Experimental behaviour of multi-storey steel frames

J. Construct. Steel Research 29 (1994) 175-189

Experimental Behaviour of Multi-Storey Steel Frames Koichi Takanashi Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan

ABSTRACT Two kinds of test were conducted on three-storey steel frames. One was a static test

under monotonically increasing loads, while the other was a pseudo-dynamic test using the on-line earthquake response test technique. The results obtained from the two tests on identical frames showed the possibility of representing dynamic load effects by an equivalent static load. It can be concluded that the seismic design of frames can be performed based on the results of a static analysis instead of dynamic analyses.

INTRODUCTION In structural design for earthquake-prone countries, seismic design load must be so large that the structures cannot resist against earthquake disturbance by the elastic strength and the structures must inevitably resist it by help of the energy absorption provided by plastic deformation.1 To achieve this design criterion, it is essential to specify the dynamic collapse mode which most efficiently dissipates the energy exerted by the earthquake. From the view point of practical design, it is preferable to determine the collapse mode from a static analysis, used in normal design practice instead of dynamic analyses which require rather complicated analytical models. This paper describes a static load test and an on-line earthquake response test (a pseudo-dynamic test). The purpose of these tests is to verify a proposed equivalent static load profile up to the height of the structure which can realize almost the same collapse mode as the mode due to earthquake excitation.

175 J. Construct. Steel Research 0143-974X/94/$07'00 © 1994 Elsevier Science Limited, England.

Printed in Malta

176

K. Takanashi

TEST STRUCTURES Steel materials All test frames were fabricated from steel plates. The steel plates used are of two kinds, measured mechanical properties of which are listed in Table 1. SS400 steel is a widely used structural steel, while HT590 steel is a newly developed high-quality steel which has high strength and low yield ratio. Yield ratio is defined here as the ratio of yield strength to tensile strength. Description of test frames The test frames are three-storey moment-resistant frames, as shown in Fig. 1. The beams and columns consist of H-shaped sections denoted by H-6 and H-8, the section properties of which are summarized in Table 2, The joint panels are enhanced by additional steel plates welded to the panel webs in order to guarantee that formation of plastic hinges in the beams and columns precedes plastification of the joint panels. The test frames made of SS400 steel are denoted by WBSC-SS1,2 and the test frames of HT590 steel are denoted by WBSC-HT1,2. SS1 and HT1 were provided for the static tests, while SS2 and HT2 were provided for the pseudo-dynamic tests.

TABLE 1

Coupon Test Results of Steels PL-9 SS400

av (MPa) atJ (MPa) YR (%) EL (%) ~st (%) ~st/~v E~t/E

255 408 63 25 2 15 1/117

PL-6 HT590

445 622 72 17 0.58 1"32 1/18"4

SS400

HT590

274 418 66 28 2 16 1/120

495 627 79 19 1.2 2"6 1/65'6

Experimental behaviour of multi-storey steel frames

177

2 000

[

H-6

.~

H-6

H i

8-a

H-6

H-6

H 6 tt -

6

FH i 6_'e ~

tt -

H

8

11

PL-50×400x400 (SM490) UNIT:mm

,

,

Fig. !. Test frame. TABLE

2

Section Properties of Members

t~(mm) tw(mm) B (mm) H(mm) B/tr d/t~

H-6

H-8

9 6 108 108

9 6 144 144

6 15

8 21

TEST PROCEDURES

Test layout The test set-up is illustrated in Fig. 2. The frame was placed on the test floor and braced laterally against lateral-torsional deformation. Three actuators were connected to the beam-to-column joints at the beam levels. The horizontal displacements were measured by transducers installed at the beam levels. The loads applied to the frame by the actuators were

178

K. Takanashi

2000

ctuator ~o.z

O.,T,mm ililllll

i IIi

ItllllIlllllllllllllll..llllllllllllllllllItllllIIl(lllllllllllllllllll Fig. 2. Test set-up of test frames.

sensed with the load cells installed in the actuators. In addition, strain gauges were mounted on the outer surfaces of the column flanges 325 mm from the beam centroid in the second and third storey, and 375 mm apart from the beam centroid in the first storey. Strains measured by these strain gauges were used for calculation of the column bending moments which were further utilized for calculation of the storey shear forces.

Static tests

Static tests were conducted in WBSC-SS1 and WBSC-HT1. Monotonically increasing loads were applied at the beam levels, with the ratio between the floor loads being kept constant. To achieve this loading scheme, the control programme shown in Fig. 3 was developed and used. The stroke $3 of the third actuator, which was installed at the third beam level, was controlled by the computer (PC9801) and other actuators were controlled to apply the prescribed loads, L2 and LI, which were calculated according to the value load La measured by the top actuator. In the tests the ratios among the applied loads were fixed at 3: 2:1 from top to bottom.

