Download - Final Presentation_25 May
Seismic Performance of Perforated Steel Plate Shear Walls Designed According to Canadian Seismic Provisions
Presented by: Kallol Barua
Supervised by: Dr. Anjan Bhowmick
A Thesis inThe Department of
Building, Civil and Environmental EngineeringConcordia University Montreal, Quebec Canada
May, 2016
Outline
Introduction
Literature Review
Methodology
Results and Discussions
Conclusions and Future work
Perforated Steel Plate Shear Wall (P-SPSW)
Improved version of Solid Infill SPSW
Effective lateral load resisting system High Stiffness and ductility Tremendous post-buckling strength Excellent energy dissipation capacity
Benefits: • Decreases member sizes and cost of the
project• Passing of utilities • Lifting and handling become easy• Equally applicable to new buildings as well
as retrofitting of existing buildings
Introduction Literature Review Methodology Results Conclusion
1/30
Thorburn et al. (1983) developed "Strip-Model” for unstiffened SPSW
Roberts and Sabouri-Ghomi (1992)
Vian and Bruneau (2005)
Purba and Bruneau (2006)
Here, α=0.7 where (D/Sdiag<0.6).
CSA/CAN-09 included the Purba et al.(2006) equation .
Previous Studies on P-SPSWs
Introduction Literature Review Methodology Results Conclusion
2/30
Motivation
Limited studies Still no study was conducted over P-SPSWs designed according to current Canadian seismic provisions
Still perforated infill plate equation was not investigated for dynamic analysis
Introduction Literature Review Methodology Results Conclusion
3/30
Introduction Literature Review Methodology Results Conclusion
4/30
Objectives Develop a detailed and simplified finite element model to study behavior
of P-SPSWs designed according to current Canadian seismic provisions
Perform non-linear time history analyses to evaluate important response parameters of P-SPSWs. Specially carefully examine the dynamic shear contribution of the perforated plate.
Examine the applicability and accuracy of the N2 method in estimating seismic demands of P-SPSWs
Investigate the applicability of Simplified Method (Strip Model ) for the selected P-SPSWs.
Introduction Literature Review Methodology Results Conclusion
Detailed Finite Element Modeling
FE model specifications Element type: Shell element S4R Material : Elasto-perfectly plastic Boundary conditions:
• Pin supported columns
Types of Analyses• Buckling analysis Pushover analysis Cyclic analysis Frequency analysis Seismic analysis
ABAQUS/CAE Extensive element and material library Advanced meshing capability Solving problems with material and
geometry non-linearities
5/30
Dummy Column
Validation of Experimental Result By Detailed FEM
Introduction Literature Review Methodology Results Conclusion
One Storey P-SPSW (Vian et al. 2005) Bay width=4 m Storey height=2 m Plate Thickness =2.6mm
Figure: Perforated test specimen of Vian et al. (2005)
6/30
0 10 20 30 40 50 600
500
Detailed FE Analysis"Vian et al.(2005) test"
Displacement (mm)
Bas
e Sh
ear(
kN)
-100 -80 -60 -40 -20 0 20 40 60 80 100
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Experiment Finite element
Displacemetn (mm)
Bas
e she
ar(k
N)
Monotonic Pushover CurveQuasi-static cyclic Curve
Openings (mm)
Sdiag(mm)
Beam Column
200 424 W460x97 W460X106
Building Geometry and Loading
Introduction Literature Review Methodology Results Conclusion
Hypothetical office building Vancouver, Soil class C Storey height=3.8 m Bay width=5.7m Floor: DL= 4.2 kPa, LL=2.4 kPa Roof: DL=1.5 kPa, SL=1.12 kPa Load Combination :
DL+0.5LL+EQ(Floor) and DL+0.25SL+EQ(Roof)
