International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 5, Issue 3, March 2016
ISSN 2319 - 4847
Seismic Demand of Steel Structural Systems
M. Sudharani1 , Dr. G. Nandini Devi2
1
P.G. Student, Adhiyamaan College of Engineering, Hosur, Tamil Nadu, India
2
Professor, Adhiyamaan College of Engineering, Hosur, Tamil Nadu, India.
Abstract
Steel is the most useful material for construction of high rise buildings and large span structures for its immense strength,
ductility and flexibility. Nonlinear static pushover analysis is recommended by FEMA to assess the actual behaviour of
structures under seismic loading. Seismic codes consider a reduction in design loads by a factor called Response reduction
factor (R) since the structures possesses significant reserve strength (Over strength) and capacity to dissipate energy (Ductility).
The seismic demand parameters like Strength factor (Rs), Ductility factor (Rµ) are calculated using Capacity curve (Base shear
Vs Roof displacement) obtained from displacement controlled pushover analysis. Steel structural systems like OMF, SMF,
OMF with braces and OMF with shear wall of 10, 15 and 20 stories are designed and its performance is studied by pushover
analysis using ETABS 2015. The present study focuses on the evaluation of Response reduction factor (R) for the structural
system considered.
Keywords: Pushover analysis, Steel structural systems, Response reduction factor, Strength factor, Ductility factor.
1. INTRODUCTION
Steel is most used material for constructing large structures in the world. Due to its large strength to weight ratio, steel
structures tend to be more economical than concrete structures for tall buildings and large span buildings. Steel
structural systems are the moment resisting frames such as ordinary moment frames, special moment frames, ordinary
moment frame with steel bracing and ordinary moment frame with steel shear wall. The assessment of the seismic
vulnerability of structures is very complex issue due to the non-deterministic characteristics of the seismic action and
the need for an accurate prediction of the seismic responses for levels beyond conventional linear behaviour. Lateral
stability has always been a major problem of structures especially in the areas with high earthquake hazard.
Bhagat et al (2015) performed the pushover analysis of 2 storey regular steel frame building with concentric bracings
like Diagonal, V, Inverted V ,K, X, and Exterior X of ISMB and ISA sections. Out of this bracing “X” bracing gives
maximum base shear of about 30% more than of diagonal or K bracing. Also using ISMB section the capacity of base
shear increases very well. Mohammed Idrees Khan et al (2014) performed pushover analysis of G+15 storey steel
frames with bracings. Exterior X-Brace gives maximum base shear, increases up to 70 % and displacement reduces to
90% as compared with bare frame. ISMB sections give more base shear whereas ISMC sections reduces more
displacements when compared to angle and channel sections. Vaseem Inamdar et al (2014) conducted pushover
analysis of complex steel frame with bracing of ISMB and ISNB sections using Etabs. Stiffness of models increased by
an amount of 71.5% using ISMB bracing and 68% using hollow pipes sections. Column beam hinge mechanism
obtained is 3.5 times more for bare frame with exterior bracing. Spectral displacement of exterior ISMB bracing at
performance point is greatly (62%) increased. Elavenil (2014) performed the pushover analysis of steel frames of
different storey height. Formation of plastic hinges was maximum when the storey levels are minimum. Vijay et al
(2013) studied the performance of steel frames by Pushover analysis for solid and hollow sections. The drift to height
ratio is limited to 35 stories despite of increased base width. Formations of plastic hinges were maximum when the
storey levels are minimum. When storey level get increased pushover load steps get decreased, so the capacity curve
become linear for some models corresponding to its storey level. Madhusudan G. Kalibhat et al (2013) analyzed the
seismic performance of concentric braced steel frames from pushover analysis. Nonlinear static pushover analysis is
used to determine parameters such as initial stiffness, yield load, yield displacement, maximum base shear and
maximum displacement. Beyond elastic limit, different states such as Immediate Occupancy, Life Safety Collapse
prevention and collapse are defined as per ATC 40 and FEMA 356. Massimiliano Ferraioli et al (2014) investigated
the accuracy of advanced methods for nonlinear static analysis of six steel moment-resisting frames (three regular and
three irregular in elevation), that according to the Italian Code have been considered in the numerical analyses.