Experimental behaviour of multi-storey steelframes I

~[~

m

'

I:

DISP. "-'--'---'~1 "~4

~ I~

I

Lz

t

I

I,,,I

7

I,ACT.

-':[

I,,,

PECIMEN I

i

- -

I

~ •

L~LI Ill '-~., I*Lz[t/zLajt/'L'

179

DATA

II


II ~-

DATA

I

I'' ECOROER ' I

I1,,~

Fig. 3. Flow diagram of static test procedure.

All load, displacement and strain data measured during the tests were stored by the data recorder. Pseudo-dynamic tests For the pseudo-dynamic tests, the on-line earthquake response test technique was used. Since a precise description of the on-line test technique has already been made in the references, 24 only the diagram showing the flow of the process is shown (Fig. 4). The strokes of all the actuators are

F ~

s!

,

~

DIS

l

r'[ ALL MEASURED1"[ y DATA II <, DATA [ II

IRECORDER I

PC

.

H~,

J

Fig. 4. Flow diagram of on-line response test (pseudo-dynamic test) procedure.

180

K. Takanashi TABLE 3 Dynamic Properties of Frames

Test frames

Mode

Period (s)

Damping ratio

WBSC-HT2

1 2 3

0"80 0'234 0'117

0"02 0"07 0"14

WBSC-SS2

1 2 3

0"80 0"22 0'13

0"02 0"07 0"13

controlled by the computer, according to the computer's calculations. In this test technique, the equation of motion is being solved numerically by the step-by-step procedure, where the restoring force of the structure to be brought into the calculation at each time step is measured instantly from the test which is conducted in parallel to the computer calculation. Dynamic properties of the test frames are summarized in Table 3. The stiffness coefficients were measured from a preliminary static test, but fictitious lumped masses are assumed at all floor levels. As the value of the mass can be arbitrarily determined at the pseudo-dynamic test, all storey masses were assumed to be the same and the value of the mass was adjusted to realize 0.8 s for the fundamental period T1. The damping ratio for the first mode was also assumed to be 0.02 and the damping ratios for the second and third modes were determined to be proportional to the ratios of the second and the third frequencies to the first. The N-S component waveform of the E1 Centro 1940 earthquake was used as the input ground acceleration. The peak value of the original waveform is 3.47 m/s z, but the peak value Area x used in the response test was adjusted as follows: A m a x = ctAv

(1)

where Av is the yield acceleration (= Qu/(3M)), Qu is the base shear at the ultimate strength measured by the static test, M is the storey mass, and a is the dynamic effect coefficient. The dynamic effect coefficient introduced above is an amplification factor to represent the peak value of the input ground acceleration on the basis of the yield acceleration. The values taken for the tests are summarised in Table 4. The time step At in the step-by-step numerical integration of the equation of motion was selected as 0.01 s.

Experimental behaviour of multi-storey steel frames

181

TABLE 4 Parameters given in Pseudo-dynamic Tests

Test frames WBSC-HT2 WBSC-SS2

Amax

Qu

M

(m/s2)

(kN)

(N s2/m)

6-06 4"30

184 137

1.21 1-27

EXPERIMENTAL

ct 1"2 1-2

RESULTS

Static tests

The static tests were conducted on WBSC-HT1 and WBSC-SS1. The horizontal displacements at the beam levels and the strains at the column flange faces were measured, as the loading increased monotonically. From these data, the storey shear force versus the inter-storey disl~lacement relationship was made for each static test as shown in Figs 5 and 6. Figure 5 and 6 also show the storey shear forces at collapse, Qua, Q,2 and Q,3, derived form a simple limit analysis carried out under the same proportional load profile as the tests. The collapse modes are shown in Figs 7 and 8. The evaluation of the collapse load by the simple plastic hinge analysis is inadequate as illustrated in Figs 5 and 6. The calculated values seem to correspond to the initiation of plastic hinge formation. This is much more evident for the case of frame WBSC-SS1 than for frame WBSC-HT1. The reason is that SS400 steel in frame WBSC-SS1 has a

150L...... /Qu1 100

5

~

0 0

--2nd stor 3rd story

~ 50

....... I00

150

200

Inter-storydisplacement (mm)

Fig.5. Storeyshearforceversusinter-storey displacement(WBSC-HTI).

182

K. Takanashi

200

i

i

WBSC-SS1 ~150 ID Lo. O 100

1st story ~

2

n

3rd story

m 50 r~

0

I

0

story

d

I

100 200 300 Inter-story displacement (ram)

Fig. 6. Storey shear force versus inter-storey displacement (WBSC-SS1). 3P

P = 24.5 KN ,

3P

II

A

P =13.9 KN

Mp ~ 49.4 KN. 2P P ~ ~Mp = 49.4 K N . ~ II

w

~ - Mp ~ 49.4 KN.m~

Mp = 90.4 KN.m WBSC-HTI Fig. 7. Collapse mechanism of test frame (WBSC-HT1).

