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Dcr is 1893 Dcr is 1893 Document Transcript

  • Seismic FORCE ESTIMATION IS 1893-2002 18931893-2002 The material contained in this lecture handout is a property of Professors Sudhir K. Jain, C.V.R.Murty and Durgesh C. Rai of IIT Kanpur, and is for the sole and exclusive use of the participants enrolled in the short course on Seismic Design of RC Structures conducted at Ahmedabad during Nov 26-30, 2012. It is not to be sold, reproduced or generally distributed. Durgesh C. Rai Department of Civil Engineering, IIT Kanpur 1 2 Structure of Revised IS:1893 • Since 1984: – More information – More experience Detailed Provisions – Practical difficulties • IS 1893: From 2002 onwards… Part 1 Part 2 EQ Behaviour is different!! Part 3 Part 4 Part 5 :: General Provisions and Buildings :: Liquid Retaining Tanks – Elevated/Ground Supported :: Bridges and Retaining Walls :: Industrial and Stack-like Structures :: Dams and Embankments 4 IS:1893-2002 What does IS:1893 Cover? IS:1893 first published in 1962. Revised in 1966, 1970, 1975, 1984, and now in 2002. Beginning 2002, this code is being split into several parts Specifies Seismic Design Force Other seismic requirements for design, detailing and construction are covered in other codes e.g., IS:4326, IS:13920, ... For an earthquake-resistant structure, one has to follow IS:1893 together with seismic design and detailing codes. So that revisions can take place more frequently! Only Part 1 and 4 of the code has been published. 5 6 1
  • Coverage of Part 1 Major Changes General Provisions Since the code has been revised after a very long time (~18 years), there are many significant changes. Some of the philosophical changes are discussed in Foreword of the code. Applicable to all structures Provisions on Buildings To address the situation that other parts of the code are not yet released, Note on page 2 of the code says in the interim period, provisions of Part 1 will be read along with the relevant clauses of IS:1893-1984 for structures other than buildings This can be problematic. For instance, what value of R to use for overhead water tanks? 7 8 Zone Map Zone Map (contd…) 1962 and 1966 maps had seven zones (0 to VI) In 1967, Koyna earthquake (M6.5, about 200 killed) occurred in zone I of 1966 map In 1970 zone map revised: Latur (1993) earthquake (mag. 6.2, about 8000 deaths) in zone I! Revision of zone map in 2002 edition Zone I has been merged upwards into zone II. Zones O and VI dropped; only five zones Now only four zones: II, III, IV and V. No change in map in 1975 and 1984 editions 9 In the peninsular India, some parts of zone I and zone II are now in zone III. 10 Zone Map (contd…) Zone Map (contd…) Notice the location of Allahabad and Varanasi in the new zone map. There is an error and the locations of these two cities have been interchanged in the map. Varanasi should be in zone III and Allahabad in zone II. Also notice another error in the new zone map Location of Calcutta has been shown incorrectly in zone IV Calcutta is in fact in zone III Annex E of the code correctly lists Kolkata is in zone III. The Annex E of the code gives correct zones for these two cities 11 12 2
  • Preface Other Effects It is clear that the code is meant for normal structures, and For special structures, site-specific seismic design criteria should be evolved by the specialists. Read second para, page 3 Earthquakes can cause damage in a number of ways. For instance: Vibration of the structure: this induces inertia force on the structure By inertia force, we mean mass times acceleration Landslide triggered by earthquake Liquefaction of the founding strata Fire caused due to earthquake Flood caused by earthquake 13 14 Intensity versus Magnitude Other Effects (contd…) The code generally addresses only the first aspect: the inertia force on the structure. The engineer may need to also address other effects in certain cases. It is important that you understand the difference between Intensity and Magnitude Magnitude tells How big was the earthquake How much energy was released by earthquake Intensity tells How strong was the vibration at a location Depends on magnitude, distance, and local soil and geology Read more about magnitude and intensity at: http://www.nicee.org/EQTips/EQTip03.pdf 15 16 Seismic Hazard Shaking Intensity Last para on page 3 The criterion for seismic zones remains same as before Shaking intensity is commonly measured in terms of Modified Mercalli scale or MSK scale. Zone Area liable to shaking intensity II VI (and lower) III VII IV VIII V 17 See Annex. D of the code for MSK Intensity Scale There is a subtle change: Modified Mercalli intensity is replaced by MSK intensity! In practical terms, both scales are same. Hence, it does not really matter. IX 18 3
  • Zone Criterion Peak Ground Acceleration Our zone map is based on likely intensity. Maximum acceleration response of a rigid system (Zero Period Acceleration) is same as Peak Ground Acceleration (PGA). Hence, for very low values of period, acceleration spectrum tends to be equal to PGA. It does not address the question: how often such a shaking may take place. For example, say Area A experiences max intensity VIII every 50 years, Area B experiences max intensity VIII every 300 years Both will be placed in zone IV, even though area A has higher seismicity We should be able to read the value of PGA from an acceleration spectrum. Current trend world wide is to Specify the zones in terms of ground acceleration that has a certain probability of being exceeded in a given number of years. 19 20 Typical shape of acceleration spectrum Peak Ground Acceleration (contd…) 1.80 Average shape of acceleration response spectrum for 5% damping (Fig. on next slide) 1.60 Spectral Acceleration (g) 1.40 Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA There can be a stray peak in the ground motion; i.e., unusually large peak. Such a peak does not affect most of the response spectrum and needs to be ignored. Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11) 0.80 0.40 PGA = 0.6g 0.20 0.00 0.0 0.5 1.0 1.5 2.0 2.5 Per iod (sec) 3.0 3.5 4.0 4.5 •Typical shape of acceleration response spectrum •Spectral acceleration at zero period (T=0) gives PGA •Value at 0.1-0.3 sec is ~ 2.5 times PGA value 22 Earthquake Level Earthquake Level (contd…) Maximum Credible Earthquake (MCE): Other terms used in literature which are somewhat similar to max credible EQ: Largest reasonably conceivable earthquake that appears possible along a recognized fault (or within a tectonic province). It is generally an upper bound of expected magnitude. Irrespective of return period of the earthquake which may range from say 100 years to 10,000 years. Usually evaluated based on geological evidence 23 1.00 0.60 There are also other definitions of EPGA, but we will not concern ourselves with those. 21 1.20 Max Possible Earthquake Max Expectable Earthquake Max Probable Earthquake Max Considered Earthquake 24 4
  • Max Considered EQ (MCE) Max Considered EQ (MCE) (contd...) Term also used in the International Building Code 2000 (USA) IS:1893 MCE motion as per Indian code does not correspond to any specific probability of occurrence or return period. Corresponds to 2% probability of being exceeded in 50 years (2,500 year return period) Uniform Building Code 1997 (USA) 10% probability of being exceeded in 100 years (1,000 year return period) For the same tectonic province, MCE based on 2,500 year return period will be larger than the MCE based on 1,000 year return period 25 26 Design Basis EQ (DBE) Design Basis EQ (DBE) (contd...) This is the earthquake motion for which structure is to be designed considering inherent conservatism in the design process UBC1997 and IBC2000: Cl. 3.6 of the code (p. 8) Earthquake that can reasonably be expected to occur once during the design life of the structure What is reasonable…not made clear in our code. Also, design life of different structures may be different. Corresponds to 10% probability of being exceeded in 50 years (475 year return period) 27 28 MCE versus DBE Modal Mass IBC2000 provides for DBE as two-thirds of MCE IS1893 provides for DBE as one-half of MCE It is that mass of the structure which is effective in one particular natural mode of vibration Can be obtained from the equation in Cl. 7.8.4.5 for simple lumped mass systems The factor 2 in denominator of eqn for Ah on p.14 accounts for this See definition of Z on p.14 of the code It requires one to know the mode shapes One must perform dynamic analysis to obtain mode shapes Next slides to appreciate the physical significance of Modal Mass 29 30 5
  • Example on Modal Mass Example on Modal Mass (contd…) Three degrees of freedom system Total mass of structure: 100,000kg 5% damping assumed in all modes To be analyzed for the ground motion for which acceleration response spectrum is given here. First mode of vibration: Period (T1)=0.6sec, Modal Mass= 90,000kg Obtained using first mode shape Maximum Acceleration, g Spectral acceleration = 0.87g Read from Response Spectrum for T=0.6sec Max Base shear contributed by first mode = = (90,000kg)x(0.87x9.81m/sec2) = 768,000 N = 768 kN Undamped Natural Period T (sec) 31 32 Example on Modal Mass (contd...) Modal Participation Factor (Cl.3.21) Second mode of vibration: A term used in dynamic analysis. Period (T2)=0.2sec Modal Mass=8,000kg Spectral acceleration (for T1=0.2sec) = 0.80g Max Base shear contributed by second mode = = (8,000kg)x(0.80x9.81m/sec2) More later Read the definition in Cl. 3.21 There seems to be a typographical error. “amplitudes of 95% mode shapes” should be read as “amplitude of mode shapes” = 62,800 N = 62.8 kN 33 34 Seismic Weight (Cl.3.29) Seismic Mass (Cl.3.28) It is the total weight of the building plus that part of the service load which may reasonably be expected to be attached to the building at the time of earthquake shaking. It is seismic weight divided by acceleration due to gravity That is, it is in units of mass (kg) rather than in the units of weight (N, or kN) In working on dynamics related problems, one should be careful between mass and weight. It includes permanent and movable partitions, permanent equipment, etc. It includes a part of the live load Mass times gravity is weight 1 kg mass is equal to 9.81N (=1x9.81) weight Buildings designed for storage purposes are likely to have larger percent of service load present at the time of shaking. Notice the values in Table 8 35 36 6
  • Centre of Stiffness Cl. 4.5 defines Centre of Stiffness as The point through which the resultant of the restoring forces of a system acts. Section 4 Terminology on Buildings It should be defined as: If the building undergoes pure translation in the horizontal direction (that is, no rotation or twist or torsion about vertical axis), the point through which the resultant of the restoring forces acts is the Centre of Stiffness 37 38 Centre of Rigidity Eccentricity In cl. 4.21, while defining static eccentricity, Centre of Rigidity is used. Both Centre of Stiffness (CS) and Centre of Rigidity (CR) are the same terms for our purposes! Cl. 4.21 defines Static Eccentricity. This is the calculated distance between the Centre of Mass and the Centre of Stiffness. Under dynamic condition, the effect of eccentricity is higher than that under static eccentricity. Experts will tell you that there are subtle differences between these two terms. But that is not important from our view point. Hence, a dynamic amplification is to be applied to the static eccentricity before it can be used in design. It would have been better if the code had used either stiffness or rigidity throughout 39 40 Dual System Eccentricity (contd…) An accidental eccentricity is also considered because: Consider buildings with shear walls and moment resisting frames. In 1984 version of the code, Table 5 (p. 24) implied that the frame should be designed to take at least 25% of the total design seismic loads. The computation of eccentricity is only approximate. During the service life of the building, there could be changes in its use which may change centre of mass. Design eccentricity (cl.4.6) is obtained from static eccentricity by accounting for (cl.7.9.2) Dynamic amplification, and Accidental eccentricity 41 42 7
