HIGH-PRECISION FE-ANALYSIS FOR GLOBAL AND LOCAL RESPONSES OF BUILDING

FRAMESMakoto Ohsaki (Hiroshima University)Masayuki Kohiyama (Keio University)Tomoshi Miyamura (Nihon University)Daigoro Isobe (Tsukuba University)Takuzo Yamashita, Koichi Kajiwara (NIED)Hiroshi Akiba (Alied Engineering)

High-precision analysis for reliability-based seismic design and risk management

• Conventional approach to RB seismic design– Evaluate probability for several dominant collapse

mode– Evaluate joint probability and reliability

• High-precision analysis of building frame– Simulate global and local responses simultaneously– Evaluate reliability for global collapse directly– Accurate evaluation of risk against seismic motions

E-Simulator Project• Hyogo Earthquake Engineering Research Center (E-

Defense) of National Research Institute for Earth Science and Disaster Prevention (NIED), Japan

• WG of Building Frame• Platform for High-precision FE-analysis of steel frame

– Do not use macro model (plastic hinge, composite beam, column base, etc.)

– Utilize only material model and FE-mesh.– Simulate global and local responses simultaneously

• Investigation of collapse behavior of members and connections– Develop new devices for seismic control– Replace physical test by numerical simulation

Constitutive model

Material test

FE-model

High-precisionFE-analysis

Local responseGlobal response

Parallel computer

First and subsequent loading

Rule for re-loading

Simulation of cyclicMaterial test

•Combine J2 evolutionary equation (explicit)and heuristic rule (implicit)

•Parameter estimation using optimization algorithm

Semi-Implicit Piecewise-LinearCombined Hardening Model for Steel Material

Total-Collapse Shaking-Table Test of4-Story Steel Frame at E-Defense

Outline of analysis• Elasto-plastic time-history analysis for the 4-story

steel frame using mesh with hexahedral solid elements using the prototype of E-Simulator

• Compare the results with those of shaking table test

(a) Plan (1st floor) (b) Y-elevation (longitudinal) (c) X-elevation (transverse)

4-Story Steel Frame Model• Steel material

– Semi-implicit piecewise-linear kinematic-isotropic hardening model

– Parameters Identified by uniaxial test results

• Concrete material for slab– Drucker-Prager model

• Damping– Rayleigh damping of 0.02 for 1st and 4th modes

(two lowest translational modes in X-direction)

Details of FE-Mesh (1)

Hexahedral solid elements

Details of FE-Mesh (2)Slabs and plates such as flanges and webs of beams are divided into, at least, two layers of solid elements.

FE-Models• Three column-base models• Spring model for exterior wall

Number of elements

Number of nodes

Number of DOF

Column base Exterior wall

Case 1 6,909,817 4,746,572 14,239,716 Fixed ––

Case 2a 6,909,817 4,746,572 14,239,716 Rotational spring Spring

Case 2b 7,145,779 4,905,692 14,717,076 FE-model Spring

(a) Case 1 (b) Case 2a (c) Case 2b

Upper face of base

Bottom of columnRigid plate modeled by rigid beams

MPC (horizontal dir.)

Connection of anchor bolt: distributed nodes connected by rigid beams to prevent stress concentration

Anchor bolt (truss element)Connect base and upper face of base plateAxial force: 100 kN

Frictionless contact between base plate and base

Column (1st story)

Base beamBase plate

Mesh

FE-Model of Column Base

Eigenvalue Analysis

Natural Period (s)

1st 2nd 3rd 4th

Case 1 0.8389 0.8144 0.5700 0.2702

Case 2a 0.8303 0.8203 0.5555 0.2700

Case 2b 0.7947 0.7833 0.5372 0.2578

Four lowest natural periods for Cases 1, 2a and 2b

• Computers: 16 cores of HP ProLiant BL465 2.6 GHz dual core

• Computation time for the four lowest modes: 5,471.6 s (1.5 hours)

1st mode

2nd mode

0 1 2 3 4 5 6 7 8 9 10-600

-400

-200

0

200

400

600

800

max: 605.5

Time [s]

Accele

rati

on [cm

/s2

]

NS

Time-History Analysis

0 1 2 3 4 5 6 7 8 9 10-800

-600

-400

-200

0

200

400

600

800 max: 657

Time [s]

Accele

rati

on [cm

/s2

]

EW

0 1 2 3 4 5 6 7 8 9 10-300

-200

-100

0

100

200

300 max: 279.3

Time [s]

Accele

rati

on [cm

/s2

]

UD

NS

EW

UD

Input Acceleration (the first half)

• Table acceleration record for 60% Takatori wave (20 s)

• Computers

- SGI Altix 4700 (CPU: Intel Itanium 1.66 GHz) at NIED

- No. of cores: 1 node×256 core/node = 256 cores

• Elapsed time

- Static analysis (self-weight): 2,414 s = 40 min.

- Dynamic analysis: 1,106 s/step(t = 0.01 s, 2000 steps)

4-Story Frame (Scale = 20)

MOVIE

Story Drift Angle of 1st Story

X (short) direction Y (long) direction

•SimulationX-direction: 0.01089 rad and –0.01357 radY-direction: 0.02300 rad and –0.007942 rad

•ExperimentX-direction: 0.0121 rad and –0.0122 radY-direction: 0.0190 rad and –0.00933 rad

Experimental results: courtesy of E-Defense Seismic Experimental Study and Simulation System Construction Proje

Max and Min Values of Story Drift Angle of 1st Story (Case 2a)

Story Shear Force of 1st Story

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

ExperimentCase 1Case 2a

Stor

y sh

ear f

orce

(kN

)

Time (sec.)

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20

ExperimentCase 1Case 2a

Stor

y sh

ear f

orce

(kN

)

Time (sec.)X (short) direction Y (long) direction

Experimental results: courtesy of E-Defense Seismic Experimental Study and Simulation System Construction Proje

•SimulationX-direction: 1142 kN and –1153 kNY-direction: 1385 kN and –1229 kN

•ExperimentX-direction: 1169 kN and –1173 kNY-direction: 1423 kN and –1058 kN

Max and Min Values of Story Shear Force of 1st Story (Case 2a)

Deformation (Time: 6 s, Scale = 10)

Y-axis X-axis

Y-axis X-axis

→Y

Column-base model: Case 2aTime: 6 s (nearly the maximum deformation)Rotational response around Z-axis is observed due to effect of exterior wall.

X←

→Y X←

Equivalent Stress at the Maximum Deformation (Case 1)

Whole frame Close view around the 2nd floor and the 1st story

Large stress is observed around the column base and beam-to-column connections.

Simulations of Component Tests

Rayleigh damping will be replaced by more accurate model of nonstructural components.

Analysis of composite beam

Detailed and precise modeling

• Concrete Slab– Wire mesh– Stud bolt

Loading history (rotation angle)

Moment-rotation relation (Pure steel)

Moment-rotation relation (Composite beam)

Equivalent Stress

Deformation at positive bendingContact between slab and column

Upper surface Lower surface

Conclusions• Cyclic elasto-plastic behavior (yield plateau,

Bauschinger effect) can be accurately simulated by the proposed semi-implicit model.

• Elasto-plastic dynamic responses of a 4-story steel frame can be simulated within a moderate accuracy using only the constitutive and structural models without resort to a macro model.

• Global and local elasto-plastic responses of composite beam can be accurately predicted using a sophisticated FE-analysis model.