Mp = 28.0 K N . ~

Mp = 51.0 KN.m WBSC-SS 1 Fig. 8. Collapse mechanism of test frame (WBSC-SS1).

lower value of strain hardening modulus than HT590 steel. The low value of the strain hardening modulus results in a large plastic deformation after yielding. The real ultimate strength of the frames cannot be obtained by simple limit analysis techniques. Pseudo-dynamic tests Typical results from the pseudo-dynamic tests are shown in Figs 9 and 10. In the tests the peak values of the input acceleration were determined from eqn (1). The base shear forces, Q, in eqn (1), were found from static tests

Experimental behaviour of multi-storey steel frames

183

Displacement (mm) 200 3rd floor

' wBsC-l-rr2'

"

AAAAA _1o -200

,

5

j

I

,

,

10

t 15

Time (Sec) Fig. 9. Time history of response displacement at third floor (WBSC-HT2).

Displacement (mm) '00 ~[3~fi~

,-7. W B S C - S S f

.

]

Time (Sec) Fig. I@. Time history of response displacement at third floor (WBSC-SS2).

on identical test frames, and the dynamic effect coefficient ~ was set to 1.2. As understood from the response displacement time histories of the top of the frames (Figs 9 and 10) the frames were still in a stable state when the input ground motions terminated. However, parts of the frames had undergone considerable inelastic deformation as shown in Figs 11 and 12.

100'5°50

200 ~ - - - - - - ~ - - ~

150 ,00

~

¢

0 0 -50 ra~

-100

-80

0

,~

-50

~

-100

, sto

,st Story

-1501 -200~

""

-150 -40

0

40

80

Inter-story drift (mm) Fig. 11. Storey shear force versus interstorey displacement (WBSC-HT2).

-80

-40

0

40

80

Inter-story-drift (mm) Fig. 12. Storey shear force versus interstorey displacement (WBSC-SS2).

184

K. Takanashi

Comparison of collapse modes and strain energy absorption A collapse condition can be presented as a plane in F1, F2, F3 space, which corresponds to a specific collapse mode. In the case of the test frame in Fig. 1 (WBSC-HT2), these collapse conditions comprise a polyhedron of faces which correspond to specific collapse mechanisms. In Fig. 13, only a half of the polyhedron is shown. The plane denoted by al is the collapse condition associated with a storey collapse mechanism produced at the first storey, where plastic hinges are formed at the tops and the bottoms of the first storey columns. The planes denoted by a2 and a 3 are the collapse condition associated with storey collapse mechanisms produced at the second and third storey, respectively. The plane denoted by b corresponds to the collapse mechanism shown in Fig. 7, where plastic hinges are formed at the ends of beams and the column bases. The vector P originated from the origin O shows a combination of the applied loads at the static test. Namely, the ratios among them are fixed at 3:2:1. In the static test, the load vector started from the origin is increasing along this direction as the applied loads increase. The point on the plane b where the vector P passes through shows the collapse state under this proportional loading. The vector Q shows the direction of inertial forces in the case that the frame is vibrated in the first mode. These two vectors are very close to each other in this case. Three figures in Fig. 14 are projections of the vectors shown in Fig. 13 to three principal planes during the pseudo-dynamic test. In

Fig. 13. A polyhedron showing collapse conditions.

Experimental behaviour of multi-storey steel frames F2(KN) 1oo

F2 (KN) 1so WBsd-rl-r2 100

•

,

•

185

•

,

.

50 0 -50 -100 ~ .

-150 . i l,S.. , . , . -150-I00-50 0 50 lO0 150

-100 -100

-50

F1 (KN)

0

(a)

100

(a) F3(KN) 100 WBSC-SS2.. 50

F3 (KN)

.

150 WBSC-HT2, 100 "

50

F1 (KN)

'

"~/~,' '

, \

•

/:

50 O,

o

¢(~

"

-50 ."

-50

-10( -150 -150 -100 -50 0 50 100 150 F2 (KN)

""N~:,~/~,. x

-10o -IO0

-50 0 50 F2 (KN) (b)

(b) F1 (KN) 150 WBSC-HT2 1o0,

100

FI(KN) ioo \ WBSC-SS2

\

\,

50 -"\

'\

o -5o

-50 ~

-100 -100 -10o

-150 ~ ~ -150-100 -50 0 50 100 150 F3 (KN)

14. Trajectories of inertial (WBSC-HT2).

i

'

50

100

F3 (KN)

Co) Fig.

\. -5o (c)

forces

Fig.