  • Dual System (contd…) Dual System (contd…) Conditions of Cl. 4.9 are not met. Here, two possibilities exist (see Footnote 4 in Table 7, p. 23): In the new code several choices are available to the designer: Frames are not designed to resist seismic loads. The entire load is assumed to be carried by the shear walls. In Example 2 above, the shear walls will be designed for 100% of total seismic loads, and the frames will be treated as gravity frames (i.e., it is assumed that frames carry no seismic loads) Frames and walls are designed for the forces obtained from analysis, and the frames happen to carry less than 25% of total load. In Example 2 above, the frames will be designed for 10% while walls will be designed for 90% of total seismic loads. When conditions of Cl. 4.9 are met: dual system. Example 1: Analysis indicates that frames are taking 30% of total seismic load while 70% loads go to shear walls. Frames and walls will be designed for these forces and the system will be termed as dual system. Example 2: Analysis indicates that frames are taking 10% and walls take 90% of the total seismic load. To qualify for dual system, design the walls for 90% of total load, but design the frames to resist 25% of total seismic load 43 44 Moment Resisting Frame Dual System (contd…) Clearly, the dual systems are better and are designed for lower value of design force. See Table 7 (p. 23) of the code. There is different value of response reduction factor (R) for the dual systems. Cl. 4.15 defines Ordinary and Special Moment Resisting Frames. Ductile structures perform much better during earthquakes. Hence, ductile structures are designed for lower seismic forces than non-ductile structures. For example, compare the R values in Table 7 IS:13920-1993 provides provisions on ductile detailing of RC structures. IS: 800-2007 does have seismic design provisions for some framing systems. 45 46 Number of Storeys (Cl.4.16) Number of Storeys (contd…) Definition of number of storeys When basement walls are connected with the floor deck or fitted between the building columns, the basement storeys are not included in number of storeys. Was relevant in 1984 version of the code wherein natural period (T) was calculated as 0.1n. In the current code, it is not relevant In new code, Cl. 7.6 requires height of building. This is because in that event, the seismic loads from upper parts of the building get transferred to the basement walls and then to the foundation. That is, See the definition of h (building height) in Cl. 7.6 Compare it with definition in Cl. 4.11. Clearly, the definition of Cl. 7.6 is more appropriate. Columns in the basement storey will have insignificant seismic loads, and Basement walls act as part of the foundation. 47 The definition of Cl. 4.11 needs revision 48 8
  • Soft Story Soft Storey (contd…) There is not much of a difference between soft storey and extreme soft storey buildings as defined in the code, and the latter definition is not warranted. Cl. 4.20 defines Soft Storey Sl. No. 1 in Table 5 (p. 18) defines Soft Storey and Extreme Soft Storey In Bhuj earthquake of January 2001, numerous soft storey buildings collapsed. Most Indian buildings will be soft storey as per this definition simply because the ground storey height is usually different from that in the upper storeys. Hence, the definition of soft storey needs a review. We should allow more variation between stiffness of adjacent storeys before terming a building as a “soft storey building” The code does not have enough specifications on computation of lateral stiffness and this undermines the definition of soft storey and extreme soft storey. Hence, the term Extreme Soft Storey and cl. 7.10 (Buildings with Soft Storey) were added hurriedly after the earthquake. 49 50 Weak Storey Weak Storey (contd…) Soft storey refers to stiffness Weak storey refers to strength Usually, a soft storey may also be a weak storey Note that the stiffness and strength are two different things. Stiffness: Force needed to cause a unit displacement. It is given by slope of the forcedisplacement relationship. Strength: Maximum force that the system can take 51 52 Storey Drift Definition of Vroof Storey Drift defined in cl. 4.23 of the Code. On p. 11, it is defined as peak storey shear force at the roof due to all modes considered. Storey drift not to exceed 0.004 times the storey height. 53 It is better to define it as peak storey shear in the top storey due to all modes considered. 54 9
  • General Principles and Design Criteria (Section 6) Four main sub-sections Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Increase in Permissible Stresses Cl. 6.4: Design Spectrum Section 6.1: General Principles IS:1893-2002(Part I) 55 56 Ground Motion (cl. 6.1.1) Ground Motion Contd… Usually, the vertical motion is weaker than the horizontal motion On average, peak vertical acceleration is onehalf to two-thirds of the peak horizontal acceleration. All structures experience a constant vertical acceleration (downward) equal to gravity (g) at all times. Hence, the vertical acceleration during ground shaking can be just added or subtracted to the gravity (depending on the direction at that instant). Cl. 6.4.5 of 2002 code specifies it as two-thirds 57 58 Ground Motion Contd… Ground Motion Contd… Example: A roof accelerating up and down by 0.20g. Main concern is safety for horizontal acceleration. Para 2 in cl. 6.1.1 (p. 12) lists certain cases where vertical motion can be important, e.g., Implies that it is experiencing acceleration in the range 1.20g to 0.80g (in place of 1.0g that it would experience without earthquake.) Large span structures Cantilever members Prestressed horizontal members Structures where stability is an issue Factor of safety for gravity loads (e.g., dead and live loads) is usually sufficient to cover the earthquake induced vertical acceleration 59 60 10
  • Design Lateral Force Effects other than shaking • Philosophy of Earthquake-Resistant Design Ground shaking can affect the safety of structure in a number of ways: – First calculate maximum elastic seismic forces – Then reduce to account for ductility and overstrength Shaking induces inertia force Soil may liquefy Sliding failure of founding strata may take place Fire or flood may be caused as secondary effect of the earthquake. Lateral Force H, ∆ Maximum Elastic Force Elastic Elastic Force reduced by R Cl. 6.1.2 cautions against situations where founding soil may liquefy or settle: such cases are not covered by the code and engineer has to deal with these separately. 61 Actual Design Force 62 0 Lateral Deflection Earthquake Design Principle Clause 6.1.3 The criteria is: Para 1 of this clause implies that Design Basis Earthquake (DBE) relates to the “moderate shaking” and Maximum Considered Earthquake (MCE) relates to the “strong shaking”. Indian code is quite empirical on the issue of DBE and MCE levels. Hence, this clause is to be taken only as an indicator of the concept. Minor (and frequent) earthquakes should not cause damage Moderate earthquakes should not cause significant structural damage (but could have some non-structural damage) Major (and infrequent) earthquakes should not cause collapse 63 64 Seismic Design Principle Overstrength A well designed structure can withstand a horizontal force several times the design force due to: The structure yields at load higher than the design load due to: Partial Safety Factors Partial safety factor on seismic loads Partial safety factor on gravity loads Partial safety factor on materials Overstrength Redundancy Ductility Material Properties Member size or reinforcement larger than required Strain hardening in materials Confinement of concrete improves its strength Higher material strength under cyclic loads Strength contribution of non-structural elements Special ductile detailing adds to strength also 65 66 11
  • Redundancy Ductility Yielding at one location in the structure does not imply yielding of the structure as a whole. Load distribution in redundant structures provides additional safety margin. Sometimes, the additional margin due to redundancy is considered within the “overstrength” term. As the structure yields, two things happen: 67 There is more energy dissipation in the structure due to hysteresis The structure becomes softer and its natural period increases: implies lower seismic force to be resisted by the structure Higher ductility implies that the structure can withstand stronger shaking without collapse 68 Response Reduction Factor ∆ Overstrength, redundancy, and ductility together lead to the fact that an earthquake resistant structure can be designed for much lower force than is implied by a strong shaking. The combined effect of overstrength, redundancy and ductility is expressed in terms of Response Reduction Factor (R) Total Horizontal Load Total Horizontal Load Maximum force if structure remains elastic Fel Linear Elastic Response Maximum Load Capacity Fy Load at First Yield Fs Due to Ductility Non linear Response Due to Redundancy First Significant Yield Due to Overstrength Design force Fdes 0 ∆w ∆y Figure: Courtesy Dr. C V R Murty ∆max Roof Displacement (∆) Response Reduction Factor = 69 Maximum Elastic Force (Fel ) Design Force (F des) 70 Para 2 and 3 of Cl. 6.1.3. Para 2 and 3 of Cl. 6.1.3 Contd… Imply that the earthquake resistant structures should generally be ductile. IS:13920-1993 gives ductile detailing requirements for RC structures. Ductile detailing provisions for some steel framing systems are available in IS:800-2007. As of now, ductile detailing provisions for precast structures and for prestressed concrete structures are not available in Indian codes. In the past earthquakes, precast structures have shown very poor performance during earthquakes. However, it is advisable to refer to international codes/literature for ductile detailing of steel structures. 71 The connections between different parts have been problem areas. Connections in precast structures in high seismic regions require special attention. 72 12
