorey drift, evaluated as the difference of the average lateral displacements ds at the top and bottom of the storey under consideration and calculated in accordance with EN1993-1-1,cl.4.3.4. d! = d!.!"# − d!.!"# 2
  • 175. Page 175 11.3 Calculation of second order effect using ETABS 3. ETABS: Run the model 4. ETABS: Display > Show tables Select the design combinations Static load case combination (include wind load) STATIC 2. 1.35DL + 1.5LL + 0.75WINDX STATIC 3. 1.35DL + 1.5LL - 0.75WINDX STATIC 4. 1.35DL + 1.5LL + 0.75WINDY STATIC 5. 1.35DL + 1.5LL - 0.75WINDY STATIC 6. 1.35DL + 1.5WINDX + 1.05LL STATIC 7. 1.35DL - 1.5WINDX – 1.05LL STATIC 8. 1.35DL + 1.5WINDY + 1.05LL STATIC 9. 1.35DL - 1.5WINDY – 1.05LL Seismic load case combination SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX
  • 176. Page 176 Figure 11.1: Displacement due to lateral load 11.3.1 Interstorey drift displacement For floor with the non use of diaphragm, the maximum displacement can be found in this table For floor with the use of diaphragm, the maximum displacement can be found in this table
  • 177. Page 177 Table 11.2: Displacement due to lateral load Storey no. Max Displacement at X Max Displacement at Y Storey 3 Storey 2 Storey 1 Sort smallest to largest in order to find the maximum displacement or Sort largest to smallest in order to find the maximum displacement Consider the maximum value Do this process for all storeys separately as showing below
  • 178. Page 178 Table 11.3: Drift displacement Storey   Displacement   Direction  x   dx.e                             (mm)   Displacement   Direction  y   dy.e                               (mm)   Behaviour   factor  q   Displacement   dsx                                   (mm)       cl.4.4.2.2   Displacement   dsy                                   (mm)     cl.4.4.2.2   Interstorey   drift                           drx                       (mm)   Interstorey   drift                           dry                       (mm)   Storey  3   11.742   11.7452   4   46.968   46.9808   6.7754   6.7776   Storey  2   8.3543   8.3564   4   33.4172   33.4256   9.0274   9.0296   Storey  1   3.8406   3.8416   4   15.3624   15.3664   7.6812   7.6832   d!" = q ∗ d!" d!" = q ∗ d!" d!" = d!".!"# − d!".!"# 2 d!" = d!".!"# − d!".!"# 2 11.3.2 Total gravity load Ptot ETABS: Display > Show tables Select the design combinations Static load case combination STATIC 10. DL + 0.3LL
  • 179. Page 179 Export the results in Excel sheet Filter the value of the bottom storey
  • 180. Page 180 Story   Load   Loc   P   STORY3   STATIC10   Bottom   1402.76   STORY2   STATIC10   Bottom   2804.93   STORY1   STATIC10   Bottom   4207.11   11.3.2 Total seismic storey shear Vtot ETABS: Display > Show tables Record the total gravity load (G+ψEiQ) of each storey Select the design combinations Seismic load case combination SEISMIC 1. DL + 0.3LL + EQX + 0.3EQY SEISMIC 2. DL + 0.3LL + EQX – 0.3EQY SEISMIC 3. DL + 0.3LL - EQX + 0.3EQY SEISMIC 4. DL + 0.3LL - EQX – 0.3EQY SEISMIC 5. DL + 0.3LL + EQY + 0.3EQX SEISMIC 6. DL + 0.3LL + EQY – 0.3EQX SEISMIC 7. DL + 0.3LL - EQY + 0.3EQX SEISMIC 8. DL + 0.3LL - EQY – 0.3EQX
  • 181. Page 181 Export the results in Excel sheet Sort smallest to largest in order to find the maximum shear force or Sort largest to smallest in order to find the maximum shear force Consider the worst load combination Do this process for all storeys separately as showing below
  • 182. Page 182 Story   Load   Loc   P   VX   STORY1   SEISMIC1  MAX   Bottom   4207.11   663.91   STORY2   SEISMIC1  MAX   Bottom   2804.93   550.8   STORY3   SEISMIC1  MAX   Bottom   1402.76   330   Repeat the above procedure in order to obtain the Vtot at Y-direction Story   Load   Loc   P   VY   STORY1   SEISMIC5  MAX   Bottom   4207.11   663.91   STORY2   SEISMIC5  MAX   Bottom   2804.93   550.8   STORY3   SEISMIC5  MAX   Bottom   1402.76   330   Filter the value of the bottom storey Filter the values using the worst case combination Record the total seismic shear of each storey for Vtot at X-direction