Adaptive nonlinear static procedures tend to have a less sensitive response to the input ground motion when compared
to response history analysis and other pushover procedures based on invariant load patterns. The modified modal
pushover analysis may give much sensitive response to the input ground motion, especially for irregular frames.
From literature review, it is observed that the provision of cross bracing enhances the base shear carrying capacity of
frames. Bracing acts as an extra redundant in frames there by reducing inter storey drift. ISMB Sections gives more
base shear compare to angle and channel section for similar type of brace.
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Web Site: www.ijaiem.org Email: editor@ijaiem.org
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2. PUSHOVER ANALYSIS
Pushover analysis is a static, nonlinear procedure in which the magnitude of the structural loading is incrementally
increased in accordance with a certain predefined pattern. With the increase in the magnitude of the loading, weak
links and failure modes of the structure are found. Pushover analysis may be classified as displacement controlled
pushover analysis when lateral displacement is imposed on the structure and its equilibrium determines the forces.
Similarly, when lateral forces are imposed, the analysis is termed as force-controlled pushover analysis. The target
displacement or target force is intended to represent the maximum displacement or maximum force likely to be
experienced by the structure during the design earthquake. Response of structure beyond maximum strength can be
determined only by displacement controlled pushover analysis.
3. RESPONSE REDUCTION FACTOR (R)
Seismic codes consider a reduction in design loads, taking advantage of the fact that the structures possess significant
reserve strength (over-strength) and capacity to dissipate energy (ductility). The overstrength and the ductility are
incorporated in structural design through a force reduction or a response modification factor (R). R factor represents
ratio of maximum seismic force on a structure during specified ground motion if it was to remain elastic to the design
seismic force. Thus, actual seismic forces are reduced by the factor "R'' to obtain design forces. The basic flaw in code
procedures is that they use linear methods but rely on nonlinear behavior. R factor reflects the capacity of structure to
dissipate energy through inelastic behavior. It is a combined effect of over strength, ductility and redundancy. Thus,
the factor R is such a factor with which the MCE level .Response Spectrum has to be scaled- it will come in the
denominator.
Figure 1 : Typical Pushover response curve for evaluation of response reduction factor, R
Generally the Response reduction factor (R) is expressed as a function of various parameters of the structural system,
such as strength, ductility, damping and redundancy:
R = Rs . Rµ . RR
where,
RS - strength factor
Rµ - ductility factor
RR - redundancy factor
3.1 Strength Factor (RS): The strength factor is defined as the ratio of maximum base shear in actual behavior VS to
first significant yield strength in structure Vy,
RS = Vy / Vs
Where Vy - Base shear at yield
Vs - Design base shear as per IS 1893 (2002)
3.2 Ductility Factor (Rµ): Using equation for ductility factor, derived by Miranda and Bertero
R µ = {(µ - 1 / Φ) + 1}
where,
µ - Ductility ratio = ∆max/ ∆y
Φ =1+{1 /(12T -µT)}–{(2 / 5T)*e-2 (ln (T) – 0.2)^2 } for medium soil
3.3 Redundancy Factor (RR): From Table 2 of ATC-19
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Table 1: Redundancy factor for moment resisting frames
Lines of vertical seismic
Drift redundancy factor
framing
(RR)
2
3
0.71
0.86
4
1.00
4. PUSHOVER ANALYSIS PROCEDURE
Displacement controlled nonlinear static pushover analysis adopted using ETABS are explained below:
a) Create the 3D model using ETABS 2015.
b) Define the material for the steel structures.
c) Define the geometry of the system.
d) Define the load patterns and load cases for static linear analysis.
e) Run the linear static analysis and check the adequacy of the sections.
f) Define the nonlinear load case for pushover analysis.
g) For pushdown case the load cases adopted are 100% DL + 25% LL.
h)For pushover case acceleration in X direction is given and the displacement of 0.04H is adopted for various
systems considered.
i) Define the nonlinear hinges for structural elements. For columns P-M2-M3 , for beams M3 and for braces axial P.
j) Run the pushover analysis and obtain the capacity curves.