  • Past Performance Para 4 of Cl. 6.1.3 The performance of flat plate structures also has been very poor in the past earthquakes. This is an important clause for moderate seismic regions. The design seismic force provided in the code is a reduced force considering the overstrength, redundancy, and ductility. For example, in the Northridge (California) earthquake of 1994. Additional punching shear stress due to lateral loads are serious concern. 73 Hence, even when design wind force exceeds design seismic force, one needs to comply with the seismic requirements on design, detailing and construction. 74 Soil Structure Interaction (Cl. 6.1.4) Soil Structure Interaction (Cl. 6.1.4) Contd… Presence of structure modifies the free field motion since the soil and the structure interact. If there is no structure, motion of the ground surface is termed as Free Field Ground Motion Normal practice is to apply the free field motion to the structure base assuming that the base is fixed. Hence, foundation of the structure experiences a motion different from the free field ground motion. The difference between the two motions is accounted for by Soil Structure Interaction (SSI) This is valid for structures located on rock sites. For soft soil sites, this may not always be a good assumption. 75 SSI is not the same as Site Effects Site Effect refers to the fact that free field motion at a site due to a given earthquake depends on the properties and geological features of the subsurface soils also. 76 Direction of Ground Motion (Cl. 6.1.5) SSI Contd… Consideration of SSI generally During earthquake shaking, ground shakes in all possible directions. Decreases lateral seismic forces on the structure Increases lateral displacements Increases secondary forces associated with Pdelta effect. Direction of resultant shaking changes from instant to instant. Basic requirement is that the structure should be able to withstand maximum ground motion occurring in any direction. For ordinary buildings, one usually ignores SSI. NEHRP Provisions provide a simple procedure to account for soil-structure interaction in buildings 77 For most structures, main concern is for horizontal vibrations rather than vertical vibrations. 78 13
  • Direction of Ground Motion (Cl. 6.1.5) (contd…) One does not expect the peak ground acceleration to occur at the same instant in two perpendicular horizontal directions. Hence for design, maximum seismic force is not applied in the two horizontal directions simultaneously. If the walls or frames are oriented in two orthogonal (perpendicular) directions: Building Plans with Orthogonal Systems It is sufficient to consider ground motion in the two directions one at a time. Else, Cl. 6.3.2: will come back to this later. 79 80 Floor Response Spectrum (Cl. 6.1.6) Equipment located on a floor needs to be designed for the motion experienced by the floor. Hence, the procedure for equipment will be: Analyze the building for the ground motion. Obtain response of the floor. Express the floor response in terms of spectrum (termed as Floor Response Spectrum) Design the equipment and its connections with the floor as per Floor Response Spectrum. walls Building Plans with Non-Orthogonal Systems 81 82 General Principles and Design Criteria (Section 6) Four main sub-sections Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Increase in Permissible Stresses Cl. 6.4: Design Spectrum Sections 6.2 and 6.3 IS:1893-2002(Part I) 83 This lecture covers sub-sections: Cl. 6.2 and Cl. 6.3 84 14
  • Cl.6.2 Assumptions Mexico Earthquake of 1985 Same as in the 1984 edition, except the Note after Assumption a) There have been instances such as the Mexico earthquake of 1985 which have necessitated this note. Earthquake occurred 400 km from Mexico City Great variation in damages in Mexico City Some parts had very strong shaking In some parts of city, motion was hardly felt Ground motion records from two sites: UNAM site: Foothill Zone with 3-5m of basaltic rock underlain by softer strata SCT site: soft soils of the Lake Zone 85 86 Mexico Earthquake of 1985 (contd…) Mexico Earthquake of 1985 (contd…) PGA at SCT site about 5 times higher than that at UNAM site Extremely soft soils in Lake Zone amplified weak long-period waves Epicentral distance is same at both locations Natural period of soft clay layers happened to be close to the dominant period of incident seismic waves This lead to resonance-like conditions Buildings between 7 and 18 storeys suffered extensive damage Natural period of such buildings close to the period of seismic waves. Time (sec) Figure from Kramer, 1996 87 88 Assumption b) Assumption c) on Modulus of Elasticity A strong earthquake takes place infrequently. A strong wind also takes place infrequently. Hence, the possibility of strong wind and strong ground shaking taking place simultaneously is very very low. It is common to assume that strong earthquake shaking and strong wind will not occur simultaneously. Modulus of elasticity of materials such as concrete, masonry and soil is difficult to specify Its value depends on Stress level Loading condition (static versus dynamic) Material strength Age of material, etc Same with strong earthquake shaking and maximum flood. 89 90 15
  • Cl.6.3 Load Combinations and Increase in Permissible Stresses Loads and Stresses • Loads Cl.6.3.1.1 gives load combinations for Plastic Design of Steel Structures – EQ forces not to occur simultaneously with maximum flood, wind or wave loads – Direction of forces • One horizontal + Vertical • Two horizontal + Vertical Same as in IS:800-1978 More load combinations in IS:800-2007 Cl.6.3.1.2 gives load combinations for Limit State Design for RC and Prestressed Concrete Structures Same as in IS:456-2000 (RC structures) and IS:1343-1980 (Prestressed structures) with one difference 91 92 Load Combinations in Cl.6.3.1.2 Load Combination 0.9DL ±1.5EL Compare combinations of this clause with those in Table 18 (p.68) of IS:456-2000 Combination 0.9DL ± 1.5EL Horizontal loads are reversible in direction. In many situations, design is governed by effect of horizontal load minus effect of gravity loads. The way this combination is written in IS:456, the footnote creates an impression that it is not always needed. In such situations, a load factor higher than 1.0 on gravity loads will be unconservative. Hence, a load factor of 0.9 specified on gravity loads in the combination 4) It has been noticed that many designers do not routinely consider this combination because of the way it is written. 93 94 Direction of Earthquake Loading Many designs of footings, columns, and positive steel in beams at the ends in frame structures are governed by this load combination Hence, this combination has been made very specific in IS:1893-2002. Direction of Earthquake Loading (contd…) During earthquake, ground moves in all directions; the resultant direction changes every instant. Ground motion can resolved in two horizontal and one vertical direction. Structure should be able to withstand ground motion in any direction Two horizontal components of ground motion tend to be comparable Vertical component is usually smaller than the horizontal motion Except in the epicentral region where vertical motion can be comparable (or even stronger) to the horizontal motion As discussed earlier, generally, most ordinary structures do not require analysis for vertical ground motion. Say, the epicentre is to the north of a site. Ground motion at site in the north-south and east-west directions will still be comparable. 95 96 16
  • Direction of Horizontal Ground Motion in Design (Cl.6.3.2.1) Cl.6.3.2.1 (contd…) Consider a building in which horizontal (also termed as lateral) load is resisted by frames or walls oriented in two perpendicular directions, say X and Y. One must consider design ground motion to act in X-direction, and in Y-direction, separately That is, one does not assume that the design motion in X is acting simultaneously with the design motion in the Y-direction 97 If at a given instant, motion is in any direction other than X or Y, one can resolve it into X- and Y-components, and the building will still be safe if it is designed for X- and Y- motions, separately. Minor typo in this clause: “direction at time” should be replaced by “direction at a time” 98 Load Combinations for Orthogonal System Non-Orthogonal Systems (Cl.6.3.2.2) Load EL implies Earthquake Load in +X, -X, +Y, and –Y, directions. Thus, an RC building with orthogonal system therefore needs to be designed for the following 13 load cases: When the lateral load resisting elements are NOT oriented along two perpendicular directions In such a case, design for X- and Y-direction loads acting separately will be unconservative for elements not oriented along X- and Ydirections. 1.5 (DL+LL) 1.2 (DL+LL+ELx) 1.2 (DL+LL-ELx) 1.2 (DL+LL+ELy) 1.2 (DL+LL-ELy) 1.5 (DL+ELx) 1.5 (DL-ELx) 1.5 (DL+ELy) 1.5 (DL-ELy) 0.9DL +1.5ELx 0.9DL-1.5ELx 0.9DL+1.5ELy 0.9DL-1.5ELy ELx = Design EQ load in X-direction ELy = Design EQ load in Y-direction 99 100 Load Combinations… Combinations… Load Combinations… Combinations… – Problem • Lateral force resisting system non-parallel in two plan directions 1 – Consider design based on one direction at a time ELx ELy 0.8 y V 0.6 Force effective along 0.4 direction of inclined 0.2 element 0 ELx x 0 15 30 45 60 75 90 θ y Orientation of inclined element with respect to x-axis x 101 ELy Elements at 450 orientation designed only for 70% of lateral force 102 17
  • Load Combinations… Combinations… Non-Orthogonal Systems (Cl.6.3.2.2) (contd…) – Solution :: Try (100%+30%) together A lateral load resisting element (frame or wall) is most critical when loading is in direction of the element. It may be too tedious to apply lateral loads in each of the directions in which the elements are oriented. For such cases, the building may be designed for: ELx x 0.3ELy y 0.3ELx x 100% design load in X-direction and 30% design load in Y-direction, acting simultaneously 100% design load in Y-direction and 30% design load in X-direction, acting simultaneously 103 ELy 104 Note that directions of earthquake forces are reversible. Hence, all combinations of directions are to be considered. Load Combinations… Combinations… Non-Orthogonal Systems (Cl.6.3.2.2) (contd…) – Justification :: Say ELx = ELy = V y Thus, EL now implies eight possibilities: +(Elx + 0.3ELy) +(Elx - 0.3ELy) -(Elx + 0.3ELy) -(Elx - 0.3ELy) +(0.3ELx + Ely) +(0.3ELx - ELy) -(0.3ELx + ELy) -(0.3ELx - ELy) Vcosθ θ x V V*=Vcosθ + 0.3Vsinθ 0.3Vsinθ 0.3V 1.5 V* ELx+0.3ELy 1 0.3ELx+ELy 0.5 0 0 105 Non-Orthogonal Systems (Cl.6.3.2.2) (contd…) 30 45 60 75 90 θ Non-Orthogonal Systems (Cl.6.3.2.2) (contd…) Therefore, one must consider 25 load cases: 1.5 (DL+LL) 1.2[DL+LL+(ELx+0.3ELy)] 1.2[DL+LL+(ELx-0.3ELy)] 1.2[DL+LL-(ELx+0.3ELy)] 1.2[DL+LL-(ELx-0.3ELy)] 1.2[DL+LL+(0.3ELx+ELy)] 1.2[DL+LL+(0.3ELx-ELy)] 1.2[DL+LL-(0.3ELx+ELy)] 1.2[DL+LL-(0.3ELx-ELy)] 107 15 106 Note that the design lateral load for a building in the X-direction may be different from that in the Y-direction Some codes use 40% in place of 30%. 1.5[DL+(ELx+0.3ELy)] 1.5[DL+(ELx-0.3ELy)] 1.5[DL-(ELx+0.3ELy)] 1.5[DL-(ELx-0.3ELy)] 1.5[DL+(0.3ELx+ELy)] 1.5[DL+(0.3ELx-ELy)] 1.5[DL-(0.3ELx+ELy)] 1.5[DL-(0.3ELx-ELy)] 0.9DL+1.5(ELx+0.3ELy)] 0.9DL+1.5(ELx-0.3ELy)] 0.9DL-1.5(ELx+0.3ELy)] 0.9DL-1.5(ELx-0.3ELy)] 0.9DL+1.5(0.3ELx+ELy)] 0.9DL+1.5(0.3ELx-ELy)] 0.9DL-1.5(0.3ELx+ELy)] 0.9DL-1.5(0.3ELx-ELy)] 108 18
  • Cl.6.3.4.1 Cl.6.3.4.2 In complex structures such as a nuclear reactor building, one may have very complex structural systems. Need for considering earthquake motion in all three directions as per 100%+30% rule. In place of 100%+30% rule, one may take for design force resultants as per square root of sum of squares in the two (or, three) directions of ground motion EL = (ELx)2 + ( ELy)2 + (ELz)2 Now, EQ load means the following 24 combinations: ± Elx ± 0.3ELy ± 0.3ELz ± Ely ± 0.3ELx ± 0.3ELz ± Elz ± 0.3ELx ± 0.3ELy Hence, EL now means 24 combinations A total of 73 load cases for RC structures! 109 110 Increase in Permissible Stresses: Cl.6.3.5.1 Typographical Errors in Table 1 Applicable for Working Stress Design Permits the designer to increase allowable stresses in materials by 33% for seismic load cases. Some constraints on 33% increase for steel and for tensile stress in prestressed concrete beams. The Table within Table 1, giving values of desirable minimum values of N. This Table pertains to Note 3 and hence should be placed between Notes 3 and 4 (and not between Notes 4 and 5 as printed currently) Caption of first column in this sub-table should read “Seismic Zone” and not “Seismic Zone level (in metres)” Caption of second column in this sub-table should read “Depth Below Ground Level (in metres)” and not “Depth Below Ground” Note 1 is also repeated within Note 4. Hence, Note 1 should be dropped. 111 112 Second Para of Cl.6.3.5.2 Liquefaction Potential It points out that in case of loose or medium dense saturated soils, liquefaction may take place. Sites vulnerable to liquefaction require Information given in cl.6.3.5.2 and Table 1 on Liquefaction Potential is very primitive: Note to Cl.6.3.5.2 encourages the engineer to refer to specialist literature for determining liquefaction potential analysis. It is common these days to use SPT or CPT results for detailed calculations on liquefaction potential analysis. Liquefaction potential analysis. Remedial measures to prevent liquefaction. Else, deep piles are designed assuming that soil layers liable to liquefy will not provide lateral support to the pile during ground shaking. 113 114 19
