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Presentation on Higher Order Analysis of Steel Space Frames
1. “Higher Order Analysis of Steel Space
Frames”
By
Prof. Vaidya Onkar A.
SRES SCOE, Kopargaon
2. Contents
• Introduction
• Literature review
• Aims & Objectives
• Analysis of Frame for validation of software
• Analysis of Space frame using different loading combinations and by
all analytical methods
3. Introduction
1.First Order Elastic Analysis (FOEA)
2.Second Order Elastic Analysis (SOEA)
3.First Order Inelastic Analysis (FOIA)
4.Second Order Inelastic Analysis (SOIA)
4. Introduction
FIRST ORDER ANALYSIS
Internal Forces & displacements are evaluated in relation to the undeformed
geometry of the structure.
Deformations & Internal Forces are proportional to the applied loads.
Internal forces & displacements may be obtained using well known methods
(Force method, displacement method etc.)
SECOND ORDER ANALYSIS
Deformation of structure as well as members is considered in evaluation of
internal forces & displacements
i.e. P-δ effects & P-Δ effects.
Deformations & Internal Forces are not proportional to the applied loads.
6. Literature Review
SR.
NO.
NAME OF AUTHOR PUBLISH
YEAR
NAME OF PAPER
01.
Agrawal Nikhil, Mittal
Achal Kr., Gupta V. K.
2009
Design of a gable frame based on wind
forces from a few international design
wind codes
02.
Alvarenga R., Silveira A.
M.
2009
Second-order plastic-zone analysis of
steel frames - Part II: effects of initial
geometric imperfection and residual
stress
03.
Dalal Sejal P., Vasanwala
S. A., Desai A. K.
2012
Comparison of steel moment Resisting
frame designed by elastic design and
performance based plastic design
method Based on the inelastic response
analysis
04.
Donald W. White, Jerome
F. Hajjar
1991
Application of Second Order Elastic
Analysis in LRFD: Research to Practice
05.
Eroz Murat ,White Donald
W. and Des Roches
Reginald
2008
Direct Analysis and Design of Steel
Frames Accounting for Partially
Restrained Column Base Conditions
7. 06.
Ingale S. S., Shiyekar M.
R.
2013
Second order inelastic behaviour of
steel moment resisting frame
07.
Iu C.K., Chen W.F., Chan
S.L., Ma T.W.
2008
Direct Second-Order Elastic Analysis
for Steel Frame Design
08. J. Dario Aristizabal-Ochoa 2003
Elastic Stability and Second-Order
Analysis of Three-Dimensional Frames:
Effects of Column Orientation
09.
Mittal Arcelor,
TragerPeiner and Corus
2008
Single-storey steel buildings part 4:
Detailed design of portal frames
10.
Ronald D. Ziemian, Alan
Ro Miller
1997
Inelastic analysis and design: frames
with members in Minor-axis bending
11.
Ronald D. Ziemian,
William McGuire,
Gregory G. Deierlein
1993
Inelastic limit states design. Part I:
Planar frame studies
8. SUMMARY
Simple Elastic analysis is most popular but least complete method
This method does not reflect actual behaviour, buckling and stability assessment of steel
frames and also it does not consider plastic behaviour of members and P-Δ and P-δ effects.
Whereas Second Order Inelastic analysis is most realistic, complete and accurate method
We can predict the actual behavior and stability assessment by using this advanced
analysis method but it makes method more complex
This analysis includes both geometric and material non-linearity’s, effects of residual
stresses, initial geometric imperfections
The focus of previous studies was to make advanced analysis method in more simplified
manner which can help structural designer to use this method in a more convenient manner
9. Aims and objectives
1. Study of structural behavior of steel frames using different methods of
analysis.
1. Using first-order elastic and second-order inelastic analysis to find out
design actions on steel frame members and to arrive at selection of section.
1. To develop relation between analysis results of first-order elastic and
second-order inelastic analysis methods under following parametric studies
of multibay multistory steel frames for its direct use in structural design,
i) Number of bay.
ii) Number of storey.
iii) Load combinations.