Three designed P-SPSWs (4-,8-,12-storeys) (CSA S16-09 and NBCC2010)
7/30
Building Plan view
P-SPSW
P-SPSW
P-SPSWP-SPSW
Introduction Literature Review Methodology Results Conclusion
Design of Perforated Steel Infill Plate
8/30
Design according to Canadian Standard
For low to mid rise structure the thickness requirement is <3mm
From practical availability and handling capability the minimum thickness requirement is 3 mm
Opening orientation : Uniformly distributed over the entire
plate in a staggered position α=45 degree D/Sdiag<0.6
e
Perforation Layout
Introduction Literature Review Methodology Results Conclusion
Capacity Design of Boundary MembersBy Burman and Bruneau (2008)
9/30
Uniform Collops Mechanismby Burman & Bruneau (2008)
Forces on HBEs (Beam)
Forces on VBEs (Column)
HBEs and VBEs Design as a Beam Column Member
Introduction Literature Review Methodology Results Conclusion
Selected of Sections for designed P-SPSWs
10/30
Plate (mm)
Hole Dia
(mm)
Beam section
Column section
Plate (mm)
Hole Dia
(mm)
Beam section
Column section
Plate (mm)
Hole Dia
(mm)
Beam section
Column section
Roof 3 200 W610X341W360X421
F-11 3 200 W460X144W360X421
F-10 3 200 W460X144W360X421
F-9 3 200 W460X144W360X421
F-8 3 200 W610X415 W360X463 3 200 W460X158W360X634
F-7 3 200 W460X144 W360X463 3 200 W460X158W360X634
F-6 3 200 W460X144 W360X634 3 200 W460X213W360X634
F-5 3 200 W460X144 W360X634 4.8 200 W460X213W360X634
F-4 3 200 W460X315 W360X314 3 200 W460X144 W360X634 4.8 200 W460X260W360X1086
F-3 3 200 W460X144 W360X314 4.8 200 W460X144 W360X634 4.8 200 W460X260W360X1086
F-2 3 200 W460X144 W360X509 4.8 200 W460X260 W360X900 4.8 200 W460X384W360X1086
F-1 3 200 W460X144 W360X509 4.8 200 W460X260 W360X900 4.8 200 W460X384W360X1086
4-storey P-SPSW 8-storey P-SPSW 12-storey P-SPSW
Introduction Literature Review Methodology Results Conclusion
Buckling and Pushover Analysis of Selected P-SPSWs
11/30
P-SPSW
Base shear (kN)From NBCC 2010 From Pushover analysis
4-storey 1508 41108-Storey 2970 495012-storey 3354 8076
Buckling Analysis To Incorporate Initial Imperfection Performed “Linear Perturbation”
Buckle analysis Pushover Analysis To check the adequacy of design Considered monotonically applied
equivalent static loads.
Buckling analysis Pushover analysis
Seismic Analysis Methods
NLTHA N2 Method
Frequency Analysis
Lateral force
Frequency Analysis
Non-linear pushover analysis base shear – roof displacement
Idealization of pushover curve
MDOF SDOF pushover
Convert to capacity curve
5% damped Elastic Demand curve
Inelastic Constant ductility demand curve
Both curves in the same plot
Intersection of T and elastic demand spectra ductility and displacement demand
oo
o
0.3o c c
TR 1 1 when T TT
R when T T
T 0.65 T T
*n n i iS m or p m
Determining damping coefficients and period
Selecting ground motions (GMs)
Scaling GMs to match Vancouver design
spectrum
Applying GMs to structure
Obtaining different response histories
n n, n
ADRS Format
Introduction Literature Review Methodology Results Conclusion
12/30
Introduction Literature Review Methodology Results Conclusion
13/30
Damping coefficient (α and β) Scaling of Earthquakes
Frequency Analysis
P-SPSW Circular frequency
(ω) in rad/sec
Time period (T1) in sec
4-storey 1st mode 6.20 1.012nd mode 17.16 0.37
8-storey 1st mode 2.97 2.102nd mode 9.39 0.67
12-storey 1st mode 1.92 3.272nd mode 6.58 0.95
1st mode 2nd mode
12-storey P-SPSW Frequency Analysis
Peak response Minimum 3 GM records
Average of Peak response Minimum 7 GM records ASCE 7-10