  • General Principles and Design Criteria (Section 6) Four main sub-sections Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Increase in Permissible Stresses Cl. 6.4: Design Spectrum Lecture 2 This lecture covers sub-section 6.4. Sections 6.4 IS:1893-2002(Part I) 115 116 Response Spectrum versus Design Spectrum Response Spectrum versus Design Spectrum (contd…) Natural period of a civil engineering structure cannot be calculated precisely Design specification should not very sensitive to a small change in natural period. Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum Spectral Acceleration, g Consider the Acceleration Response Spectrum Notice the region of red circle marked: a slight change in natural period can lead to large variation in maximum acceleration Undamped Natural Period T (sec) 117 118 Design Spectrum Design Spectrum (contd…) Spectral Acceleration, g Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure. The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well. Natural vibration period Tn, sec See Fig. next slide. Fig. from Dynamics of Structures by Chopra, 2001 119 120 20
  • Design Spectrum (contd…) Design Spectrum (contd…) Design Spectrum must be accompanied by: Design Spectrum is a design specification It must take into account any issues that have bearing on seismic safety. Load factors or permissible stresses that must be used Different choice of load factors will give different seismic safety to the structure Damping to be used in design Variation in the value of damping used will affect the design force. Method of calculation of natural period Depending on modeling assumptions, one can get different values of natural period. Type of detailing for ductility Design force can be lowered if structure has higher ductility. 121 122 Design SPECTRUM… SPECTRUM… Design Lateral Force… Force… • Design Horizontal Acceleration Spectrum • Two methods of estimation of design seismic lateral force Maximum Elastic Acceleration – Seismic Coefficient Method – Response Spectrum Method S  Z  a (T ) I  g   Ah (T ) =  2R – In both methods • Seismic Design Force Fd = Fe /R = A W A = Design acceleration value W = Seismic weight of structure 123 124 Seismic zone factor Design SPECTRUM… SPECTRUM… • Seismic Zone Factor Seismic Zone Z II – Relative Values Consistent III IV Seismic Zone 0.10 0.10 III 1.6 IV V 0.16 0.24 0.36 1.5 – Factor of 2 in Ah for reducing PGA for MCE to PGA for Design Basis Earthquake (DBE) PGA Time PGA (ZPA:: Zero Period Acceleration)0 II Z 0.16 0.24 0.36 Spectral Acceleration Acceleration 1.5 V – Reflects Peak Ground Acceleration (PGA) of the region during Maximum Credible Earthquake (MCE) 125 Reduction to account for ductility and overstrength Natural Period 126 (Earthquake which can be reasonably expected to occur at least once during the lifetime of structures) 21
  • Importance factor • Importance factor I – – – – Soil Effect Degree of conservatism Willing to pay more for assuring essential services Domino effect of disaster Important & community buildings Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site S.No. Building I 1 Important, Community & Lifeline Buildings 1.5 2 All Others 1.0 • Can use higher value of I • Buildings not mentioned can be designed for higher value of I depending on economy and strategic considerations • Temporary (short term) structures exempted from I Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996 Period (sec) 127 128 Soil Effect (contd…) This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites. Design Spectrum depends on Type I, II, and III soils Type I, II, III soils are indirectly defined in Table 1 of the code. See Note 4 of Table 1: The value of N is to be taken at the founding level. What is the founding level of a pile or a well foundation? Spectral Acceleration Coefficient (Sa /g) Soil Effect (contd…) Fig. from IS:1893-2002 This is left open in the code. Period(s) 129 130 Shape of Design Spectrum Soil Effect (contd…) The International Building Code (IBC2000) classifies the soil type based on weighted average (in top 30m) of: The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes. In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected. Soil Shear Wave Velocity, or Standard Penetration Resistance, or Soil Undrained Shear Strength I feel our criteria should also use the average properties in the top 30m rather than just at the founding level. 131 132 22
  • Response Reduction Factor Response Reduction Factor (contd…) As discussed earlier, the structure is allowed to be damaged in case of severe shaking. Hence, structure is designed for seismic force much less than what is expected under strong shaking if the structure were to remain linear elastic Earlier code just provided the required design force For buildings, Table 7 gives values of R For other structures, value of R is to be given in the respective parts of code It gave no direct indication that the real force may be much larger Now, the code provides for realistic force for elastic structure and then divides that force by (2R) This gives the designer a more realistic picture of the design philosophy. 133 134 Response Reduction Factor (R) (contd…) Response Reduction Factor (R) (contd…) Study Table 7 very carefully including all the footnotes. We have already discussed terms: Dual systems, OMRF, and SMRF Note 6 prohibits ordinary RC shear walls in zones IV and V. Such a note is not there for OMRF. This confuses people and they take it to mean that the code allows Ordinary Moment Resisting Frames in zones IV and V. Notes 4 and 8 were covered earlier when we discussed Dual systems. The values of R were decided based on engineering judgment. The effort was that design force on SMRF as per new provisions should be about the same as that in the old code. For other building systems, lower values of R were specified. It is hoped that with time, these values will be refined based on detailed research. 135 As per IS:13920, all structures in zones III, IV and V should comply with ductile detailing (as per IS:13920). Hence, Ord. RC shear walls prohibited in zones III also. This needs to be corrected in the code. 136 Response Reduction Factor (R) (contd…) Response Reduction Factor (contd…) Moreover, there are a number of other systems that are prohibited in high zones and those are not listed in this table. For instance, Note the definition of R on page 14 contains the statement: However, the ratio (I/R) shall not be greater than 1.0 (Table 7) OMRF’s are also not allowed in zones III, IV and V as per IS:13920. Load bearing masonry buildings are required to have seismic strengthening (lintel bands, vertical bars) in high zones as per IS:4326. This statement should not be there. For buildings, I never exceeds 1.5 and the lowest value of R is 1.5 in Table 7 Thus, this statement does not kick in for buildings It would be better for this table to drop Note 6. For other structures, there are situations where (I/R) will need to exceed 1.0 In its place, there could be a general note that some of the above systems are not allowed in high seismic zones as per IS:4326 or IS:13920. 137 For instance, for bearings of important bridges. 138 23
  • Design Spectrum for Stiff Structures Response Reduction Factor … – R values can be taken as for Dual Systems, only if both conditions below are satisfied For very stiff structures (T < 0.1sec), ductility is not helpful in reducing the design force. Codes tend to disallow the reduction in force in the period range of T < 0.1sec • Shear walls and MRFs are designed to resist VB in proportion to their stiffness considering their interaction at all floor levels • MRFs are designed to independently resist at least 25% of VB Spectral acceleration Shear Wall Design spectrum assumes peak extends to T=0 Actual shape of response spectrum (may be used for higher modes only) MRF T(seconds) 139 Concept sometimes used by the codes for response spectrum in low period range. 140 Underground Structures Cl.6.4.4 Design Spectrum for Stiff Structures (contd…) Statement in Cl.6.4.2 When seismic waves hit the ground surface, these are reflected back into ground The reflection mechanics is such that the amplitude of vibration at the free surface is much higher (almost double) than that under the ground Cl.6.4.4 allows the design spectrum to be onehalf if the structure is at depth of 30m or below. Provided that for any structure with T ≤ 0.1s, the value of Ah will not be taken less than Z/2 whatever be the value of I/R This statement attempts to ensure a minimal design force for stiff structures. Note that this statement is valid only when the first (fundamental) mode period T ≤ 0.1sec even though the code does not specify so. For higher modes, this restrictions should not be imposed. 141 Linear interpolation for structures and foundations if depth is less than 30m. 142 Equations for Design Spectrum Underground Structures (contd…) The clause is also applicable for calculation of seismic inertia force on foundation under the ground, say a well foundation for a bridge. Hence, the wording Underground structures and foundations Note that in case of a bridge (or any aboveground structure) with foundation going deeper than 30m: Second para of Cl.6.4.5 and the equations This should not be a part of C.6.4.5 and should have had an independent clause number Note the word “proposed” in this para is misleading and should not be there. This clause (Cl. 6.4.4) can be used to calculate seismic inertia force due to mass of foundation under the ground, and not for calculation of inertia force of the superstructure. 143 144 24
  • Equations for Design Spectrum Site Specific Design Criteria Cl.6.4.6 Response spectrum shapes in Fig. 2 are for 5% damping. These shapes are also given in the form of equations Table 3 gives multiplying factors to obtain design spectrum for other values of damping Note that the multiplication is not to be done for zero period acceleration (ZPA) Seismic design codes meant for ordinary projects For important projects, such as nuclear power plants, dams and major bridges site-specific seismic design criteria are developed 145 These take into account geology, seismicity, geotechnical conditions and nature of project Site specific criteria are developed by experts and usually reviewed by independent peers A good reference to read on this: Housner and Jennings, “Seismic Design Criteria”, Earthquake Engineering Research Institute, USA, 1982. 146 Buildings (Section 7) Sub-sections Cl. 7.1: Regular and Irregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight Cl. 7.5: Design Lateral Force Cl. 7.6: Fundamental Natural Period Cl. 7.7: Distribution of Design Force Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations Cl. 7.12 Miscellaneous Sections 7.1 to 7.7 on Buildings IS:1893-2002(Part I) 147 148 Regular and Irregular Configuration (Cl. 7.1) The statement of Cl. 7.1 is an attempt to emphasize the importance of structural configuration for ensuring good seismic performance. Good structural configuration has implications for both safety and economy of the building. 149 Importance of Configuration To quote Late Henry Degenkolb, the wellknown earthquake engineer in California: If we have a poor configuration to start with, all the engineer can do is to provide band-aid – improve a basically poor solution as best as he can. Conversely, if we start off with a good configuration and a reasonable framing system, even a poor engineer can’t harm its ultimate performance too much. 150 25