5. STRUCTURAL MODELLING
For the present work, 12 models of high rise steel frame buildings are made to know the realistic behaviour of buildings
during earthquake. The buildings are assumed to be symmetric in plan, and regular in elevation. Three bays of width
5m in both X and Y directions are considered. Column height of 4.2m and 3m for ground storey and other upper
storeys respectively are considered. Storeys of 10, 15 and 20 stories are considered. The building is analysed and
designed for Indian seismic zone III with medium soil conditions. Dead and live loads are as per IS 875. Seismic loads
are in accordance with IS 1893 (2002). The frame is designed as per IS 800:2007.
5.1 STUDIED STRUCTURAL CONFIGURATION
Model 1.1: G+9 steel OMF
Model 1.2: G+9 steel SMF
Model 1.3: G+9 OMF with cross bracing
Model 1.4: G+9 OMF with steel shear wall
Model 2.1: G+14 steel OMF
Model 2.2: G+14 steel SMF
Model 2.3: G+14 OMF with cross bracing
Model 2.4: G+14 OMF with steel shear wall
Model 3.1: G+19 steel OMF
Model 3.2: G+19 steel SMF
Model 3.3: G+19 OMF with cross bracing
Model 3.4: G+19 OMF with steel shear wall
The typical plan and elevation of 10 storey steel structural systems are shown in fig 2,3 4 and 5
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5.2 BUILDING DESCRIPTION
Sl.N
o.
1.
2.
3.
a.
b.
Zone
III
Zone Factor
0.16
Response Reduction Factor
OMF
4
SMF
5
4.
Importance Factor
5.
6.
7.
8.
9.
10.
Column Details
Beam Details
Bracing Details
Shear wall Details
Thickness of Slab
Floor to Floor Height
Ground
storey
Height
Grade
of
Steel
Section
Dead Load
Floor Finish on slab
Live Load on slab
11.
12.
13.
14.
15.
IS code and Clause
Building Description
Annex E, Table 2 of
IS 1893:2002
Table 23 of IS
800:2007
Table 6 of IS
1893:2002
1
Hinges
ISWB 600
ISLB 600
ISMB 200
3mm thick plate
125 mm
3m
4.2m
Fe - 250
Gravity load
1.0 kN/m2
3.0 kN/m2
M3 for beams, P-M2-M3 for
columns, P for braces
6. RESULTS AND DISCUSSIONS
Pushover analysis was performed for various steel structural systems and results are tabulated in Table 2
Table 2: Results of pushover analysis @ ultimate
Max
base
shear
Max
displace
ment
Max
interstorey
drift
Max
storey
force
Max
overturning
moment
kN
mm
Unit less
kN
kN-m
Base
shear at
Yield
Vy
kN
G+9 OMF
10189.00
116.12
0.007
10161.00
212928
G+9 SMF
G+9 OMF WITH
SHEARWALL
G+9 OMF WITH
BRACES
10682.09
102.90
0.005
10658.00
216382
15647.14
118.07
0.004
15612.00
12515.29
78.47
0.003
G+14 OMF
8423.24
159.04
G+14 SMF
G+14 OMF WITH
SHEARWALL
G+14 OMF WITH
BRACES
8853.88
Yield
disp
Dy
Sa
Stiffness
Ke
W
mm
g
kN/m
kN
7882.63
88.80
0.68
88787.58
28394.03
8744.50
79.50
0.74
104943.20
28854.45
214256
11713.19
86.20
0.86
135865.67
28570.07
12476.00
246481
3614.40
20.90
0.99
173312.38
29085.09
0.005
8408.00
319222
5848.70
108.40
0.45
53957.87
42568.41
143.87
0.005
8821.00
324403
6586.73
105.10
0.48
62664.67
43259.04
10438.38
137.33
0.004
10423.00
321245
7845.48
102.70
0.55
76380.78
42836.61
9915.32
113.63
0.003
9894.00
347848
3060.00
33.40
0.61
