II th INTERNA TlONAL BRICKlBLOCK MASONR Y CONFERENCE

TONGJJ VNIVERSITY, SHANGHAI, CHINA, 14 - 16 OCTOBER 1997

lHE SfUDIES ON DISPLACEMENT CONTROLLED

PSEUDODYNAMIC TEST ME'lHOD OF MASONRY HOUSE

Tang Daixin1 Zhu BenquanZ

1. ABSTRACT

The lateral rigidity of masonry house is large and the displacement reaction is

smal1. As a result, in the course of pseudodynamic test, the displacement aug­

mentations in most steps are in the range of actuator's deviation, so that the

step-by-step test can not be continued. This artical supplies an amended dis­

placement control1ed method. The application of tbis method to pseudodynamic

test on large rigidity model showes good resulto

2. INTRODUCTION of PSEUDODYNAMIC TEST PRINCIPLE

The structural pseudodynamic test is an effective method to imitate the seismic

behavior of structure compared with vibro-bench test, pseudodynamic test can

be used to study seismic behavior of large structural modelo 1t can decrease the

material diversity between the model and original structure. The principIe of

pseudodynamic test is as follwes.

Key Words: Masonry House, Pseudodynamic Test

1.2 Professor , Department 01 Structural Engineering, HArbin University 01 Civil Engineering and Archi­

tecture, 66 Dazhi Street HArbin 150006 China

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2. 1 Motion equation

[M]{a) + [c]{u) + [K]{d) = {f)

[M]{a) + [C]{u) + {r) = {f)

where {r) = [K]{d) is structural restoring force

2.2 Magnitude integration of motion equation

(l)

(2)

There are many .nagnitude integration methods used in structural pseudody­

nalnic testo Newmark implicit integration method is adopted in this artical

The motion equation of i + 1 step "is:

(3)

it is supposed

(4)

(5)

put Eq (5) into Eq (3), then

or (7)

2. 3 The control methods in pseudodynarnic test

Generolly, there are two ways to control test, displacement controlling and

force controlling.

1) When the test is controlled by displacement, the procedure is:

(I ) Calculate next step 's displacement by Eq (4);

(2) Execute {4.+.) to test model by actuator;

(3) measure the the structural restoring force;

(4) Calculate {aó+l) by Eq. (6);

(5) C''llculate {VH.) by Eq. (5);

set up the original data {tl;+I), {"'+1) and {a,+l) for next step circulates until the

test is accomplished.

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2) When the test is controlled by force, theprocedure is

(1) Estimate riext step's displacement by Eq. (4);

(2) Calculate the structural restoring force C'.aused by {d;+,}

h+, } = [K;]{d,+,}

(3) Apply {T.+ , } to the test model by actuator;

( 4) Measure the displacment {d.+,} ;

(5) Calculate the rigidity [ K.+,] ;

(6) Calculate {a.+ .} by Eq. (7) i (7) Calculate {VH .} by Eq. (5);

set up the original data {d;+.}. {VH'} anti {a,+.} for next step circulates until the

test is accomplished.

In the range of elastic, these two methods have no essential difference. When

the rigidity goes to decline, the test could not be controlled by force but by dis­

placemect

3. PROBLEMS IN PSEUDODYNAMIC TEST ON LARGE RlGIDITY

MODEL

If the test model's rigidity is large, the corresponding displacement will be

slight, so that the test c.an not go on because of the restriction of actuator's dis­

placement precision. In the test, we find:

3. I If the pseudodynarnic test on multi-degree system is controlled by dis­

placement ., the actuator's resistance will show "stick" pnenomenon when the

actuator exerts slight displacement augmentation. That is, when one of the ac­

tuators applies a displacement and the others are fixed at the same time, theo­

retic.ally, the fixed actuators' resistances will change and the displacements will

not change. But actually, in the test, we find that the fixed actuators' resis­

tances do not change. Moreover, the sensor corresponding to each fixed actua­

tor showes difference in displacement. Only if theapplied displacement is big

enough could this "stick" phenomenon disappear. As we have said, the dis­

placement reaction of large rigidity model is so slight in ~t time step that the

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step-by-step pseudodynamic 'test can not be controlled normally by displace­

ment.