  • Regular versus Irregular Configuration Importance of Configuration (contd…) Quote from NEHRP Commentary: Tables 4 and 5 list out the irregularities in the building configuration The major factors influencing the cost of complying with the provisions are: 1. The complexity of the shape and structural framing system for the building. (It is much easier to provide seismic resistance in a building with a simple shape and framing plan.) 2. The cost of the structural system (plus other items subject to special seismic design requirements) in relation to the total cost of the building. (In many buildings, the cost of providing the structural system may be only 25 percent of the total cost of the project.) 3. The stage in design at which the provision of seismic resistance is first considered. (The cost can be inflated greatly if no attention is given to seismic resistance until after the configuration of the building, the structural framing plan, and the materials of construction have already been chosen). 151 Table 4 and Fig. 3 for Irregularities in Plan Table 5 and Fig. 4 for Irregularities in Elevation 152 A Remark on IS:13920 Design Imposed Load…(Cl. 7.3) Recently, BIS has issued some amendments to IS:13920-1993 (see next slide). In the context of Table 7, note that provisions of IS:13920 are now mandatory for all RC structures in zones III, IV and V. There could be differences of opinion about Cl. 7.3.3. Say the imposed load is 3 kN/sq.m This clause implies that we take only 25% of imposed load for calculation of seismic weight, and also for load combinations. This amounts to: 1.2 DL + 0.3LL + 1.2LL The Cl. 7.3.3 should be dropped. 153 154 Design Lateral Force (Cl. 7.5) Note that the code no longer talks of two methods: seismic coefficient method and response spectrum method. There have been instances of designer calculating seismic design force for each 2-D frame separately based on tributary mass shared by that frame. Mass that causes Earthquake Force in X-Direction EQx Mass being considered for calculation of inertia force due to earthquake This is erroneous since only a fraction of the building mass is considered in the seismic load calculations. EQx Plan of building 155 Calculation of design seismic force on the basis of tributary mass on 2-D frames leads to significant underdesign. 156 26
  • Design Lateral Force (Cl. 7.5) … Design Lateral Force (Cl. 7.5) (contd…) • Seismic Weight of Building W Now, Cl. 7.5.2 makes it clear that one has to evaluate seismic design force for the entire building first and then distribute it to different frames/ walls. Cl. 7.5.2 does not mean that one has to necessarily carry out a 3-D analysis. – Dead load – Part of imposed loads % of Imposed Load Imposed Uniformly Distributed Floor Loads to be considered (kN/m2) Up to and including 3.0 Above 3.0 One could still work with 2-D frame systems. 25 50 157 158 Fundamental Natural Period (Cl. 7.6) Fundamental Natural Period (Cl. 7.6) (contd…) For frame buildings without brick infills Needless to say, brick infill in Cl. 7.6 really implies masonry infills Ta = 0.075h0.75 These need not just be bricks: could be stone masonry or concrete block masonry. For all other buildings, including frame buildings with brick infill panels: Ta = 0.09h d d where h is in meters d 159 160 Rationale for new equations for T Observations on Steel Frame Buildings During San Fernando EQ Experimental observations on Indian RC buildings with masonry infills clearly showed that T = 0.1n significantly over-estimates the period. For instance, see Jain S K, Saraf V K, and Mehrotra B, “Period of RC Frame Buildings with Brick Infills,” J. of Struct. Engg, Madras, Vol. 23, No 4, pp 189-196. Arlekar, J N, and Murty, C V R, “Ambient Vibration Survey of RC MRF Buildings with URM Infill Walls,” The Indian Concrete Journal, Vol.74, No.10, Oct. 2000, pp 581-586. For frame buildings with masonry infills, T = 0.09h/(√d) was found to give a much better estimate. Fig. from NEHRP Commentary 161 162 27
  • Observations on RC Frame Buildings During San Fernando EQ Observations on RC Shear Wall Buildings During San Fernando EQ Fig. from NEHRP Commentary 163 Fig. from NEHRP Commentary 164 Vertical Distribution of Seismic Load (Cl. 7.7.1) Lateral load distribution with building height depends on Vertical Distribution of Seismic Load (Cl. 7.7.1) (contd…) Hence, NEHRP provides the following expression for vertical distribution of seismic load Natural periods and mode shapes of the building Shape of design spectrum Qi = V B In low and medium rise buildings, ∑W h j Fundamental period dominates the response, and Fundamental mode shape is close to a straight line (with regular distribution of mass and stiffness) k j j =1 Where k = 1 for T ≤ 0.5sec, and k = 2 for T ≥ 2.5 sec. Value of k varies linearly for T in the range 0.5 sec to 2.5 sec. In IS:1893 over the years, k = 2 has been taken regardless of natural period For tall buildings, contribution of higher modes can be significant even though the first mode may still contribute the maximum response. 165 Wi hik n This is conservative value and has been retained in the code. 166 Horizontal Distribution... (Cl. 7.7.2) Floor diaphragm plays an important role in seismic load distribution in a building. Consider a RC slab For horizontal loads, it acts as a deep beam with depth equal to building width, and the beam width equal to slab thickness. Being a very deep beam, it does not deform in its own plane, and it forces the frames/walls to fulfil the deformation compatibility of no in-plane deformation of floor. This is rigid floor diaphragm action. Concept of Floor Diaphragm Action Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 167 168 28
  • Horizontal Distribution... (Cl. 7.7.2) (contd…) Implications of rigid floor diaphragm action: In case of symmetrical building and loading, the seismic forces are shared by different frames or walls in proportion to their own lateral stiffness. Lateral Load Distribution Due to Rigid Floor Diaphragm: Symmetric Case – No Torsion Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 169 170 When building is not symmetrical, the floor undergoes rigid body translation and rotation. Analysis of Forces Induced by Twisting Moment (Rigid Floor Diaphragm) Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 171 172 Rigid Diaphragm Action Buildings without Diaphragm Action In-plane rigidity of floors is sometimes misunderstood to mean that When the floor diaphragm does not exist, or when the diaphragm is extremely flexible as compared to the vertical elements The beams are infinitely rigid, and The columns are not free to rotate at their ends. The load can be distributed to the vertical elements in proportion to the tributary mass Rotation of columns is governed by out-of-plane behavior of slab and beams. (a) In-plane floor deformation, (b) Outof-plane floor deformation. Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 173 174 29
  • Flexible Floor Diaphragms Analysis for Flexible Floor Diaphragm Buildings There are instances where floor is not rigid. “Not rigid” does not mean it is completely flexible! One can actually model the floor slab in the computer analysis. Fig. on next slide shows the vertical analogy method to consider diaphragm flexibility in lateral load distribution Hence, buildings with flexible floors should be carefully analyzed considering in-plane floor flexibility. Note 1 of Cl. 7.7.2.2 gives the criterion on when the floor diaphragm is not to be treated as rigid. Definition of Flexible Floor Diaphragm (Cl. 7.7.2.2) Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 (Plan View of Floor) In-plane flexibility of diaphragm to be considered when ∆2>1.5{0.5(∆1+ ∆2)} 175 176 Analysis for Flexible Floor Diaphragm Buildings (contd…) Alternatively, one can take the design force as envelop of (that is, the higher of) the two extreme assumptions, i.e., Rigid diaphragm action No diaphragm action (load distribution in proportion to tributary mass) Lateral Load Distribution Considering Floor Diaphragm Deformation: Vertical Analogy Method Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90 177 178 Buildings (Section 7) Sub-sections Cl. 7.1: Regular and Irregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight Cl. 7.5: Design Lateral Force Cl. 7.6: Fundamental Natural Period Cl. 7.7: Distribution of Design Force Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations Cl. 7.12 M iscellaneous Section 7.8: Dynamic Analysis IS:1893-2002(Part I) This lecture covers sub-section 7.8 179 180 30
  • About This Lecture Requirement of Dynamic Anal. Cl. 7.8.1 The intent is not to teach Structural Dynamics or to teach how to carry out dynamic analysis of a building. Seismic Zone Irregular Buildings II and III Ht > 90 m Ht > 40 m IV and V Interested persons may learn Structural Dynamics from numerous excellent text books available on this subject. Regular Building Ht > 40 m Ht > 12 m Notice wordings of section b) in Cl. 7.8.1 All framed buildings higher than 12m…. 181 182 Why Dynamic Analysis? Why Dynamic Analysis? (contd…) Expressions for design load calculation (cl. 7.5.3) and load distribution with height based on assumptions In tall buildings, higher modes can be quite significant. In irregular buildings, mode shapes may be quite irregular Hence, for tall and irregular buildings, dynamic analysis is recommended. Note that industrial buildings may have large spans, large heights, and considerable irregularities: Fundamental mode dominates the response Mass and stiffness distribution are evenly distributed with building height Thus, giving regular mode shape These too will require dynamic analysis. 183 184 Lower Bound on Seismic Force (Cl. 7.8.2) Lower Bound on Seismic Force (Cl. 7.8.2) (contd…) There are considerable uncertainties in modeling a building for dynamic analysis, e.g., This clause requires that in case dynamic analysis gives lower design forces, these be scaled up to the level of forces obtained based on empirical T. Stiffness contribution of non-structural elements Stiffness contribution of masonry infills Modulus of elasticity of concrete, masonry and soil Moment of inertia of RC members Implies that empirical T is more reliable than T computed by dynamic analysis Depending on how one models a building, there can be a large variation in natural period. Ignoring the stiffness contribution of infill walls itself can result in a natural period several times higher 185 186 31
