Benchmark Example No. 47

Pushover Analysis: SAC LA9 Building

SOFiSTiK | 2020

VERiFiCATiONBE47 Pushover Analysis: SAC LA9 Building

VERiFiCATiON Manual, Service Pack 2020-4 Build 54

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Front Cover

Project: Queensferry Crossing | Photo: Bastian Kratzke

Pushover Analysis: SAC LA9 Building

Overview

Element Type(s): B3D

Analysis Type(s): MNL

Procedure(s): EIGE

Topic(s): EQKE

Module(s): ASE, SOFiLOAD

Input file(s): pushover sac la9.dat

1 Problem Description

In this example a pushover analysis of a moment resisting frame structure is performed. The pushovercurve is identified and compared to the reference solution, as described in Chopra [1].

Figure 1: Problem Description

2 Reference Solution

In this Benchmark the interest is focused in the retrieval of the pushover curve. The steps involved inthis process are described schematically in Figure 2. Important is the definition of the pushover lateralload case pattern. The pushover analysis is performed by subjecting the structure to this monotonicallyincreasing load pattern of lateral forces. Here the first three eigenmodes of the structure will be used.Choosing the characteristic force and displacement of the structure, a so called pushover curve of themulti-degree-of-freedom (MDOF) system can be obtained. The force, here denoted as Vb, is usuallybase-shear, while the displacement is a displacement of the characteristic point on the structure cnod,also called the roof displacement and the control node displacement.

3 Model and Results

The properties of the model are presented in Table 1 and Figure 3. The model utilised in this Benchmarkconsists of the benchmark structure for the SAC project, as has been described by Gupta and Krawinkler[2], Chopra and Goel [1] and FEMA [3].

“The 9-story structure, was designed by Brandow & Johnston Associates for the SAC2 Phase II SteelProject. Although not actually constructed, this structure meets seismic code and represents typical

SOFiSTiK 2020 | Benchmark No. 47 3

Pushover Analysis: SAC LA9 Building

AQUAv+vSOFIMSHMat.v/vHingesv+vSystem

SOFILOADPushvLoad

ASEPushvAnalysis

SOFILOADPushovervCurve

cnod

Vb

Vb

cnod

Figure 2: Pushover curve determination workflow

medium-rise buildings designed for the Los Angeles, California, region. The building is square in planand rises nine floors above ground in elevation. The bays are 9.15 m on center, in both directions,with five bays each in the north-south (N-S) and east-west (E-W) directions. The buildingaC™s lat-eral load-resisting system is composed of steel perimeter moment-resisting frames (MRFS) with simple(simple hinged connection) framing on the farthest south E-W frame. The columns are steel wide-flangesections. The levels of the 9-story building are numbered with respect to the ground level, with the ninthlevel being the roof. The building has a basement level, denoted B-1. The column lines employ two-tierconstruction, i.e., monolithic column pieces are connected every two levels beginning with the first level.Column splices, which are seismic (tension) splices to carry bending and uplift forces, are located on thefirst, third, fifth, and seventh levels at hs = 1.83 m above the center-line of the beam to column joint.The column bases are modeled as pinned and secured to the ground (B-1). Concrete foundation wallsand surrounding soil are assumed to restrain the structure at the ground level from horizontal displace-ment. The floor system is composed of steel wide-flange beams in acting composite action with the floorslab. Each frame resists one half of the seismic mass associated with the entire structure. The seismicmass of the structure is due to various components of the structure. The model is based on centerlinedimensions of the bare frame in which beams and columns extend from centerline to centerline. Thestrength, dimension, and shear distortion of panel zones are neglected.” [1]

“Shear deformations in beam and column elements are neglected. Plastic zones in beams and columnsare modeled as point hinges. The hysteretic behavior at plastic hinge locations is described by a bilinearmoment-rotation diagram. All elements have 3% strain hardening. Expected rather than nominal yieldstrength values are used (49.2 ks for A 36 steel and 57.6 ks for A 50 steel). Viscous damping 2%is used in first mode and at T = 0.2 sec.” [3]

Table 1: Model Properties

Material Geometry

A 50 = 9.15m

A 36 hb = 3.65m, hg = 5.49m

hƒ = 3.96m, hs = 1.83m

4 Benchmark No. 47 | SOFiSTiK 2020

Pushover Analysis: SAC LA9 Building

N

8×hƒ

hg

hb

5 × B-1

Ground

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

Figure 3: Model Description

(a) Mode 1 (b) Mode 2(c) Mode 3

Figure 4: Eigenmodes

Table 2: First three natural-vibration periods

Periods Ref. [1] SOF.