  • 183. Page 183 Table 11.4: Second order effects check (EN1993-1-1,cl.4.4.2.2(2)) Storey   Displacement   Direction  x   dx.e                             (mm)   Displacement   Direction  y   dy.e                               (mm)   Behaviour   factor  q   Displacement   dsx                                   (mm)       cl.4.4.2.2   Displacement   dsy                                   (mm)     cl.4.4.2.2   Interstorey   drift                           drx                       (mm)   Interstorey   drift                           dry                       (mm)   Storey  3   11.742   11.7452   4   46.968   46.9808   6.7754   6.7776   Storey  2   8.3543   8.3564   4   33.4172   33.4256   9.0274   9.0296   Storey  1   3.8406   3.8416   4   15.3624   15.3664   7.6812   7.6832   Total   gravity  load               Ptot                     (kN)   Total   seismic   storey  shear   Vtotx  (kN)   Total   seismic   storey  shear   Vtoty  (kN)   Height  of   each   storey   (mm)   Interstorey  drift   sensitivity  coefficient  θ   at                                                                                           X  direction   Interstorey  drift   sensitivity  coefficient  θ   at                                                                             Y  direction   663.91   663.91   663.91   3000   OK   OK   550.8   550.8   550.8   3000   OK   OK   330   330   330   3000   OK   OK           Θ = P!"! ∙ d!" V!"!# ∙ h ≤ 0.10 Θ = P!"! ∙ d!" V!"!# ∙ h ≤ 0.10
  • 184. Page 184 12.0 Damage limitation according to EN1998-1-1,cl.4.4.3 The “damage limitation requirement” is considered to have been satisfied, if, under a seismic action having a larger probability of occurrence than the design seismic action corresponding to the “no-collapse requirement” in accordance with 2.1(1)P and 3.2.1(3), the interstorey drifts are limited in accordance with 4.4.3.2. The damage limitation requirements should be verified in terms of the interstorey drift (dr) (EN 1998-1-1,cl.4.4.3.2) using the equation below: d! ∙ v ≤ 0.005 ∙ h     dr: is the difference of the average lateral displacement ds in CM at the top and bottom of storey. v: is the reduction factor which takes into account the lower return period of the seismic action. h: is the storey height Table 12.1: Damage limitation (EN1998-1-1,cl.4.4.3) For non-structural elements of brittle material attached to the structure drv≤0.005h For building having ductile non structural elements drv≤0.0075h For building having non-structural elements fixed in a way so as not to interfere with structural deformation drv≤0.010h Table 12.2: Reduction factor of limitation to interstorey drift (CYA NA EN1998-1- 1,cl.NA.2.15) Importance class Reduction factor v I 0.5 II 0.5 III 0.4 IV 0.4
  • 185. Page 185 12.1 Calculation of damage limitation Table 12.3: Interstorey drift (see table 11.3) Storey   Displacement   Direction  x   dx.e                             (mm)   Displacement   Direction  y   dy.e                               (mm)   Behaviour   factor  q   Displacement   dsx                                   (mm)       cl.4.4.2.2   Displacement   dsy                                   (mm)     cl.4.4.2.2   Interstorey   drift                           drx                       (mm)   Interstorey   drift                           dry                       (mm)   Storey  3   11.742   11.7452   4   46.968   46.9808   6.7754   6.7776   Storey  2   8.3543   8.3564   4   33.4172   33.4256   9.0274   9.0296   Storey  1   3.8406   3.8416   4   15.3624   15.3664   7.6812   7.6832   Reduction   factor                             v                                     cl.4.4.3.2(2)   Heigh  of   each   storey   (mm)   Damage  limitation   check                                                   X-­‐direction   Damage  limitation   check                                                   Y-­‐direction   0.4   3000   OK   OK   0.4   3000   OK   OK   0.4   3000   OK   OK       d! ∙ v ≤ 0.005 ∙ h   d! ∙ v ≤ 0.005 ∙ h  
  • 186. Page 186 ANNEX - A ANNEX A.1 - Assumptions made in the design algorithm (Manual of ETABS – EC3 & EC8) 1. Load combination • The automated load combinations are based on the STR ultimate limit states and the characteristic serviceability limit states. 2. Axial force check • Tubular sections are assumed to be hot finished for selecting the appropriate buckling curve from EC3 Table 6.2. This is non conservative if cold formed sections are used. 3. Bending moment check • The load is assumed to be applied at the shear center for the calculation of the elastic critical moment. • Any eccentric moment due to load applied at other locations is not automatically accounted for. 4. Shear Force Check • Plastic design is assumed such that Vc,Rd is calculated in accordance with EC3 6.2.6(2). • The shear area, Av is taken from the input frame section property, rather than using the equations defined in EC3 6.2.6(3). • Transverse stiffeners exist only at the supports and create a non-rigid end post for the shear buckling check. No intermediate stiffeners are considered.