  • Lower Bound on Seismic Force (Cl. 7.8.2) (contd…) Value of Damping Cl. 7.8.2.1 Empirical expressions for period Damping to be used Based on observations of actual as-built buildings, and hence Are far more reliable than period from dynamic analysis based on questionable assumptions Steel buildings: 2% of critical RC buildings: 5% of critical For masonry buildings? Not specified. Recommended value is 5% Even when the results of dynamic analysis are scaled up to design force based on empirical T: Implies that a steel building will be designed for about 40% higher seismic force than a similar RC building. The code should specify 5% damping for both steel and RC buildings. The load distribution with building height and to different elements is based on dynamics. 187 188 Value of Damping Cl. 7.8.2.1 (contd…) Value of Damping Cl. 7.8.2.1 (contd…) Damping value depends on the material and the level of vibrations Choice of damping has implications on seismic safety. Hence, damping value and design spectrum level go together. Most codes tend to specify 5% damping for buildings. What value of damping to be used in “static procedure” of Cl. 7.5? Higher damping for stronger shaking Means that during the same earthquake, damping will increase as the level of shaking increases. We are performing a simple linear analysis, while the real behaviour is non-linear. Hence, one fixed value of damping is used in our analysis. 189 Not specified. I recommend 5% be mentioned in the code. 190 A Note on Static Procedure Number of Modes Cl. 7.8.4.2 The procedure of Cl.7.5 to 7.7 does not require dynamic analysis. The code requires sufficient number of modes so that at least 90% of the total seismic mass is excited in each of the principal directions. There is a problem in wordings of this clause. First sentence reads as: Hence, this procedure is often termed as static procedure or equivalent static procedure or seismic coefficient method. However, notice that this procedure does account for dynamics of the building in an approximate manner The number of modes to be used in the analysis should be such that the sum total of modal masses in all modes considered is at least 90 percent of the total seismic mass and missing mass correction beyond 33 percent. Even though its applicability is limited to simple buildings The portion highlighted in red should be deleted. 191 192 32
  • Modal Combination Cl. 7.8.4.4 Number of Modes Cl. 7.8.4.2 (contd…) Last sentence reads as: This clause gives CQC method first and then simpler method as an alternate. CQC is a fairly sophisticated method for modal combination. It is applicable both when the modes are well-separated and when the modes are closely-spaced. Many computer programs have CQC method built in for modal combination. The effect of higher modes shall be included by considering missing mass correction using well established procedures It should read as: The effect of modes with natural frequency beyond 33 Hz shall be included by…. 193 194 Modal Combination Cl. 7.8.4.4 (contd…) Alternate Method to CQC Response Quantity could be any response quantity of interest: Use SRSS (Square Root of Sum of Squares) if the natural modes are not closely-spaced. Base shear, base moment, … Force resultant in a member, e.g., 2 λ = λ1 + λ2 + λ2 + λ2 + .... 2 3 4 Moment in a beam at a given location, Axial force in column, etc. Use Absolute Sum for closely-spaced modes Deflection at a given location λ = λ1 + λ 2 + λ 3 + λ 4 + ... To appreciate the alternative method, consider two examples. 195 196 Example 1 on Modal Combination: Example 1 on Modal Combination (contd…) For first five modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure. Mode 2 3 4 0.95 0.35 0.20 0.14 1.05 2.86 5.00 7.14 9.09 Response Quantity 1100 350 As per section a) in Cl. 7.8.4.4, we can use Square Root of Sum of Squares (SRSS) method to obtain resultant response as 0.11 Natural Frequency As per Cl. 3.2, none of the modes are closelyspaced modes. 5 Natural Period 197 1 All natural frequencies differ from each other by more than 10%. 230 150 = (1100) 2 + (350) 2 + ( 230) 2 + (150) 2 + (120) 2 = 1193 120 198 33
  • Example 2 on Modal Combination Example 2 on Modal Combination (contd…) As per Cl. 3.2, modes 2 and 3 are closed spaced since their natural frequencies are within 10% of the lower frequency. Similarly, modes 5 and 6 are closely spaced. Combined response of modes 2 and 3 as per section b) in Cl.7.8.4.4 = 230+190=420 Combined response of modes 5 and 6 = 90 + 80 = 170 Combined response of all the modes as per section a) For first six modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure. Mode 1 3 4 Natural period (sec) 0.94 0.78 2 0.74 0.34 0.26 0.25 Natural frequency (Hz) 1.06 1.28 1.35 2.94 3.85 4.00 Response Quantity 850 190 200 80 230 5 90 6 199 = (850) 2 + (420) 2 + (200) 2 + (170) 2 = 984 200 Lumped Mass Model for Cl. 7.8.4.5 Dynamic Analysis as per Cl. 7.8.4.5 The analysis procedure is valid when a building can be modeled as a lumped mass model with one degree of freedom per floor (see fig. next slide) If the building has significant plan irregularity, it requires three degrees of freedom per floor and the procedure of Cl. 7.8.4.5 is not valid. X3(t) X2(t) X1(t) 201 202 Summary Dynamic analysis requires considerable skills. Just because the computer program can perform dynamic analysis: it is not sufficient. One needs to develop in-depth understanding of dynamic analysis. Lecture 3 There are approximate methods (such as Rayleigh’s method, Dunkerley’s method) that one should use to evaluate if the computer results are right. This lecture covers Sections 7.9 to 7.11 IS:1893-2002(Part I) It is not uncommon to confuse between the units of mass and weight when performing dynamic analysis. Leads to huge errors. 203 204 34
  • Torsion Buildings (Section 7) • Uncertainties Sub-sections Cl. 7.1: Regular and Irregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight Cl. 7.5: Design Lateral Force Cl. 7.6: Fundamental Natural Period Cl. 7.7: Distribution of Design Force Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations Cl. 7.12 M iscellaneous – Location of imposed load – Contributions to structural stiffness • Accidental Eccentricity – Torsion to be considered in Symmetric Buildings • Design Eccentricity 1.5 esi + 0.05 bi e di = Worst of   esi − 0.05bi This lecture covers sub-sections 7.9 to 7.11 bi 205 206 Design eccentricity First Equation for Design Eccentricity Now the equation for design eccentricity is: The intention is to add the effect of accidental eccentricity to 1.5 times calculated eccentricity. Hence, the first equation should be taken to mean having + and - sign for the second term, whichever is critical: 1.5esi+0.05bi edi = esi-0.05bi Notice: First equation has 1.5 times the computed eccentricity, plus additional term due to accidental eccentricity edi = 1.5esi ± 0.05bi Accidental eccentricity is specified as 5% of plan dimension. Second equation does not have factor of 1.5, and sign of accidental eccentricity is different. In lecture 2, we discussed dynamic amplification of 1.5 and the accidental eccentricity. 207 208 Torsion… Torsion… First Equation for Design Eccentricity (contd…) – Two cases of Design Eccentricity bi esi CM* CM CS CM CM* CS 0.05bi esi 0.5esi 1.5esi + 0.05bi Calculated locations of CM and CR CR 0.05bi CM CR ith CM CM floor * esi 1.5esi+0.05 bi esi − 0.05bi Location CM* to be used in analysis for first eqn. of cl. 7.9.2 Considering EQ in Y-Direction 209 210 35
  • Second Equation for Design Eccentricity Second Equation for Design Eccentricity (contd…) bi In second equation, it is expected that there is accidental eccentricity in the opposite sense, i.e., it tends to oppose the computed eccentricity. esi Calculated locations of CM and CR CM CR ith floor Hence, factor 1.5 is not applied to the computed eccentricity. Again, this equation also should be understood to mean having + and - sign for second term, whichever is critical: * CM CR CM edi = esi ± 0.05bi Location CM* to be used in analysis for first eqn. of cl. 7.9.2 esi 0.05 bi Considering EQ in Y-Direction 211 212 Torsion… Torsion… Torsion… Torsion… • Incorporating the provision in practice • Incorporating the provision in practice… 1.5 esi + 0.05bi edi =   esi − 0.05bi CS – Effect of shear and torsion (esi) • Analysis A CM 213 CS CM 214 Torsion… Torsion… Torsion… Torsion… • Incorporating the provision in practice… • Incorporating the provision in practice… – Effect of shear only – Effect of shear, torsion esi and 0.05bi • Analysis B • Analysis C CS CM CS CM CM* 0.05bi 215 216 36
  • Definition of Centre of Rigidity Torsion… Torsion… • Incorporating the provision in practice… Earlier we defined Centre of Rigidity as: – Solution If the building undergoes pure translation in the horizontal direction (that is, no rotation or twist or torsion about vertical axis), the point through which the resultant of the restoring forces acts is the Centre of Rigidity. • Effect of esi only A-B • Effect of 0.05bi only This definition was for single-storey building. How do we extend it to multi-storey buildings? Recall that I mentioned in Lecture 2 that we will not distinguish between the terms Centre of Rigidity and Centre of Stiffness. C-A • Effect of 1.5esi+0.05bi along with shear B+1.5(A-B)+(C-A) = 0.5(A-B)+C 217 218 CR for Multi-Storey Buildings All Floor CR Definition It can be defined in two ways: Centre of rigidities are the set of points located one on each floor, through which application of lateral load profile would cause no rotation in any floor. All Floor Centre of Rigidity, and Single Floor Centre of Rigidity As per this definition, location of CR is dependent on building stiffness properties as well as on the applied lateral load profile. 219 220 All Floor Definition of CR Single Floor CR Definition Centre of rigidity of a floor is defined as the point on the floor such that application of lateral load passing through that point does not cause any rotation of that particular floor, while the other floors may rotate. CR Fny F(j+1)y CR Fjy CR F(j-1)y CR F2y F1y 221 CR This definition is independent of applied lateral load. No rotation in any floor CR Figure 1: ‘All floor’ definition of center of rigidity Fig. Dhiman Basu 222 37
  • Single Floor Definition of CR CR Choice of Definition Question is: which definition of CR to choose for multi-storey buildings? In fact, some people also use the concept of Shear Center in place of CR. But, we need not concern ourselves about it. Results could be somewhat different depending on which definition is used. But, the difference is not substantial for most buildings. jth floor does not rotate (other floors may rotate) Use any definition that you find convenient to use. For computer-aided analysis, the all-floor definition is more convenient. Fig. Dhiman Basu 223 224 To Calculate Eccentricity To Locate CR Need to locate The way we defined it, one needs to apply lateral loads at the CR. Centre of Mass, and Centre of Rigidity But, we do not know CR in the first place. Centre of Mass is easy to locate. Notice the condition that the floor should not rotate. Unless there is a significant variation in mass distribution, we take it at geometric centre of the floor. Hence, we could apply the load at CM, and restrain the floor from rotation by providing rollers The resultant of the applied load and reactions at the rollers will pass through CR Locating CR is not so simple for a multi-storey building. 225 226 To Locate All-Floor CR To Locate Single-Floor CR Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement Column shear Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement Lateral load proportional to the mass distribution distributed along the floor length (a) Lateral loads are applied at all floors of the constrained model Column shear Resultant of column shears passes through the center of rigidity of the floor Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement (a) Lateral load is applied at the constrained floor (b) Free body diagram of a particular floor Fig. Dhiman Basu 227 Lateral load proportional to the mass distribution distributed along the floor length Resultant of column shears passes through the center of rigidity of the floor (b) Free body diagram of a particular floor Fig. Dhiman Basu 228 38