15. Trajectories of inertial (WBSC-SS2).

forces

186

K. Takanashi

the figures, trajectories of the inertial forces induced at the floors are also represented. A set of chained parallel lines in each figure show the intersection lines produced by the collapse condition plane b in Fig. 13 on the principal planes. The trajectories of the inertial forces seem entangled around the vectors. Figures 15(a)-(c) show the same results in the case of test frame WBSC-SS2. This is the case in the usual moment resistant frames of low and medium rise. Response vibration of these frames is strongly controlled by the first mode vibration. A collapse mode produced by this vibration is most likely the same as the collapse mode identified by the static loading in this case. This fact suggests that the dynamic collapse mode, namely, the collapse mode produced by the response vibration can be identified by finding the collapse mode under the suitable equivalent static load. The method proposed above is supported by evidence that the cumulative strain energy absorbed at each storey, El, E2 and E3, increases in almost the same manner both in the static test and in the pseudo-dynamic test as shown in Figs 16 and 17. The proportions of the strain energy

Absorbed strain energy ( K N . m)

40t I3020 WBSC:HTI~ / /

0

200

E2EI~I

400

600

800

Load step Absorbed strain energy ( K N . m)

40 WBSC-HT2 30 20 10 00 5

10

15

Time (see)

Fig. 16. Cumulativeabsorbedstrainenergyat eachfloor(WBSC-HT1,-HT2).

Experimental behaviour of multi-storey steel frames

187

Absorbed strain energy (KN. m)

20

2

-

0 L~...~f ~ . . . . . . 0 2O0 4OO 6OO 8OO IOOO120014OO1600 Load step Absorbed strain energy ( K N . m)

°tw.scss 0

5 10 Time (sec)

15

Fig. 17. Cumulative absorbed strain energy at each floor (WBSC-SS1, -SS2). absorbed at each storey, ~01, ~/2 and clearly in Tables 5 and 6.

~/3, show close correspondence very

Evaluation of ultimate strength A problem left unsolved is how to determine the required strength against anticipated earthquakes. It is not only hard to develop hysteretic rules for the members of a structure to be designed for dynamic analysis, but also impractical for dynamic analyses to be always required in design procedures. It would be considerably easier to evaluate the strength using a static analysis rather than a dynamic one. General conclusions cannot be extracted from the results of these tests, but the pseudo-dynamic test (the on-line earthquake response test) showed that the frames remained stable, at least for the earthquake excitation with peak acceleration determined by eqn (1) with a = 1-2. This fact suggests that the strength evaluation by a static analysis gives a conservative design peak value of input acceleration.

188

K. Takanashi

TABLE 5 Portions of Absorbed Strain Energy at Each Floor (WBSC-HT1, -HT2) Test frames

WBSC-HT1 WBSC-HT2

~ 1

ull 2

~ 3

(%)

(%)

(%)

47'7 45"5

38-3 40'0

14-0 14.5

TABLE 6 Portions of Absorbed Strain Energy at Each Floor (WBSC-SS1, -SS2) Test frames

WBSC-SS1 WBSC-SS2

~ 1

W2

~g3

(%)

(%)

(%)

48"8 46"5

37"7 37"6

13'5 15"9

CONCLUSIONS The following conclusions can be drawn from the test results: (1) The dynamic collapse mode during response vibration can be identified by the collapse mode determined in static analyses. For this purpose, the limit analysis under proportional loading and the incremental load analysis under a fixed load profile are available. (2) In the static analysis mentioned above, an inverse triangle profile of the horizontal loads, and a profile proportional to the inertial forces induced by the first mode vibration are possible profiles for the design of low- and medium-rise buildings. (3) From the fact that strain energy absorption during vibration can be evaluated by static analysis, ductility evaluation is also possible by static analysis. (4) Only a conservative strength evaluation for seismic design was confirmed by the tests. An exact translation of the strength from that evaluated under dynamic excitations to that evaluated under static external loads is left for further reseach. (5) Although not one of the main objectives of the present tests, it was found that the difference in mechanical properties between the newly developed high strength steel and conventional mild steel does not

Experimental behaviour of multi-storey steelframes

189

influence strength evaluation. Usual evaluation techniques can be applied to the high-strength steel.

REFERENCES 1. Earthquake-resistant design method for buildings. In Earthquake Resistant Regulations: A World List--1992. IAEE, Tokyo, Japan July 1992, pp. 2355-23-71. 2. Takanashi, K. & Nakashima, M., Japanese activities on on-line testing. J. Engng Mech. ASCE, 113, (1987) 1014-32. 3. Elnashai, A. S. et al., Verification of pseudo-dynamic testing of steel members. J. Constr. Steel. Res., 16 (1990) 153-61. 4. Nakashima, M., Kato, H. & Takaoka, E., Development of real-time psuedodynamic testing. Earthquake Engng Struct. Dynamics, 21 (1992) 79-92.