  • 187. Page 187 • The contribution from the flanges is conservatively ignored for the shear buckling capacity. 5. Combined Forces Check • The interaction of bending and axial force is checked in accordance with EC3 6.2.1(7), which may be conservative compared to EC3 6.2.9. • The calculation of the equivalent uniform moment factors, Cm, assumes uniform loading, which is conservative. A1.1:Limitation made in the design algorithm (Manual of ETABS – EC3&EC8) 6. General • Class 4 sections are not designed (EC3 5.5) and should be considered using other methods. • The effects of torsion are not considered in the design (EC3 6.2.7) and should be considered using other methods. 7. Axial Force Check • The net area is not determined automatically. This can be specified on a member-by- member basis using the Net Area to Total Area Ratio overwrite. • The axial buckling check does not consider torsional or torsional-flexural buckling. 8. Combined Forces Check • The effect of high shear is checked only for Class 1 or 2 I-sections when combined with bending. Other section shapes and classes require independent checks to be carried out.
  • 188. Page 188 ANNEX –B: Steel design flowcharts w1 = Initial part of the deflection under permanent loads wc = Precamber in the unloaded structural member w2 = due to Permanent load w3 = due to Variable load STEEL MEMBERS (CYS NA EN1993-1-1,table NA.1) Vertical deflection Limits wmax Cantilevers L/180 Beams carrying plaster or other brittle finish L/360 Other beams (except purlin and sheeting rails) L/250 Purlins and sheeting rails To suit cladding General use L/300 Vertical deflection (EN1993-1-1,cl.7.2.1) BASIS OF STRUCTURAL DESIGN (EN1990:2002) u = Overall horizontal displacement over the building height H ui = Horizontal displacement over height Hi STEEL MEMBERS (CYS NA EN1993-1-1,table NA.2) Horizontal deflection Limits wmax Top of columns in single storey buildings, exept portal frames H/300 Columns in portal frame buildings, not supporting crane runways To suit cladding In each storey of the building with more than one storey Storey height/300 On the multi-storey building as a whole Building height/500 Horizontal deflection (EN1993-1-1,cl.7.2.2)