  • Alternative to Locating CR Superposition Method It is tedious to locate CR’s first and then calculate eccentricity. One could follow an alternate route using computer analysis, provided one is using AllFloor Definition. This method is based on superposition concept and was first published by Goel and Chopra (ASCE, Vol 119, No. 10). Apply lateral load profile at the CM’s and analyse the building; say the solution is F1 This incorporates the effect of computed eccentricity (without dynamic amplification or accidental ecc.) Apply lateral load profile at CM’s but restrain the floors from rotating; say this solution is F2 This amounts to solving the problem as if the lateral loads were applied at the CRs since the floors did not rotate. The difference of F1 and F2 gives the solution due to torsion caused by computed eccentricity. 229 230 Superposition Method (contd…) Superposition Method (contd…) Hence, solution for loads applied at 1.5 times computed eccentricity = solution F1 + 0.5(solution F1 – solution F2) To this, add solution due to accidental torsion: Loads applied at CMs Floors can translate and rotate Solution F1 Apply on every floor a moment profile equal to load profile times accidental eccentricity; say solution F3 Loads applied at CMs Floors can only translate Solution F2 Fig. CVR Murty 231 232 Suggestions on Cl.7.9 Superposition Method (contd…) Following solution for ed = 1.5es + 0.5b i In Cl.7.9.1, the following statement should be deleted: F1 + 0.5 (F1 – F2) ± F3 However, negative torsional shear shall be neglected Following solution for ed = e s − 0.5b i F1 ± F3 This statement is needed only when second equation of design eccentricity is not specified. Notice that Cl.7.8.4.5 says if highly irregular buildings are analyzed as per 7.8.4.5, while 7.8.4.5 says that it is applicable only for regular or nominally irregular buildings! Indeed, 7.8.4.5 is not applicable to buildings highly irregular in plan. 233 234 39
  • Bldgs with Soft Storeys Cl. 7.10 Most of the time, soft storey building is also the weak storey building. In the code, distinction between soft storey and weak storey has not been made. Soft/weak storey buildings are well-known for poor performance during earthquakes. In Bhuj earthquake of 2001, most multistorey buildings that collapsed had soft ground storey. Buildings with Soft Storeys… Storeys… • Need to increase Stiffness and Strength of Open or Soft Storeys • Inverted pendulum !! 235 236 Buildings with Soft Storeys… Storeys… Bldgs with Soft Storeys Cl. 7.10 (contd…) • Dynamic Analysis – Include strength and stiffness of infills – Inelastic deformations in members OR Static Design Fig from Murty et al, 2002 Open ground story – Design columns and beams in soft storey for 2.5 times the Storey Shears and Moments calculated under seismic loads – Design shear walls for 1.5 times the Storey Shears calculated under seismic loads Bare frame Notice that the soft-storey is subject to severe deformation demands during seismic shaking. 237 238 Buildings with Soft Storeys Cl. 7.10 (contd…) Buildings with Soft Storeys Cl. 7.10 (contd…) This clause gives two approaches for treatment of soft storey buildings. First approach is as per 7.10.2 There are reservations on the way entire Cl. 7.10 has been included in the code. First approach is too open ended and does not enable the designer to implement it. Second approach is too empirical and may be impractical in some buildings. It is a very sophisticated approach. Based on non-linear analysis. Code has no specifications for applying this approach. Cannot be applied in routine design applications with current state of the practice in India. Also note that Table 5 defines Soft Storey and Extreme Soft Storey And yet, nowhere the treatment is different for these two! Second approach as per 7.10.3 is an empirical provision. 239 240 40
  • Buildings with Soft Storeys Cl. 7.10 (contd…) Deformations Cl. 7.11 We need considerable amount of research on Indian buildings with soft storey features in order to develop robust design methodology. For a good seismic performance, a building needs to have adequate lateral stiffness. Low lateral stiffness leads to: Large deformations and strains, and hence more damage in the event of strong shaking Significant P-∆ effect Damage to non-structural elements due to large deformations Discomfort to the occupants during vibrations. Large deformations may lead to pounding with adjacent structures. 241 242 Deformations C.7.11… C.7.11… Deformations Cl. 7.11 (contd…) • Inter-storey Drift Note that real displacement in a strong shaking will be much larger than the displacement calculated for design seismic loads – Storey drift under design lateral load with partial load factor 1.0 δ < 0.004hi Because design seismic force is a reduced force. δ As a rule of thumb, the maximum displacement during the MCE shaking (e.g., PGA of 0.36g in zone V) will be about 2R times the computed displacement due to design forces. hi 243 244 Computation of Drift Computation of Drift (contd…) Note that higher the stiffness, lower the drift but higher the lateral loads. Hence, Thus, in computation of drift: Stiffness contribution of non-structural elements and non-seismic elements (i.e., elements not designed to share the seismic loads) should not be included. For computation of T for seismic design load assessment, all sources of stiffness (even if unreliable) should be included. For computation of drift, all sources of flexibility (even if unreliable) should be incorporated. 245 This is because such elements cannot be relied upon to provide lateral stiffness at large displacements All possible sources of flexibility should be incorporated, e.g., effect of joint rotation, bending and axial deformations of columns and shear walls, etc. 246 41
  • Para 2 of Cl. 7.11.1 Para 3 of Cl. 7.11.1 Cl. 7.8.2 required scaling up of seismic design forces from dynamic analysis, in case these were lower than those from empirical T. This para allows drift check to be performed as per the dynamic analysis which may have given lower seismic forces, i.e., no scaling-up of forces needed for drift check. This para allows larger than the specified drift for single-storey building provided it is duly accounted for in the analysis and design. 247 248 Compatibility of Non-Seismic Elements (Cl. 7.11.2) Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…) Important when not all structural elements are expected to participate in lateral load resistance. During shaking, gravity columns do not carry much lateral loads, but deform laterally with the shear walls due to compatibility imposed by floor diaphragm Moments and shears induced in gravity columns due to the lateral deformations may cause collapse if adequate provision not made. ACI Code for RC design has a separate section on detailing of gravity columns to safeguard against this kind of collapse. Examples include flat-plate buildings or buildings with pre-fabricated elements where seismic load is resisted by shear walls, and columns carry only gravity loads. During 1994 Northridge (Calif.) earthquake, many collapses due to failure of gravity columns. 249 250 Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…) Pi ∆ i F1 Gravity columns Shear Wall F2 F3 ∆ Floor slab Imposed displ. at all floors Gravity column 251 h1 h2 P4 F4 Shear Wall Since deflections are calculated using design seismic force (which is a reduced force), the deflection is to be multiplied by R. Multiplier R could be debated since it will only ensure safety against Design Basis Earthquake. P2 P3 Floor slab ∆ Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…) P1 For safety against Maximum Considered Earthquake, multiplier should be (2R). h3 h4  n  Pi ∆ i + ∑ Fi  ∑ h j   j= 1  252 42
  • Separation Between Adjacent …Cl. 7.11.3 Separation Between Adjacent …Cl. 7.11.3 (contd…) During seismic shaking, two adjacent units of the same building, or two adjacent buildings may hit each other due to lateral displacements (pounding or hammering). This clause is meant to safeguard against pounding. Multiplication with R is as explained earlier: since deflection is calculated using design seismic force which are reduced forces. 253 Pounding effect is much more serious if floors of one building hit at the mid height of columns in the other building. Hence, when two units have same floor elevations, the multiplier is reduced from R to R/2. 254 Separation Between Adjacent …Cl. 7.11.3 Separation Between Adjacent …Cl. 7.11.3 (contd…) Potential pounding location Two adjacent buildings Two adjacent units of same building Amount of separation Potential pounding location • Floors levels are at same elevation ∆> Building 1 Building 2 Building 1 Building 2 ( R ⋅ δ 1 design + δ 2 design 2 ) • Floors levels are at different elevations a ( b ∆ > R ⋅ δ 1 design + δ 2 design ) R1 ⋅ δ 1 R2 ⋅ δ 2 Pounding in situation (b) is far more damaging. 255 256 Separation Between Adjacent …Cl. 7.11.3 (contd…) To handle pounding by roof of one unit to the middle of columns of the other unit: Soft Timber Structural Grade Steel Section 7.12: Miscellaneous, and Section 7.1: Regular and Irregular Configuration IS:1893-2002(Part I) Fig. From Arnold and Reitherman 257 258 43
  • Foundations Cl. 7.12.1 Foundations Cl. 7.12.1 (contd…) This clause is to prevent use of foundation types vulnerable to differential settlement. In zones IV and V, ties to be provided for isolated spread footings and for pile caps Recall newly-introduced Note 7 inside Table 1 of the code which states: Isolated R.C.C. footing without tie beams, or unreinforced strip foundation shall not be permitted in soft soils with N<10. Except when footings directly supported on rock 259 This note is applicable for all seismic zones. It would be better to bring this note inside Cl. 7.12.1. 260 Cantilevers and Projections Foundations Cl. 7.12.1 (contd…) • Towers, Parapets, Stacks, Balconies (Small) Ties to be designed for an axial load (in tension and in compression) equal to Ah/4 times the larger of the column or pile cap load. – Design of these attachments – Design of their connections to main structure This is fairly empirical, and the specification appears on the low side. Many structural engineers design the ties for 5% of the larger of the column or pile cap load. • Design force – 5× vertical seismic coefficient for horizontal projections – 5× horizontal seismic coefficient for vertical projections Any other alternative design approaches? 5Ah 5Av 261 262 Compound Walls Cl. 7.12.3 To be designed for design horizontal coefficient Ah and importance factor = 1 263 Cl. 7.1 Regular and Irregular Configuration 264 44
  • Building Configuration Building Configuration… Configuration… • Plan Irregularities • Configuration emphasised – Torsion Irregularity – Comprehensive section on identifying irregularities – Qualitative definitions of irregular buildings Heavy Mass • Two types Irregular Orientation of Lateral Force Resisting System – Plan Irregularities – Vertical Irregularities ∆1 265 Floor ∆2  ∆ + ∆2  ∆ 2 > 1.2 1   2  266 Torsional Irregularity Torsional Irregularity (contd…) Look at the top two figures of page. 19 (Fig. 3) These figures were taken from NEHRP Commentary where it appears as follows: Can you make out anything what this figure is trying to show? Heavy Mass Vertical Components of Seismic Resisting System The figures have not been traced correctly for IS:1893! There is a problem with these two figures! 267 268 Building Configuration… Configuration… Building Configuration… Configuration… – Re-entrant Corners – Diaphragm Discontinuity Flexible A L A Opening A A L 269 A A > 0.15 − 0.20 L Opening 270 45