Real Ground motion (From PEER 2010 database) 0.8<A/V <1.2 Magnitude M6-M7 Simulated Ground motion (From Seismotoolbox) Magnitude 6.5-7.5
Selection of Ground Motion Records
Real Ground Motion Records
Simulated Ground Motion Records
Introduction Literature Review Methodology Results Conclusion
14/30
Event Year M PGA(g) PGV (m/s) A/V 4-storey 8-storey 12-storey
Imperial Valley-6,California,USA 1979 6.53 0.525 0.502 1.04 0.99 1.04 1.01Kern County, California, USA 1952 7.3 0.156 0.153 1.02 1.86 1.81 1.89Kobe city, Japan 1995 6.6 0.143 0.147 0.97 1.71 1.57 1.61Loma Prieto, USA 1989 6.93 0.233 0.221 1.05 1.31 1.38 1.47Northridge-I,USA 1994 6.7 0.231 0.183 1.2 1.38 1.34 1.42San Fernando, USA 1972 6.6 0.188 0.179 1.05 1.61 1.64 1.68
Event name Magnitude(M) Distance (Km)
Peak acceleration
(cm/s2)4-storey 8-Storey 12-storey
6C1 6.5 8.8 487 0.7 0.78 0.886C2 6.5 14.6 265 1.3 1.48 1.647C1 7.5 15.2 509 0.83 0.91 0.977C2 7.5 45.7 248 1.66 1.45 1.83
Scaled Response Spectra of GM records
Introduction Literature Review Methodology Results Conclusion
Acceleration Spectra for 4-Storey P-SPSWs Acceleration Spectra for 8-Storey P-SPSWs
Acceleration Spectra for 12-Storey P-SPSWs
Partial area method for scaling
Design spectrum of Vancouver
Range between 0.2 T1 and 1.5T1
Scale Factor 0.5-2.0
15/30
Introduction Literature Review Methodology Results Conclusion
Non-linear Time History Analysis Results (Inter-storey Drift)
Inter-storey Drift for 4-Storey (Left), 8-storey (Middle), 12-storey (Right) P-SPSWs
16/30
Comparison of Dynamic and static Base Shear
P-SPSW Average NTHA(kN)
Static Base Shear (kN) % of variation
4-STOREY 3168 1508 1108-STOREY 10645 2970 230
12-STOREY 8030 3354 150
Introduction Literature Review Methodology Results Conclusion
Non-linear Time History Analysis Results (Dynamic Storey Shear in Perforated Infill)
17/30
P-SPSWS 4-Storey 8-Storey 12-Storey
1st Floor 1st Floor 1st Floor 2nd FloorAverage (NTHA) 1657 3292 3129 3163Code
Equation 2050 3275 3275 3275
Variation(%) 19 0.5 4.5 3.4
Mid-section shear force for 4-storey Mid-section shear force for 8-storey Mid-section shear force for 12-storey
Comparison of Shear Force(kN) in Perforated Infill
𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 :𝑉 𝑝𝑒𝑟𝑓=𝑉 𝑠(1−0.7 𝐷𝑆𝑑𝑖𝑎𝑔 )
Introduction Literature Review Methodology Results Conclusion
(Axial Force for 4-,8-&12-storey SPSW and P-SPSW Left column)Non-linear Time History Analysis Results
Axial Force for 4-storey (left), 8-storey (middle) and 12-storey (right )
18/30
28% 22% 20%Bottom:
Introduction Literature Review Methodology Results Conclusion
(Yielding Pattern)
Perforated infill fully yielded
At the peak acceleration time
Simultaneous yielding in all infill
Beam plastic hinges formed for some
earthquakes (7C1 & 7C2 etc) All columns remain elastic
19/30
7C2Kern Country
12-storey P-SPSW yielding pattern
Non-linear Time History Analysis Results
Introduction Literature Review Methodology Results Conclusion
NLTHA N2 Method
Frequency Analysis
Lateral force
Frequency Analysis
Non-linear pushover analysis base shear – roof displacement
Idealization of pushover curve
MDOF SDOF pushover
Convert to capacity curve
5% damped Elastic Demand curve
Inelastic Constant ductility demand curve
Both curves in the same plot
Intersection of T and elastic demand spectra ductility and displacement demand
oo
o
0.3o c c
TR 1 1 when T TT
R when T T
T 0.65 T T
*n n i iS m or p m
Determining damping coefficients and period
Selecting ground motions (GMs)
Scaling GMs to matchVancouver design
spectrum
Applying GMs to structure
Obtaining different response histories