  • 189. Page 189 STEEL MEMBERS (CYS NA EN1993-1-1,table NA.3) Design situation Limits natural frequency Floors over which people walk regularly 5Hz Floor which is jumped or danced on in a rhythmical manner 9Hz Dynamic effects (vibration of floors) (EN1993-1-1,cl.7.2.3) Effective length (Design Guidance of EC3) Figure 1: Effective length columns (Design Guidance of EC3) End restraints Fixed/Fixed Partial restrain in direction Pined/Fixed Pinned/Pined Free in position/Fixed Free/Fixed Effective length factor, ky,z 0.7L 0.85L 0.85L 1.0L 1.2L 2.0L
  • 190. Page 190 𝑀!.!" = 𝑊!",! 𝑓! 𝛾!! 𝑀!.!" = 𝑊!",!"# 𝑓! 𝛾!! Bending resistance (EN1993-1-1,cl. 6.2.5) Class 1 or 2 Class 3 𝑴 𝑬𝒅 ≤ 𝑴 𝒄.𝑹𝒅 Compression resistance (EN1993-1-1,cl. 6.2.4) Class 1 or 2and3 𝛮!.!" = 𝛢𝑓! 𝛾!! 𝑵 𝑬𝒅 ≤ 𝑵 𝒄,𝑹𝒅 Fastener holes in tension flange may be ignored if: 𝑨 𝒇,𝒏𝒆𝒕 𝟎. 𝟗𝒇 𝒖/𝜸 𝑴𝟐 ≥ 𝑨 𝒇 𝒇 𝒚/𝜸 𝑴𝟎
  • 191. Page 191 Shear resistance (EN1993-1-1,cl. 6.2.6) Rolled I and H sections (load parallel to web) CHS 𝐴! = 𝐴 − 2𝑏𝑡! + 𝑡! + 2𝑟 𝑡! 𝐴! = 2𝐴/𝜋 RHS 𝐴! = 𝐴ℎ/(𝑏 + ℎ)Load parallel to depth 𝐴! = 𝐴𝑏/(𝑏 + ℎ)Load parallel to width 𝑽 𝑬𝒅 ≤ 𝑽 𝒄,𝑹𝒅 𝐴! = ℎ! ∙ 𝑡! 𝐴!/𝐴! ≥ 0.6 𝜏!" = 𝑉!" 𝐴! 𝑉!,!" = 𝜏!" 𝑓!/( 3𝛾!!) Elastic design 𝑽 𝑬𝒅 𝑽 𝒄.𝑹𝒅 ≤ 𝟏. 𝟎 Plastic design 𝑉!".!" = 𝐴!(𝑓!/ 3) 𝛾!! Rolled C channel sections (load parallel to web) but ≥𝜂ℎ! 𝑡! 𝜂= 1.0 (conservative value) Ignore Shear buckling resistance for webs without intermediate stiffeners 𝒉 𝒘 𝒕 𝒘 > 72 𝜺 𝜼
  • 192. Page 192 Combine Bending and shear (EN1993-1-1,cl. 6.2.8) Shear design resistanceNO Reduction of resistances (effect on Mc,Rd) YES NO Reduction of resistances (no effect on Mc,Rd)𝑉!" ≤ 0.5 ∙ 𝑉!".!" 𝜌 = 1 − 2𝑉!" 𝑉!",!" − 1 ! 𝑉!".!" = 𝐴!(𝑓!/ 3) 𝛾!! 𝑓!" = 1 − 𝜌 𝑓! Reduced design plastic resistance moment 𝐴! = ℎ! 𝑡! 𝑴 𝒚.𝑽,𝑹𝒅 = (𝑾 𝒑𝒍,𝒚 − 𝝆𝑨 𝒘 𝟐 𝟒𝒕 𝒘 )𝒇 𝒚 𝜸 𝑴𝟎      ≤ 𝑴 𝒚,𝒄,𝑹𝒅 If torsion present: 𝜌 = 1 − 2𝑉!" 𝑉!",!,!" − 1 ! For an I and H sections 𝑉!",!,!" = 1 − 𝜏!,!" 1.25 𝑓!/ 3 /𝛾!! 𝑉!",!"
  • 193. Page 193 Bending & Axial force (EN1993-1-1,cl. 6.2.9) Doubly symmetrical I and H sections Z-Z axis Doubly symmetrical I and H sections Y-Y axis 𝑁!" ≤ 0.5 ∙ ℎ! ∙ 𝑡! ∙ 𝑓! 𝛾!! 𝑁!" ≤ 0.25𝑁!".!" 𝑀!,!,!" = 𝑀!",!,!"(1 − 𝑛)/(1 − 0,5𝑎) MN,y,Rd≤ Mpl,y,Rd 𝑛 = 𝑁!" 𝑁!",!" 𝑎 = 𝐴 − 2𝑏𝑡! 𝐴 ≤ 0,5 𝑁!" ≤ ℎ! ∙ 𝑡! ∙ 𝑓! 𝛾!! 𝑛 = 𝑁!" 𝑁!",!" 𝑎 = 𝐴 − 2𝑏𝑡! 𝐴 ≤ 0,5 𝑀!,!,!" = 𝑀!",!,!" 1 − 𝑛 − 𝑎 1 − 𝑎 ! 𝑛 > 𝑎 𝑀!,!,!" = 𝑀!",!,!" 𝑛 < 𝑎 NO YES Ignored axial force Consider axial force NO YES Ignored axial force Consider axial force Class 1 or 2 𝑵 𝑬𝒅 𝑵 𝑹𝒅 + 𝑴 𝒚,𝑬𝒅 𝑴 𝒚,𝑹𝒅 + 𝑴 𝒛,𝑬𝒅 𝑴 𝒛,𝑹𝒅 ≤ 𝟏. 𝟎