  • Out-of-Plane Offsets Out- of- Building Configuration… Configuration… – Out of Plane Offsets • This is a very serious irregularity wherein there is an out-of-plane offset of the vertical element that carries the lateral loads. • Such an offset imposes vertical and lateral load effects on horizontal elements, which are difficult to design for adequately. • Again, there is a problem in figure for this in the code – Shear walls are not obvious. 271 Shear Wall Shear Wall Shear Wall 272 Building Configuration… Configuration… Building Configuration… Configuration… – Non-Parallel System • Vertical Irregularities – Stiffness Irregularity (Soft Storey) y x ki < 0.7ki +1 ki+1 ki ki-1 273 274 Mass and Stiffness Irregularity Building Configuration… Configuration… – Mass Irregularity • induced by the presence of a heavy mass on a floor, say a swimming pool. Wi+1 Wi Wi-1 275 k +k +k  ki < 0.8 i +1 i + 2 i + 3  3   • It is really the ratio of mass to stiffness of a storey that is important. • Our code should provide a waiver from mass and stiffness irregularities if the ratio of mass to stiffness of two adjacent storeys is similar. Wi > 2 Wi −1 Wi > 2 Wi +1 276 46
  • Building Configuration… Configuration… Building Configuration… Configuration… – Vertical Geometric Irregularities L1 A A A A > 0.15 − 0.20 L L2 > 1.5L1 L1 L2 L L A A L L2 277 278 Building Configuration… Configuration… Building Configuration… Configuration… – In-plane Discontinuity in Lateral Load Resisting Elements – Strength Irregularity (Weak Storey) S i < 0.8Si +1 Upper Floor Plan Si+1 Si Si-1 Lower Floor Plan 279 280 Building Configuration… Geometrically building may appear to be regular and symmetrical, but may have irregularity due to distribution of mass and stiffness. It is better to distribute the lateral load resisting elements near the perimeter of the building rather than concentrate these near centre of the building. (a) (b) Arrangement of shear walls and braced frames-not recommended. Note that the heavy lines indicate shear walls and/or braced frames Fig. From NEHRP Commentary (a) (b) Arrangement of shear walls and braced frames- recommended. Note that the heavy lines indicate shear walls and/or braced frames 281 282 47
  • Diaphragm Discontinuity Diaphragm Discontinuity (contd…) Diaphragm discontinuity changes the lateral load distribution to different elements as compared to what it would be with rigid floor diaphragm. Also, it could induce torsional effects which may not be there if the floor diaphragm is rigid. Observe the top two figures of page 20. Notice the words “mass resistance eccentricity” do not make sense. Fig in Code Again, these are from NEHRP Commentary and not traced correctly in our code. RIGID FLEXIBLE O DIAPHRAGM P E N DIAPHRAGM Fig in NEHRP Vertical Components of Seismic Resisting System Discontinuity in Diaphragm Stiffness 283 284 Problems with Irregularities Problems with Irregularities (contd…) In buildings with vertical irregularity, load distribution with building height is different from that in Cl. 7.7.1. In irregular building, there may be concentration of ductility demand in a few locations. Special care needed in detailing. Just dynamic analysis may not solve the problem. Dynamic analysis is required. In buildings with plan irregularity, load distribution to different vertical elements is complex. Floor diaphragm plays an important role and needs to be modelled carefully. A good 3-D analysis is needed. 285 286 Code on Irregularity Our code has simplistic method of treating the irregularities. For irregular buildings, it just encourages dynamic analysis. Compare Tables of NEHRP shown earlier in this lecture. Seismic Force Estimation For each type of irregularity and for each seismic performance category, different requirements are imposed. Dynamic analysis is not always sufficient for irregular buildings, and Dynamic analysis is not always needed for irregularities. 287 288 48
  • Design Seismic Lateral Force • Two ways of calculating – Equivalent Static Method • Seismic Coefficient Method Single mode dynamics Simple and regular structures – Dynamic Analysis Method Origin of Equivalent Static Method • Response Spectrum Method Multi-mode dynamics Irregular structures • Time History Method Special structures 289 290 Dynamics of 2 DOF System Dynamics of 2 DOF System… System… • Lateral Force • Dynamic Characteristics m2 m2 k2 k2 m1 m1 k1 k1 Property Property Mode 1 Mode 1 Equivalent SDOFs Mode 2 Mode 2 M1 M2 K1 Property Property Mode 1 Mode 1 PSA2 K2 M2 T2 = 2π / ω2 K1 M1 T1 = 2π / ω1 PSA1 ω2 = ω1 = Natural Period 291 T1 292 Dynamics of 2 DOF System… System… SD1 = SD m2 k2 m1 k1 Mode 1 Mode 1 Γ1 = {ϕ}T [m ]{1} 1 M1 {u}1 = SD1{ϕ}1 Γ1 u11  =  u12  293 SD2 = 2 ω1 ω2 2 m1 F12 F22 F11 F21 k1 Property Property Lateral Displacement T PSA2 • Lateral Force… m2 Mode Participation Factor T2 T PSA1 Dynamics of 2 DOF System… System… • Lateral Force… k2 PSA (g) K2 PSA Natural Frequency Mode 2 Mode 2 PSA (g) Mode 2 Mode 2 Γ2 = Property Property Mode 1 Mode 1 Mode 2 Mode 2 {ϕ}T [m ]{1} 2 M2 Lateral Force F11   F12  {F}1 = [k ]{u}1 =  {u}2 = SD2 {ϕ}2 Γ2 u21  =  u22  Base Shear 2 VB1 = ∑ F1i i =1 294 F21   F22  {F}2 = [k ]{u}2 =  2 VB 2 = ∑ F2i i =1 49
  • Dynamics of 2 DOF System… System… • Lateral Force m2 k2 Dynamics of 2 DOF System… System… • Equivalent Static Force F12 F22 F11 m1 – Since mode 1 is dominant F21 F12 k1 Property Property Mode 1 Mode 1 F11 F11 (VB1 )2 + (VB2 )2 VB = Resultant Base Shear Mode 2 Mode 2 F12 Usually, for regular buildings 295 296 MDOF System • Vibration modes k3 k2 k1 m3 VB1 Mode 1 Mode 1 VB ≈ VB1 MDOF System… System… Mode 2 Mode 2 Mode 3 Mode 3 • Lateral Force k3 m2 k2 m1 ( Property Property k1 ) m3 Mode 1 Mode 1 Mode 2 Mode 2 Mode 3 Mode 3 m2 m1 Eigen Value Problem : [k ] − ω2 [m ] {ϕ} = {0} m1 0 [m] =  0 m2  0 0   k11 [k ] = k21   0  297 Mode 1 Mode 1 VB Building Building  VB1   VB2   V > V      B   B  k12 k 22 k 32 0  0   m3   ω1 , {ϕ}1 ω2 ,{ϕ}2 ω3 ,{ϕ}3 Property Property M1 , K 1 M 2 , K2 M 3 , K3 Base Shears 0  k 23    k 33  298 First Mode Analysis • Typical first mode shapes VB2 VB1 VB3 Response of the whole building is usually Response of the whole building is usually that of its dominant first mode. that of its dominant first mode. First Mode Analysis… Analysis… • Base Shear VB using T1 VB = M ⋅ PSA1 Linear ⋮     ⋮  h i   {ϕ}1 = ϕ01i ⋅      H   ⋮     ⋮   Low-to-Medium Period Buildings Low-to-Medium Period Buildings (T<1s) (T<1s) 299 Parabolic ⋮     ⋮  2 h {ϕ}1 = ϕ01i ⋅  i       H   ⋮     ⋮   • Distribution of force along height W h2 Fi = VB ⋅ N i i Fi 2 ∑ Wk h k Long Period Buildings Long Period Buildings (T>2s) (T>2s) k =1 300 50
  • Equivalent lateral Force Method • IS:1893 (Part1) - 2002 Perform the usual static elastic structural analysis with these forces. Fi No dynamic analysis is done. (But, it is hidden in concept of Response Spectrum used in assumed vertical distribution of Base Shear VB.) Example VB 301 302 Three Storey Frame Building • Seismic Zone V Step 1 • Decide a structural system – OMF and SMF 3m 5m 3.0m 3m 3.0m 4.0m 5m 4m 3.5m 5.0m 3m 3.5m 3.5m 5.0m 303 3.0m 3.5m 3.5m Plan 3.0m 3.5m Elevation 304 STEP 2 • Estimate Seismic Weight W Step 2… 2… • Estimate Seismic Weight W… – Clause 7.4 of IS:1893(1)-2002 – Imposed load as per Clause 7.3 • W = Full DL + Part LL • % of Imposed Load to be considered from Table 8 • No imposed load on roof – Unit weights of dead loads from IS:875(1) • Steel sections : 78.5 kN/m3 • Reinforced concrete : 25 kN/m3 • Masonry infill : 19.0 kN/m3 • Mortar plaster : 20.0 kN/m3 • Floor finish on floors : 1 kN/m2 • Weathering course on roof : 2.25 kN/m2 Imposed Load (kN/m2) % of Load to be considered ≤ 3.0 25 > 3.0 50 – Imposed loads from IS 875(2) 305 • On floors : 3.0 kN/m2 • On roof : 0.75 kN/m2 306 51
  • Step 3 Step 2… 2… • Estimate Seismic Weight W… • Estimate Design Horizontal Acceleration Spectrum Value Ah – Total Seismic Weight W W = 4900 kN – Clause 6.4 of IS:1893(1)-2002 Maximum Elastic Acceleration DL=1340 kN; LL=0 S  Z  a (T ) I  g   Ah (T ) =  2R 3m DL=1620 kN; LL=75 kN 3m DL=1800 kN; LL=75 kN 4m 3.5m 3.0m 3.5m 307 Reduction to account for ductility and overstrength 308 Step 3… 3… Step 3… 3… • Estimate Ah… • Estimate Ah… – Seismic Zone Factor Z – Response Reduction Factor R from Draft IS:800 Seismic Zone II III IV Z 0.10 0.16 0.24 4 OMF R= 5 SMF V 0.36 – Importance factor I S.No. Building I 1 Important, Community & Lifeline Buildings 1.5 2 All Others 1.0 309 310 Step 3… 3… • Estimate Ah… Step 3… 3… • Estimate Ah… – Empirical Natural Period Ta – Structure Flexibility Factor Sa/g 0.085 h 0.75 = 0.085 × 10 0.75 = 0.48 sec Bare Frame   Ta =   0.09 h = 0.09 × 10 = 0.28 sec Infilled Frame  10  d • Structure on Type I (Rock or Hard Soil) • 5% damping Sa /g 2.5 2.08 The first expression is independent of the base dimension of the building!! 311 Rock/ Hard Soil 1.0 Note 0 0.28 312 0.48 Natural Period Ta 52
  • Step 4 Step 3… 3… • Estimate Ah… • Calculate Design Base Shear Vb – OMF – Clause 7.5.3 of IS:1893(1)-2002  0.36 × 1.0 × 2.5 = 0.15 Infilled Frame  2× 3 Ah =  0.36 × 1.0 × 2.08  = 0.125 Bare Frame  2× 3 VB = Ah (Ta )× W 0.09× 4900= 441kN SMF VB =  0.15× 4900= 735kN OMF – SMF  0.36 × 1.0 × 2.5 = 0.090 Infilled Frame  2× 5 Ah =  0.36 × 1.0 × 2.08  = 0.075 Bare Frame  2× 5 313 314 Step 5 Step 5 • Distribute Design Base Shear Vb along height • Locate point of application of Qi at each floor – At each floor level at design eccentricity – Clause 7.7.1 of IS:1893(1)-2002 Qi = VB • Clause 7.9.1 of IS:1893(1)-2002 Wi hi2  1.5esi + 0.05bi , or edi =  esi − 0.05bi  N ∑ Wjh2 j j =1 EQ EQ b 238.4 kN 397.4 kN 148.9 kN 53.7 kN 248.1 kN 89.5 kN EQ EQ SMF SMF OMF OMF 315 esi 316 Step 5… 5… b Step 5… 5… • Locate point of Qi … • Locate point of Qi … – Two cases of Design Eccentricity CM* CM CS – Incorporating the provision in practice 1.5 esi + 0.05bi edi =   esi − 0.05bi CM CM* CS CS 0.05bi esi 0.5esi 1.5esi + 0.05bi 317 CM 0.05bi esi esi − 0.05bi 318 53
  • Step 5… 5… Step 5… 5… • Locate point of Qi … • Locate point of Qi … – Incorporating the provision in practice… – Incorporating the provision in practice… • Effect of shear and torsion: esi • Effect of shear only Analysis A Analysis B CS CS CM 319 CM 320 Step 5… 5… Step 5… 5… • Locate point of Qi … • Locate point of Qi … – Incorporating the provision in practice… – Incorporating the provision in practice… • Effect of shear, torsion esi and 0.05bi • Solution Analysis C CS CM Effect of esi only A A A-B Effect of 0.05bi only CS CM B B C-A CS CM CM* Effect of 1.5esi+0.05bi along with shear B+1.5(A-B)+(C-A) = 0.5(A-B)+C 322 Step 6 Step 6… 6… • Load Combinations • Load Combinations… – Lateral force resisting system orthogonal in two plan directions – Lateral force resisting system non-parallel in two plan directions • 9 load cases for unsymmetrical buildings • Consider design based on one direction at a time y Can reduce to 5 for beams ELx 1.7 (DL + LL) 1.3 (DL + LL ± ELx) 1.3 (DL + LL ± ELy) 1.7 (DL ± ELx) 1.7 (DL ± ELy) x y x x 323 CS CM CM* 0.05bi 0.05bi 321 C C 324 ELy 54
  • Step 6… 6… Step 6… 6… • Load Combinations… • Load Combinations… – Two/Three Component Motion – Non-parallel system • Response (EL) due to earthquake force is maximum of :: • Consider design based on one direction at a time • Replace ± ELx ± 0.3ELy ± 0.3ELz  EL = ± ELy ± 0.3ELz ± 0.3ELx ± EL ± 0.3EL ± 0.3EL z x y  ELx by (ELx ± 0.3ELy) and ELy by (ELy±0.3ELx) in the combinations for orthogonal systems Thus, 17 load cases for unsymmetrical buildings 1.7 (DL + LL) 1.3 (DL + LL ± (ELx± 0.3ELy)) 1.3 (DL + LL ± (ELy±0.3ELx)) 1.7 (DL ± (ELx ± 0.3ELy)) 1.7 (DL ± (ELy±0.3ELx)) 325 • Alternately, SRSS Method may be employed as :: EL = (ELx )2 + (ELy )2 + (ELz )2 • If any one component is not being considered, the corresponding response quantity is dropped. 326 55