n n, n
ADRS Format
Seismic Analysis Methods
20/30
Introduction Literature Review Methodology Results Conclusion
N2 Method
Freemen (1975) proposed graphical procedure of Capacity Spectrum
Method
Fajfar (1999) :
Relatively simple N2 procedure with
a constant ductility demand spectrum
Recommended method by EC-08
Non-linear static analysis procedure
Compares capacity of the structure with the demands of ground motion
Fast method to evaluate seismic performance
20/30
FramesEffective mass
m*
(ton)
Modal Participation
Factor
Yield Strength F*y
(kN)
Yield Displacement D*
y
(mm)
Elastic Period T*
(sec)
4-Storey 1308 1.39 2860 37.4 0.828-Storey 2302 1.49 3000 111 1.84
12-Storey 3035 1.56 3900 255 2.80
Introduction Literature Review Methodology Results Conclusion
Seismic Demand Evaluation by N2 Method(Capacity curve of P-SPSWs)
Structural Properties of Equivalent SDOF System
21/30
0 100 200 300 400 5000
1000
2000
3000
4000
Dt, Top Displacement(mm)
Vb,
Bas
es sh
ear(
KN
)
0 50 100 150 200 250 300 350 4000
500
1000
1500
2000
2500
3000
0.00
0.03
0.06
0.09
0.12
0.15
0.18
0.21
Displacement, D*
Forc
e, F
* (K
N)
Say(
g)
Fig: First Mode Load Displacement curve for 4-storey P-SPSW
Fig: Idealized Load Displacement curve of ESDOF for 4-storey P-SPSW
Introduction Literature Review Methodology Results Conclusion
Seismic Demand Evaluation by N2 Method
22/30
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
Sd(cm)
Sa(g)
T=0.2
T=0.5
T=1.0
T=2.0
T=4.0
µ=1.0
µ=1.8
µ=5.0
T=0.82
Capacity curve
Fig: Constant Ductility Acceleration Displacement Format for Vancouver
Introduction Literature Review Methodology Results Conclusion
Parameters 4-Storey 8-Storey 12-StoreyMax Top Displacement
(N2 Method) (mm)
95 228 335
Max Top Displacement(NLTHA) (mm)
84.5 185 272
Percentage Error (%)(CSM W.R.T NLTHA)
12 18.5 23
Ductility 1.8 1.4 1
Application of N2 Method on 4-Storey P-SPSW
(Displacement Demand and Ductility )
Comparisons of N2 method and NTHA
Introduction Literature Review Methodology Results Conclusion
Seismic Demand Evaluation by N2 Method
23/30
Introduction Literature Review Methodology Results Conclusion
(Inter-storey Drift)
Inter-storey drift for 4-storey (left), 8-storey (middle), 12-storey(right) P-SPSW
0 0.5 1 1.5 2 2.5 30
1
2
3
4
Inter-storey Drift%
Stor
ey
0 0.5 1 1.5 2 2.5 30
1
2
3
4
5
6
7
8
Inter-storey Drift
Stor
ey
0 0.5 1 1.5 2 2.5 30123456789
101112
The N2 Method
Average NTH Analysis
NBCC2010
Interstorey Drift %
Stor
ey
Introduction Literature Review Methodology Results Conclusion
Modified Strip Model (MSM) For P-SPSW
24/30
Tension Strip: Pin connected truss element Strip width:
Edge to edge (E/E) Center to center (C/C)
Strip Layout : Exact layout Crosshatch layout( by Timler et al. (1998))
Deterioration Strips: For tearing and welding failure Compression Strut : Area: Equivalent Brace Model Material Strength : 15% of Tension strip Panel Zone: Same as column property
(Geometry ) Simple and easy analysis tool for unstiffened SPSW. Effectively capture the elastic to inelastic behavior for large scale SPSW.SAP 2000(CSI) Widely used software package in industries
Introduction Literature Review Methodology Results Conclusion
Modified Strip Model For P-SPSW
25/30
Boundary Condition
h=800mm
(Hinge Location and Boundary Condition )
Plastic Hinges: Bi-linear Beam: Flexural Plastic Hinges
(M3) Column: Axial load actuated
Flexural hinges (P-M3) Tension Strip : Axial hinge(P) Detrition Strip: ten times yield of
tension strip Compression Strip: Axial
hinges(P) Boundary Condition: Pin support condition