10. Analysis of Frame for validation of software
Validation of MASTAN software
Problem:
In a warehouse, an area of 10mX40m is to be covered by rectangular frames to be placed at 5 m
cc. If floor consist of 150 mm thick RCC slab with 50 mm thick finishing, design section
of frame. The live load on frame is 5 kN/m2
.
Solution:
The load calculation and analysis is explained in book, “Limit state design in structural steel”.
Elastic Analysis Plastic analysis
Results:
Manual calculated Elastic moment = 340 kNmManual calculated Plastic moment = 478.12 kNm
Software calculated Elastic moment = 342.3 kNm Software calculated Plastic moment = 480.4 kNm
11. loading combinations & by all analytical
methods
Two bays, three bays and four bays up to five story & two frames are solved by FOEA and
SOIA methods using software and its results are compared. Out of these numbers of solution,
2 bay 3 storey & 2 frame analysis for DL+LL, DL+WL and DL+LL+WL combinations are
given as under.
Problem:
- Public building of 2 bay 3 storey and 2 frames
- Distance between two frame cc = 4m
- Thickness of slab = 150mm
- Live load intensity = 5 kN/m2
- Floor finish intensity = 1.5 kN/m2
- Wind Load = 12 kN at floor level
Solution for DL+LL:
For First order Elastic analysis :
Total DL+LL on external beam per meter = 26.30 + 6.67 = 32.97 kN/m
Total DL+LL on middle beam per meter = 33.30 + 13.33 = 46.63 kN/m
For Second order Inelastic analysis :
Factored DL+LL on external beam per meter = 1.5 X 32.97 = 49.455 kN/m
Factored DL+LL on middle beam per meter = 1.5 X 46.63 = 69.945 kN/m
12. combinations
FOEA (First order elastic analysis)
ISMB300--------Beam and Column
Properties Material properties:
Results: Max B.M. = 83.25 kNm
A 5.78E-03 m2
Izz (Ixx) 8.87E-05 m4
Iyy 6.00E-06 m4
J 2.51E-07 m4
Cw 1.23E-07 m6
Zzz(Zp = Zxx) 5.91E-04 m3
Zyy 8.57E-05 m3
E 200000000 kN/m2
v 0.3 -
Fy 250000 kN/m2
wt. Density 77.084 kN/m3
13. Analysis of Space frame using different loading combinations
SOIA (Second order inelastic analysis)
ISWB250--------Beam and Column
Properties Material properties:
Results: Max B.M. = 110.1 kNm
A 5.15E-03 m2
Izz (Ixx) 5.93E-05 m4
Iyy 1.20E-05 m4
J 1.20E-07 m4
Cw 1.74E-07 m6
Zzz(Zp = Zxx) 5.45E-04 m3
Zyy 1.20E-04 m3
E 200000000 kN/m2
v 0.3 -
Fy 250000 kN/m2
wt. Density 77.084 kN/m3
14. Analysis of Space frame using different loading
combinations
Solution for DL+WL:
Total DL intensity on external beam = 26.3 kN/m
Total DL intensity on middle beam = 33.3 kN/m
Wind load at floor level on each floor = 12 kN
For First order Elastic analysis :
Total DL intensity on external beam per meter = 7 + 18.4 + 0.9 = 26.3 kN/m
Total DL intensity on middle beam per meter = 7 X 2 + 18.4 + 0.9 = 33.3 kN/m
Wind load at floor level on each floor = 12 kN
For Second order Inelastic analysis :
Factored DL on external beam per meter = 1.5 X 39.45 = 39.45 kN/m
Factored DL on middle beam per meter = 1.5 X 33.30 = 49.95 kN/m
Factored WL at floor level on each floor = 1.5 X 12 = 18 kN
15. Analysis of Space frame using different loading combinations
FOEA (First order elastic analysis)