  • 194. Page 194 For RHS Y-Y axis Z-Z axis 𝑁!" ≤ ℎ! ∙ 𝑡! ∙ 𝑓! 𝛾!! NO YES Ignored axial force Consider axial force Hollow section Welded box section 𝑎! = (𝐴 − 2𝑏𝑡)/𝐴) ≤ 0.5 𝑎! = (𝐴 − 2ℎ𝑡)/𝐴) ≤ 0.5 𝑎! = (𝐴 − 2𝑏𝑡!)/𝐴) ≤ 0.5 𝑎! = (𝐴 − 2ℎ𝑡!)/𝐴) ≤ 0.5 𝑀!,!,!" = 𝑀!",!,!" 1 − 𝑛 1 − 0.5𝑎! ≤ 𝑀!",!,!" 𝑀!,!,!" = 𝑀!",!,!" 1 − 𝑛 1 − 0.5𝑎! ≤ 𝑀!",!,!" Bending & Axial force (EN1993-1-1,cl. 6.2.9) Class 1 or 2 𝑴 𝒚,𝑬𝒅 𝑴 𝑵,𝒚,𝑹𝒅 𝒂 + 𝑴 𝒛,𝑬𝒅 𝑴 𝑵,𝒛,𝑹𝒅 𝜷 ≤ 𝟏. 𝟎 I and H section CHS RHS 𝑎 = 2 𝛽 = 5𝑛   ≥ 1 𝑛 = 𝑁!"/𝑁!",!" 𝑎 = 2 𝛽 = 5𝑛   ≥ 1 𝑛 = 𝑁!"/𝑁!",!" 𝑎 = 𝛽 = 1.66 1 − 1.13𝑛! but𝑎 = 𝛽 ≤ 6
  • 195. Page 195 Buckling resistance in compression (EN1993-1-1,cl. 6.3.1.1) 𝑁!,!" = 𝜒𝐴𝑓! 𝛾!!) Class 1 or 2and3 𝑵 𝑬𝒅 ≤ 𝑵 𝒃,𝑹𝒅 Φ = 0,5 1 + 𝑎 𝜆 − 0,2 + 𝜆! λ = 𝐴𝑓! 𝑁!" Buckling curve ao a b c d Imperfection factor a 0,13 0,21 0,34 0,49 0,76 χ = 1 Φ + Φ! − λ! ≤ 𝜒 ≤ 1,0 Slenderness for flexural buckling 𝑁!" = !!!" !! for ideal strut Cross-section Limits Buckling about axis Buckling curve Rolled I sections h/b>1.2 tf≤40mm y-y a z-z b 40mm<tf≤100mm y-y b z-z c h/b≤1.2 tf≤ 100mm y-y b z-z c tf> 100mm y-y d z-z d U-T and solid section any C L-sections any b Hollow sections Hot finished any a Cold formed any c 𝜆 ≤ 0.2 𝑁!"/𝑁!" ≤ 0.04 NO (consider buckling effects) YES (ignored buckling effects)
  • 196. Page 196 Buckling resistance in bending (EN1993-1-1,cl. 6.3.2) 𝑀!,!" = 𝜒!" 𝑊! 𝑓! 𝛾!! Class 1 or 2and3 𝑴 𝑬𝒅 𝑴 𝒃.𝑹𝒅 ≤ 𝟏. 𝟎 λ!" = 𝑊! 𝑓! 𝑀!" Slenderness for flexural buckling λ! = 𝜋 𝐸 𝑓! = 93,9𝜀𝜀 = 235 𝑓! Class 1 or 2 Class 3 Wy=Wpl,y Wy=Wel,y χ!" = 1 Φ!" + Φ!" ! − λ!" ! ≤ 𝜒!" ≤ 1,0 Φ!" = 0,5 1 + 𝑎!" 𝜆!" − 0,2 + 𝜆!" ! Buckling curve a b c d Imperfection factor aLT 0,21 0,34 0,49 0,76 Cross-section Limits Buckling curve Rolled I-sections h/b≤2 h/b>2 a b Welded I-sections h/b≤2 h/b>2 c d Other cross-sections - d See following pages for calculation of Mcr and λL
  • 197. Page 197 Calculation process of Mcr (www.access-steel.com - Document SN003a&b) 𝛭!" = 𝐶! 𝜋! 𝐸𝐼! (𝑘𝐿!")! 𝑘 𝑘! ! 𝐼! 𝐼! + (𝑘𝐿!")! 𝐺𝐼! 𝜋! 𝐸𝐼! + 𝐶! 𝑧! ! −   𝐶! 𝑧! Step 1: Define the properties of member Term Description Values L Distance between point of lateral restraint Lcr=kl E Young’s modulus 210000 N/mm2 G Shear modulus 80770 N/mm2 Iz Second moment of area about the weak axis From section table It Torsion constant Iw Warping constant k Effective length factor 1.0 unless justified otherwise kw Factor for end warping 1.0 unless justified otherwise zg Distance between the point of load application and the shear centre +/-(h/2) or 0 if the load is applied through the shear centre Step 2: Calculate the coefficient C1 and C2 Loading and support conditions C 2 Ψ=M1/M2 C1 Pinned UDL 0,454 1.00 1,00 Fixed UDL 1,554 0.75 1.14 Pinned central P 0,630 0.50 1,31 Fixed central P 1,645 0.25 1,62 0 1,77 -0.25 2,05 -0.50 2,33 -0.75 2,57 -1.00 2,55 Pinned UDL 1,127 Pinned, central P 1,348 𝛭!" = 𝜋! 