Introduction Literature Review Methodology Results Conclusion
26/30
Validation of Modified Strip ModelVain et al. (1997) Test Specimen
Vain et al. (2005) test specimen
Loading and Geometry of Vain et at. (2005) test specimen for MSM
Fig: Strip C/C
Load displacement curve for test and MSM
0 10 20 30 40 50 600
500
1000
1500
2000
Vain et al.(2005) Modified Strip Model (C/C)Modified Strip Model (E/E)
Displacement(mm)
Bas
e sh
aer
(kN
)
Strip E/E
Introduction Literature Review Methodology Results Conclusion
Seismic Performance Evaluation of P-SPSWs Using MSM(Pushover analysis of 4-storey P-SPSWs)
27/30
Loading and Geometry of 4-storey P-SPSWs (Exact layout and C/C strip
width)
Load Displacement Curve
Monitored node
Detailed Finite Element Modeling
0 50 100 150 200 250 3000
500
1000
1500
2000
2500
3000
3500
4000
4500
Detaile Finite element analyis by ABAQUSModified Strip model by SAP2000(Exact layout & C/C Strip)Modified Strip Model by SAP2000 ( Cross-hatch layout and C/C strip)
Top Displacement (mm)
Base
she
ar(k
N)
Loading and Geometry of 4-storey P-SPSWs (Cross-hatch layout and C/C strip width)
Exact Layout and C/C strip
Cross-hatchLayout and C/C strip
28/30
Seismic Performance Evaluation of P-SPSWs Using MSM(Pushover Analysis over 8-&12-storey P-SPSWs)
0 100 200 300 400 500 600 700 8000
1000
2000
3000
4000
5000
Detaile Finite Element Model in ABAQUS
Modified Strip Model by SAP2000
Top Displacement (mm)
Bas
e Sh
ear(
kN)
0 500 1000 1500 20000
1000
2000
3000
4000
5000
6000
7000
8000
Detailed Finiet Element model in ABAQUS(2011)Modified Strip Model in SAP2000
Top Displacement (mm)B
ase
Shea
r (k
N)
Load Displacement curve for 8-storey (left) and 12-storey (right) P-SPSWs
Introduction Literature Review Methodology Results Conclusion
For Exact layout and C/C strip Width
Introduction Literature Review Methodology Results Conclusion
Non-linear Time history Analyses for P-SPSWs
FE model able to predict behavior of P-SPSWs accurately, perfect agreement
All P-SPSWs behavior In compliance with the capacity design approach
The inter-storey drifts in all P-SPSWs well below limit of 2.5% of storey height
Critical response parameters: Base Shear, Storey shear, Axial Force are well below the standard limit
The average perforated plate shear contribution for dynamic analysis slightly underestimate the standard equation
The selection of perforated infill plate thickness as well as for the design of boundary members as per capacity design, the current code equation of CSA/CAN S16-09 can be considered safe.
29/30
Introduction Literature Review Methodology Results Conclusion
N2 Method For P-SPSWS
Sufficient accuracy was found for predicting the displacement and ductility demands of 4-and 8- storey P-SPSWs by N2 Method.
For the 12-storey, the method was not capable of providing good result due to higher mode effect in few instance.
30/30
Modified Strip Model for P-SPSWs Capable of predicting the behavior of P-SPSW well( exact layout
and C/C strip) when compared to detailed finite element modeling. Slightly underestimated the initial stiffness; however, the ultimate
strength was predicted very well.
Introduction Literature Review Methodology Results Conclusion
Future Work
More research works are required on P-SPSWs of different types, geometry and height to verify the achievement of the desired frame behavior of P-SPSWs designed according to current Canadian provisions.
N2 method is applicable for the structure which have first mode of vibration, so more study required to capturing seismic demand for high-rise structure.