91713.98
43603.64
G+19 OMF
7056.49
204.33
0.005
6753.00
425516
4314.54
112.20
0.32
35294.63
56742.80
G+19 SMF
G+19 OMF WITH
SHEARWALL
7394.15
188.62
0.004
7077.00
432424
3715.43
109.20
0.35
40135.10
57663.64
8206.50
183.50
0.003
7866.00
432000
6422.68
142.20
0.38
45172.15
57605.84
System
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Volume 5, Issue 3, March 2016
G+19 OMF WITH
BRACES
7147.83
136.44
0.002
6837.00
447845
1336.21
24.80
ISSN 2319 - 4847
0.42
53810.55
58122.19
Base shear Vs Displacement curve for various stories are shown in Fig 6,7,8
Fig 6: Capacity curve for G+9 structural system
Fig 7: Capacity curve for G+14 structural system
Fig 8: Capacity curve for G+19 structural system
Displacement profile for each system is shown in Fig 9,10,11
Fig 9: Displacement of G+9 structural system
Fig 9: Displacement of G+14 structural system
Fig 11: Displacement of G+19 structural system
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Time period for various systems are shown in Fig 12
Fig 12: Time period of structural system
Codal Time period is compared with actual time period obtained for systems are tabulated in Table 3
Table 3: Time period of structural systems
STOREY
OMF
SMF
Codal time period
(0.085h0.75)
OMF with
brace
OMF with
shear wall
Codal time period
(0.09h/√d)
G+9
1.32
1.15
1.122
1.05
1.16
0.725
G+14
1.76
1.6
1.51
1.58
1.75
0.954
G+19
2.16
2.01
1.86
2.11
2.32
1.422
Response reduction factor (R) for the various steel structural system is calculated and tabulated in Table 4
Table 4: Response reduction factor for structural system
Ductilit
y ratio
µ
(∆max/
Dy)
Strengt
h Factor
Rs
(Vy/Vs)
RR
Vy
Vs
∆max
(0.004H
)
kN
kN
mm
mm
G+9 OMRF
7882.63
650.82
124.80
88.80
1.41
1.32
12.11
1.00
G+9 SMRF
8744.50
627.89
124.80
79.50
1.57
1.15
13.93
1.00
G+9 OMF WITH
SHEARWALL
11713.1
9
923.86
124.80
86.20
1.45
1.16
12.68
1.00
G+9 BRACES
3614.40
1064.66
124.80
20.90
5.97
1.05
3.39
1.00
G+14 OMRF
5848.70
976.62
180.00
108.40
1.66
1.76
5.99
1.00
G+14 SMRF
6586.73
616.17
180.00
105.10
1.71
1.60
10.69
1.00
G+14 OMF WITH
SHEAR WALL
7845.48
866.03
180.00
102.70
1.75
1.75
9.06
1.00
G+14 BRACES
3060.00
964.13
180.00
33.40
5.39
1.58
3.17
1.00
G+19 OMRF
4314.54
1302.42
240.00
112.20
2.14
2.16
3.31
1.00
G+19 SMRF
3715.43
581.17
240.00
109.20
2.20
2.01
6.39
1.00
5422.68
796.70
240.00
142.20
1.69
2.32
6.81
1.00
1336.21
867.04
240.00
24.80
9.68
2.11
1.54
1.00
System
G+19 OMF WITH
SHEAR WALL
G+19 OMF WITH
BRACES
Dy
Time
period
T
Rµ
R
(Rs*Rµ*RR)
s
1.5
3
1.7
8
1.6
1
7.2
6
1.7
5
1.8
4
1.8
6
6.0
2
2.2
0
2.2
9
1.7
1
8.8
9
18.53
24.79
20.41
24.65
10.48
19.67
16.85
19.11
7.29
14.64
11.64
13.70
7. CONCLUSION
From the analytical study, the following conclusions are derived:
1. Irrespective of storey height buildings with shear wall is having maximum base shear and Storey force. Base
shear and Storey force of shear wall is 54% , 46% and 25% higher than OMF, SMF and Braces for 10 stories,
24%, 18%,and 5% for 15 stories and 16%, 11% and 15% for 20 stories respectively.