T1 2.27 2.26

T2 0.85 0.85

T3 0.49 0.49

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Pushover Analysis: SAC LA9 Building

0 20 40 60 800

0.2

0.4

0.6

0.8

1·104

Roof Displacement [cm]

Bas

eS

hear

[kN

]

Chopra [1]SOFiSTiK

(a) Mode 1 Pushover Curve

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1·104

Roof Displacement [cm]

Bas

eS

hear

[kN

]

Chopra [1]SOFiSTiK

(b) Mode 2 Pushover Curve

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1·104

Roof Displacement [cm]

Bas

eS

hear

[kN

]

Chopra [1]SOFiSTiK

(c) Mode 3 Pushover Curve

Figure 5: Pushover Curves

The first three vibration modes and periods of the building for linearly elastic vibration are shown inFigure 4. The vibration periods are 2.26, 0.85, and 0.49 sec, respectively. The force distributionsof these first three modes are used in the pushover analysis in order to retrieve the pushover curves.The pushover curves for the first three eigenmodes, are presented in Figures 5. The hinge formationdistribution for each pushover analysis, corresponding to approximatelly the last load case depicted in

6 Benchmark No. 47 | SOFiSTiK 2020

Pushover Analysis: SAC LA9 Building

each pushover curve, is presented in Figures 6.

-2.23 2.19 -2.19 2.19-2.19 -2.17 2.162.14

-2.08 2.00 2.00-2.001.99-1.99 -1.98

-1.95

1.95

1.841.84-1.84 -1.841.84 -1.831.80

-1.71 -1.65 1.65 -1.65 1.65 1.62-1.621.59

-1.50

-1.35

-1.19

-0.989

-0.982

0.9660.965 -0.931

0.625

0.612

0.609

0.480

0.297

-0.291

-0.267

-0.172-0.153 0.130

-0.127

0.117

0.0742-0.0676

(a) Mode 1

-1.80 1.76-1.751.75-1.75 1.75-1.741.71

-1.50 -1.381.38 1.38-1.37 -1.36 1.341.34

-1.22 1.071.04 -1.02-1.021.01-1.01

-0.892

-0.571

-0.132

0.111

0.103

0.0899

-0.0815 0.0217

(b) Mode 2-0.942

0.856-0.920 0.853

0.834

0.830

0.7540.727

(c) Mode 3

Figure 6: Hinge distribution

4 Conclusion

This example adresses the determination of the pushover curve for a benchmark structure. It has beenshown that the results obtained are in a good agreement with the reference given by Chopra [1].

5 Literature

[1] A.K. Chopra and R. K. Goel. A Modal Pushover Analysis Procedure to Estimate Seismic Demandsfor Buildings: Theory and Preliminary Evaluation. Tech. rep. PEER Report 2001/03. Pacific Earth-quake Engineering Research Center - University of California Berkeley, 2001.

[2] A. Gupta and H. Krawinkler. Seismic Demands for Performance Evaluation of Steel Moment Re-sisting Frame Structures. Tech. rep. Report No. 132. The John A. Blume Earthquake EngineeringCenter, 1999.

[3] Prepared for the SAC Joint Venture Partnership by Helmut Krawinkler. State of the Art Report onSystems Performance of Steel Moment Frames Subject to Earthquake Ground Shaking. Tech. rep.FEMA-355C. Federal Emergency Management Agency (FEMA), 2000.

SOFiSTiK 2020 | Benchmark No. 47 7