The applicability of the modified strip model for non-linear time history analysis shall be investigated.
Contribution Barua, K. and Bhowmick, A. 2016. "Seismic Performance of
Perforated Steel Plate Shear Walls." Steel and Composite Structures To be submitted.
References ASCE/SEI. 2007. Seismic rehabilitation of existing buildings. American Society of Civil Engineers, Reston, VA, USA
Berman, J.W., and Bruneau, M. 2008. Capacity design of vertical boundary elements in steel plate shear walls. ASCE,
Engineering Journal, first quarter 57-71. 125.
CSA. 2009. Limit states design of steel structures. Canadian Standards Association. Toronto, Ontario.
Driver, R.G., Kulak, G.L., Kennedy, D.J.L. and Elwi, A.E. 1997. Seismic Behaviour of Steel Plate Shear Walls;
Structural Engineering Report No. 215. Department of Civil Engineering, University of Alberta, Edmonton, Alberta,
Canada. 127.
Driver, R.G., Kulak, G.L. Elwi, A.E. and Kennedy, D.J.L 1998b. FE and Simplified Models of Steel Plate Shear Wall.
ASCE Journal of Structural Engineering 124(2): 121-130.
Fajfar, P. 1999. Capacity Spectrum Method Based on Inelastic Demand Spectra. Earthquake Engineering and
Structural Dynamics 28 (9): 979-993.
Hibbitt, Karlsson, and Sorensen. 2011. ABAQUS/Standard User’s Manual. Pawtucket, RI: HKS.Inc. NBCC. 2010. National Building Code of Canada. Canadian Commission on Building and Fire Codes. National
Research Council of Canada (NRCC), Ottawa, Ontario. Purba, R. H. 2006. Design recommendations for perforated steel plate shear walls. M.Sc. Thesis, State Univ. of New
York at Buffalo, Buffalo, N.Y. Shishkin, J.J., Driver, R.G., and Grondin, G.Y., 2005. Analysis of Steel Plate Shear Walls Using the Modified Strip
Model. Structural Engineering Report No. 261, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB.
Vian, D., and Bruneau, M. 2005. Steel Plate Shear Wall for Seismic design and retrofit of building structures. Technical Report No. MCEER -05-0010, Multidisciplinary Center for Earthquake Engineering Research, State university of New York at Buffalo, Buffalo, N.Y. USA.
Thank You
Performance Evaluation Methods
Linear analysis methods: Dynamic and Static
Inaccurate results for the case of highly non-linear responses
Non-linear analysis methods: Dynamic and Static
Non-linear time history analysis very accurate
but time consuming and complex
not practical for design level evaluation
Non-linear static analysis Selected
(NLTHA)
N2 Method /Capacity Spectrum
Method (CSM)
Simple and effective
Introduction Literature Review Methodology Results Conclusion
3/33
Rayleigh Proportional DampingRayleigh proportional damping is the damping proportional to the mass and stiffness:
C=M+K
is mass proportional damping coefficient and is stiffness proportional damping coefficient.For the nth natural mode of vibration the following relation applies:
i j
i j i j
2 2
nn
n
12 2
For i and j modes:
CSM Formula
Acceleration response spectrum can be converted in to acceleration-displacement response spectrum (ADRS):
2
de ae2
TS S4
The acceleration spectra Sa and displacement spectra Sd for an inelastic SDOF system can be obtained by using strength reduction factor
aea d a2
S TS S SR 4
oo
TR 1 1 when T TT
oR when T T 0.3o c cT 0.65 T T
Introduction Literature Review Methodology Results Conclusion
24/33
Validation of Modified Strip Model(MSM)Driver et al. (1997) Test Specimen
Monitored Node
Fig: Driver et at. (1997) test specimen Fig: Loading and Geometry of Driver et at.
(1997) test specimen For MSM
Fig: Load displacement curve for test and MSM
Equal energy rule and Equal displacement rule
Equal energy rule: For short period structure, the equal energy rule applies. In this method the energy absorbed by an inelastic system is approximated to be equal to the energy absorbed by an elastic system with same stiffness and damping ratio.