ISMB250--------Beam and Column
Properties Material properties:
Results: Max B.M. = 61.07 kNm
A 4.68E-03 m2
Izz (Ixx) 5.07E-05 m4
Iyy 4.08E-06 m4
J 1.87E-07 m4
Cw 5.75E-08 m6
Zzz(Zp = Zxx) 4.05E-04 m3
Zyy 6.52E-05 m3
E 200000000 kN/m2
v 0.3 -
Fy 250000 kN/m2
wt. Density 77.084 kN/m3
16. Analysis of Space frame using different loading combinations
SOIA (Second order inelastic analysis)
ISMB300--------Column ISMB175+(120*12)P--------Beam
Properties: Properties:
Results: Max B.M. = 89.52 kNm
A 5.78E-03 m2
Izz (Ixx) 8.87E-05 m4
Iyy 6.00E-06 m4
J 2.51E-07 m4
Cw 1.23E-07 m6
Zzz(Zp = Zxx) 6.80E-04 m3
Zyy 8.57E-05 m3
A 5.32E-03 m2
Izz (Ixx) 3.76E-05 m4
Iyy 4.38E-06 m4
J 1.90E-07 m4
Cw 3.83E-08 m6
Zzz(Zp = Zxx) 4.35E-04 m3
Zyy 7.30E-05 m3
17. Analysis of Space frame using different loading combinations
Solution for DL+LL+WL:
DL on external beam = 26.3 kN/m
DL on middle beam = 33.3 kN/m
LL on external beam = 6.67 kN/m
LL on middle beam = 13.33 kN/m
DL+LL on external beam = 32.97 kN/m
DL+LL on middle beam = 46.63 kN/m
Wind load at floor level on each floor = 12 kN
For First order Elastic analysis :
Total DL+LL on external beam per meter = 26.30 + 6.67 = 32.97 kN/m
Total DL+LL on middle beam per meter = 33.30 + 13.33 = 46.63 kN/m
Wind load at floor level on each floor = 12 kN
For Second order Inelastic analysis :
Factored DL+LL on external beam per meter = 1.2 X 32.97 = 39.564 kN/m
Factored DL+LL on middle beam per meter = 1.2 X 46.63 = 55.956 kN/m
Factored WL at floor level on each floor = 1.2 X 12 = 14.4 kN
18. combinations
FOEA (First order elastic analysis)
ISMB300--------Beam and Column
Properties Material
Properties:A 5.78E-03 m2
Izz (Ixx) 8.87E-05 m4
Iyy 6.00E-06 m4
J 2.51E-07 m4
Cw 1.23E-07 m6
Zzz(Zp = Zxx) 5.91E-04 m3
Zyy 8.57E-05 m3
E 200000000 kN/m2
v 0.3 -
Fy 250000 kN/m2
wt. Density 77.084 kN/m3
19. combinations
SOIA (Second order inelastic analysis)
ISMB175+(120*16)P--------Column & Beam
Properties Material Properties:
Results: Max B.M. = 94.12 kNm
A 6.28E-03 m2
Izz (Ixx) 4.75E-05 m4
Iyy 5.53E-06 m4
J 3.79E-07 m4
Cw 5.05E-08 m6
Zzz(Zp = Zxx) 5.28E-04 m3
Zyy 9.22E-05 m3
E 200000000 kN/m2
v 0.3 -
Fy 250000 kN/m2
wt. Density 77.084 kN/m3
20. Comparison of a typical case by all 4 analytical methods
Problem:
Public building of 3 bay 2 storey and 2 frames
Distance between two frame cc = 4m
Thickness of slab = 120mm
Live load intensity = 5 kN/m2
Floor finish intensity = 1.5 kN/m2
Wind Load = 12 kN on each frame
For Elastic analysis :
Total DL intensity on external beam per meter = 6 + 18.4 + 1 = 25.4 kN/m
Total DL intensity on internal beam per meter = 6 X 2 + 18.4 + 1 = 31.4 kN/m
Wind load at floor level on each floor = 12 kN
For Inelastic analysis :
Factored DL on external beam per meter = 1.5X 25.4 = 38.1 kN/m
Factored DL on internal beam per meter = 1.5 X 31.4 = 47.1 kN/m
Factored WL at floor level on each floor = 1.5 X 12 = 18 kN
Results:
First order Elastic Analysis (Max. B.M) = 55.05 kNm
First order Inelastic Analysis (Max. B.M) = 71.58 kNm
Second order Elastic Analysis (Max. B.M) = 55.22 kNm
Second order Inelastic Analysis (Max. B.M) = 71.78 kNm