2. Out of two Moment Resisting frames, Base shear of SMF is 5% higher than OMF irrespective of storey height.
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3. Out of two Lateral Load Resisting System (LLRS), Base shear of Shear wall is 25%, 5% and 15% higher than
Braces for 10, 15 and 20 stories respectively.
4. When the no. of storey increases, the corresponding Base shear decreases and displacement increases.
5. The maximum displacement and interstorey drift of OMF higher than SMF, Shear wall and Braces in all storey
height.
6. For LLRS, interstorey drift (∆/H) is within codal limits (0.004). Therefore other Non-structural will not be
damaged and structures can be easily put in function after earthquake with less repairs.
7. Out of two LLRS, Max displacement and interstorey drift of system with braces is less when compared to shear
wall.
8. Overturning moment of Braces is 16%, 14% and 15% higher than OMF, SMF and shear wall for 10 stories, 9%,
7% and 8% for 15 stories, 5%, 4% and 4% for 20 stories.
9. Time period (T) is found to increase with increase in number of stories.
10. Natural period of the systems is found higher than codal recommended time period (0.085h0.75 for MRF and
0.09h/√d for LLRS). The observed time periods are 0.0995 h0.75 for OMF, 0.09 h0.75 for SMF, 0.132 h/√d for
Braces and 0.146 h/√d for Shear wall.
11. Strength factor of SMF is higher than OMF, Shear wall and Braces in all storey height.
12. Ductility factor of Braces are higher than OMF, SMF and Shear wall in all storey height.
13. Response reduction factor for SMF is higher when compared to all four systems. R value of SMF is 34%, 88%
and 1% higher than OMF for 10, 15 and 20 stories respectively.
14. 'R' value of Braces are 21%, 13% and 18% higher for 10, 15 and 20 storey when compared to Shear wall.
15. 'R' is directly proportional to strength factor and ductility factor and inversely proportional to natural period
irrespective of storey height.
References
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Safety Commission, Redwood City, California, (1996).
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[4]. B.S.S Council, " NEHRP recommended provisions for seismic regulations for new buildings (1997 ed.)" in Federal
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[5]. Elavenil.S (2014) “Seismic Behaviour and Pushover Analysis of Steel Frames” Middle-East Journal of Scientific
Research 22 (11): 1718-1725.
[6]. Esmaeili.H, Kheyroddin.A and Naderpour (2013) “seismic behavior of steel moment resisting frames associated
with rc shear walls’’IJST, Transactions of Civil Engineering, Vol. 37, pp 395-407
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[8]. Ferraioli, Lavino & Mandara (2012) “Behaviour Factor for seismic design of moment-resisting steel frames”
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[9]. IS code IS1893-2002 (Part 1), Indian Standard Criteria for Earthquake Resistant Design of Structures, fifth
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[10]. IS Code IS 800-2007 Design of Steel Structure.
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 5, Issue 3, March 2016
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[18]. Vijay, Vijayakumar (2013) ‘Performance of Steel Frame by Pushover Analysis for Solid and Hollow Sections’
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Author
Sudharani.M received the B.E. degree in civil engineering from Adhiyamaan College of Engineering,
Hosur, Anna University, Chennai, India, in 2013.Currently doing M.E. in structural engineering in
Adhiyamaan College of Engineering, Hosur, Anna University, Chennai, India.
Dr. G. Nandini Devi currently working as Professor, Department of Civil Engineering. She obtained
her B.E in Civil Engineering and M.E Structural Engineering from Bharathiyar University,
Coimbatore, India and Ph.D from Anna University-Chennai, India. She is having 13 years of
experience and published 22 papers in international journals. Her research area is development of new
construction materials, FRP rebars, Earthquake Resistant Structures
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