Equal displacement rule: For more flexible structure with medium and long period, displacement of inelastic system is equal to by that of elastic system (Newmark and Hall 1973)
Beam:
Column:
PsiPsi
Pbli Pbri
Pbli Pbri
𝑀𝑝𝑟𝑙𝑖=1.18 (1− |𝑃 𝑏𝑙𝑖|𝐹 𝑦𝑏𝐴𝑏𝑖
)𝑍𝑥𝑏𝑖 𝑖𝑓 1.18(1− |𝑃𝑏𝑙𝑖|𝐹 𝑦𝑏 𝐴𝑏𝑖
)≤1.0……………….. 8
𝑀𝑝𝑟𝑙𝑖=𝑍𝑥𝑏𝑖 𝐹 𝑦𝑏𝑖𝑓 1.18 (1− |𝑃𝑏𝑙𝑖|𝐹 𝑦𝑏𝐴𝑏𝑖
)>1.0………………… .. 9
𝑴 𝒑𝒓𝒍𝒊 𝑴 𝒑𝒓 𝒓 𝒊
𝑉 𝑏𝑟𝑖=𝑀𝑝𝑟𝑟𝑖+𝑀𝑝𝑟𝑙𝑖
𝐿 +(𝑤𝑦𝑏𝑖−𝑤 𝑦𝑏𝑖+1 ) 𝐿2 ………………………………10
Moment:
Shear:
𝑉 𝑏𝑙𝑖=𝑉 𝑏𝑟𝑖− (𝑤𝑦𝑏𝑖−𝑤𝑦𝑏𝑖+1 )𝐿……………………………… .11
𝑉 𝑏𝑟𝑖 𝑉 𝑏𝑙𝑖
Horizontal Boundary Element (HBEs)
Pbli
𝑴 𝒑𝒓𝒍𝒊
𝑉 𝑏𝑟𝑖
Vertical Boundary Elements (VBEs)
HBEs and VBEs Design as a Beam Column Member:
a. Local Buckling Check b. Cross Sectional Strength Check C. Overall Member Strength -In plane Stability check ( Beam ) d. Lateral Torsional Buckling check ( Column)
0 0.5 1 1.5 2 2.5 30
50
100
150
200
250
300
350
400
450
500
Actual
FE
Strain %
Stre
ss(M
Pa)
Material Properties
Design : yp=350MPa,FE: yp=385MPa and Bi-linearG40.21-350W: yp=345Mpa , strain hardening 0.5%-5%
2%
Introduction Literature Review Methodology Results Conclusion
Modified Strip Method For P-SPSW
27/33
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
Column Flexure Hinge
ϴ(Rad)
M/M
p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1 Beam Flexure Hinge
θ (rad)
M/M
p
0 10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5Tension Strip (Axial Hinge)
Δ/Δy
P/Py
-500 -450 -400 -350 -300 -250 -200 -150 -100 -50 0
-1
-0.5
0
Compression Strip (Axial Hinge)
Δ/Δy P/Py
Deterioration strip :
10 times yield
Boundary Condition
h=800mm
(Hinge Location and Boundary Condition )
Introduction Literature Review Methodology Results Conclusion
Modified Strip Method For P-SPSW
24/30
Tension Strip: Pin connected truss element Strip width:
Edge to edge (E/E) Center to center (C/C)
Strip Layout : Exact layout Crosshatch layout( by Timler et al. (1998))
Compression Strut : Area: Equivalent Brace Model Material Strength : 15% of Tension strip Panel Zone: Same as column property
(Geometry ) Simple and easy analysis tool for unstiffened SPSW. Effectively capture the elastic to inelastic behavior for large scale SPSW.SAP 2000(CSI) Widely used software package in industries
Contribution Barua, K. and Bhowmick, A. 2016. "Seismic Performance of
Perforated Steel Plate Shear Walls." Steel and Composite Structures To be submitted.
Kallol Barua, H.M.H. Rhaman and S. Das " Performance Based Analysis of Seismic Capacity of Mid Rise Building“ Website: www.ijetae.com, ISSN 2250-2459, Volume 3, Issue 11, November 2013
Contribution (Other than thesis)