𝐸𝐼! 𝐿!" ! 𝐼! 𝐼! + 𝐿!" ! 𝐺𝐼! 𝜋! 𝐸𝐼! !.! Point of application of the load is through the shear centre YES zg=0 NO zg
  • 198. Page 198 Alternative method to calculate the Mcr and λLT 𝝀 𝑳𝑻 = 𝟏 𝑪 𝟏 𝑼𝑽𝝀 𝒛 𝜷 𝒘 Non-dimensional slenderness Simply supported rolled I, H and C section ! !! = 1.0(conservative value) 𝑈 = 0.9(conservative value) 𝑉 = 1.0 (conservative value) 𝜆! = 𝑘𝐿 𝑖! K=1.0 for beams k=1.0 for free cantilever k=0.9 for lateral restraint to top flange k=0.8 for torsional restraint k=0.7 for lateral and torsional restraint βw = 1.0 (conservative value)
  • 199. Page 199 Member combined bending and axial compression (EN1993-1-1,cl. 6.3.3) 𝑵 𝑬𝒅 𝝌 𝒚 𝑵 𝑹𝒌 𝜸 𝑴𝟏 + 𝒌 𝒚𝒚 𝑴 𝒚,𝑬𝒅 𝝌 𝑳𝑻 𝑴 𝒚,𝑹𝒌 𝜸 𝑴𝟏 + 𝒌 𝒚𝒛 𝑴 𝒛,𝑬𝒅 𝑴 𝒛,𝑹𝒌 𝜸 𝑴𝟏 ≤ 𝟏. 𝟎 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌 𝜸 𝑴𝟏 + 𝒌 𝒛𝒚 𝑴 𝒚,𝑬𝒅 𝝌 𝑳𝑻 𝑴 𝒚,𝑹𝒌 𝜸 𝑴𝟏 + 𝒌 𝒛𝒛 𝑴 𝒛,𝑬𝒅 𝑴 𝒛,𝑹𝒌 𝜸 𝑴𝟏 ≤ 𝟏. 𝟎 Class 1 and 2 Class 3 Method 2:Interaction factor kij for members not susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.1) Interaction factors Type of sections Plastic cross-sectional properties Class 1 and 2 Elastic cross-sectional properties Class 3 kyy I-sections RHS-sections 𝑪 𝒎𝒚 𝟏 + 𝝀 𝒚 − 𝟎. 𝟐 𝑵 𝑬𝒅 𝝌 𝒚 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≤ 𝑪 𝒎𝒚 𝟏 + 𝟎. 𝟖 𝑵 𝑬𝒅 𝝌 𝒚 𝑵 𝑹𝒌/𝜸 𝑴𝟏 𝑪 𝒎𝒚 𝟏 + 𝟎. 𝟔𝝀 𝒚 𝑵 𝑬𝒅 𝝌 𝒚 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≤ 𝑪 𝒎𝒚 𝟏 + 𝟎. 𝟔 𝑵 𝑬𝒅 𝝌 𝒚 𝑵 𝑹𝒌/𝜸 𝑴𝟏 kyz I-sections RHS-sections 0.6kzz kzz kzy I-sections RHS-sections 0.6kyy 0.8kyy kzz I-sections 𝑪 𝒎𝒛 𝟏 + 𝟐𝝀 𝒛 − 𝟎. 𝟔 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≤ 𝑪 𝒎𝒚 𝟏 + 𝟏. 𝟏𝟒 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 𝑪 𝒎𝒛 𝟏 + 𝟎. 𝟔𝝀 𝒛 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≤ 𝑪 𝒎𝒚 𝟏 + 𝟎. 𝟔 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 RHS-sections 𝑪 𝒎𝒛 𝟏 + 𝝀 𝒛 − 𝟎. 𝟐 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≤ 𝑪 𝒎𝒛 𝟏 + 𝟎. 𝟖 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏
  • 200. Page 200 Method 2:Interaction factor kij for members susceptible to torsional deformations (Recommended by CYS NA EN 1993-1-1,cl.NA2.20 – Table B.2) Interaction factors Plastic cross-sectional properties Class 1 and 2 Elastic cross-sectional properties Class 3 kyy Kyy from Table B.1 Kyy from Table B.1 kyz Kyz from Table B.1 Kyz from Table B.1 kzz 𝟏 − 𝟎. 𝟏𝝀 𝒛 𝑪 𝒎𝑳𝑻 − 𝟎. 𝟐𝟓 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≥ 𝟏 − 𝟎. 𝟏 𝑪 𝒎𝑳𝑻 − 𝟎. 𝟐𝟓 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 for𝜆! < 0.4: 𝒌 𝒛𝒚 = 𝟎. 𝟔 + 𝝀 𝒛 ≤ 𝟏 − 𝟎. 𝟏𝝀 𝒛 𝑪 𝒎𝑳𝑻 − 𝟎. 𝟐𝟓 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 𝟏 − 𝟎. 𝟎𝟓𝝀 𝒛 𝑪 𝒎𝑳𝑻 − 𝟎. 𝟐𝟓 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏 ≥ 𝟏 − 𝟎. 𝟎𝟓 𝑪 𝒎𝑳𝑻 − 𝟎. 𝟐𝟓 𝑵 𝑬𝒅 𝝌 𝒛 𝑵 𝑹𝒌/𝜸 𝑴𝟏
  • 201. Page 201 Summary design of steel member in bending Choose yield strength of section, fy from table 3.1 in EN 1993-1-1 Get starinε from table 5.2 in EN 1993-1-1 Substitute the value of εinto the class limits in table 5.2 to work out the class of the flange and web Take the latest favourable class from the flange outstand, web in bending and web in compression results Use the required value of W for the defined class to work out Mc,Rd Cross-section Resistance check Design step Results fy ε Flange Class Web class Overall Section Class Mc,Rd Steel grade fy (N/mm2) Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80 S275 275 265 255 245 S355 355 345 335 325 𝜀 = 235 𝑓! fy 235 275 355 420 ε 1.00 0.92 0.81 0.75 Flange under compression: c=(b-tw-2r)/2 c/tf Web under pure bending: c=(h-2tf-2r) c/tw Mc,Rd = Mpl,Rd = Wpl,yfy/γM0 Class 1 & 2 Mc,Rd = Mel,Rd = Wel,minfy/γM0 Class 3 Mc,Rd = Weff,minfy/γM0 Class 4 Class 1 or 2 Class 3 Class 4
  • 202. Page 202 Summary design of steel member in shear Calculate the shear area of the section, Av Calculate the design plastic shear resistance, Vpl,Rd Shear resistance check Design step Results Av Vpl,Rd VEd≤Vc,Rd Steel grade fy (N/mm2) Nominal thickness of element t (mm) t≤16 16≤t≤40 40≤t≤63 63≤t≤80 S275 275 265 255 245 S355 355 345 335 325 𝑉!".!" = 𝐴!(𝑓!/ 3) 𝛾!!
  • 203. Page 203 Summary of buckling resistance in bending Calculate the design bending moment and shear Section classification Design step Results MEd &VEd Wy&fy Calculate critical length Lcr Calculate Critical moment Mcr Calculate non-dimensional slenderness λLT λLT Calculate imperfection factor αLT αLT Calculate reduction factor φLT φLT Calculate modified/reduction factor for lateral-torsional buckling χLTorχLT,mod χLTχLT,mod Buckling resistance check 𝑴 𝑬𝒅 𝑴 𝒃,𝑹𝒅 ≤ 𝟏. 𝟎 Calculate buckling resistance Mb,Rd Mb,Rd