3. 2 If the pseudodynamic test is controlled by force and the displacemect

augmentation caused by actuator is slight, the calculated rigidity showes unsta­

ble. During t.t time step, the rigidity can be computed through app1ying force

and measuring displacement. But the rigidity values are unstab1e. Sometimes

are large and sometimes are small. When it is in the range of e1astic, the rigid­

ity rnaybe even come to be negative. The reasons for unstability are model's

large rigidity and slight displacement reaction.

4. AMENDED DISPLACEMENT CONTROLLED METIIOD

From the introduction we can see that the displacemect in each step must be so

big as to the peseudodynamic test can be acrried out normally. If the time step

t.t is extended, the displacement augmentation in each step will also increase.

But too 10ng t.t will effect the precision and even make the results dispersed.

This artical provides an amended dispacement controlled method. The proce­

dure is: When the calcuiated displacement increases slightly. the actuator will

not take actión" but the computre will still calcu1ate the restoring force

through present rigidity. Mter the displacement accumulates to be big e­

nough, the actuator applies this displacement and the measurement takes the

restoring force. In fact, this method supposes the rigidity do not change during

the course of accumulating displacement. For multi-degee system. the relative

disp1acement between stories should be taken into account when we calculate

the rigdity between stories. Sometimes, the relative displacement between sto­

ries and the absolute displacement of floors do not occur simu1taneously.

Therefore, tbis artical adopts the accumulated, relative displacement between

stories to calculate rigidity and insures the stability of rigidity values. This

means, a storey's rigidity will he calcu1ated after its relative displacement has

added up to be big eough. The control process is shown in Fig. 1.

5. TFST RFSULTS

The original structure is a eight-storey house. By usin'e sub-structure pseudo-

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r-------tCOmpute displacement {d,.,} = {d,}+ ~ t{v,}+ ~t' {d,} ~

big enough for actuator

Compute restoring force

{rJ=[ K,l{ d,.,}

No i= i+ 1

t

Decide whether the accumulated No displacement is big enough

for calculating rigidity

Compute accelern.tion

{a,.,}=([Ml+ ó/ [C]) - '({f..,}~[K;]{d,.,} Ót

-[Cl{v,}- T [Cl{a,})

Compute velocity

6t {vi.,}={v.} + 2 ({a,} + {a,.,})

END

Fig I COntrolling Process

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dynomic test method, two stories model with YJ scale was made, In orger to

imitate the moment at the top of the second floor, tne actural model was made

into four stories. The test results are shown in Fig. 2.

300 o.e

Z o.e

200 ! -'" ... n •

B 100 . <=

f\.(I~r' .... ..:: Q.2

J3

I~ co ·ã · 100 9 i .0.' ~ -200 :li -<la

..1CO -<la -0,8 -O.e .0.-4 ..Q.2 o Q.2 0.4 o.s 0..11 o 0.2 n. o.e 0.8 1.2

displacement (111m) time (s)

(a) Restoring Force curve and Displacement-Time curve of the first storey

400 1.' r---------------, 300

3JO

Z -'" 100

§ J3 co ·ã ~

".().4 .Q.2 o D.2 0.4 0.8 -1.5 ~ ___ ~_~ ______ ~_-l

o 0.2 n. 1.2 o.S na displacement (mm ) time (5)

(b) Restoring Force curve and Displacement-Time curve of the second storey

Fig. 2 The Test Results of Amended Displacement Controlled Method

6. CONCLUDING REMARKS

By using amended displacement controlled method, the pseudodynamic test of

large lateral tigidity model under slight displacement conditionwas done. If the

acceleration peak is high, the displacements are applied step-by-step during the

test, which is as same as basic method. When the acceleration peak is small,

accumulating method should be used. In the above test, the actural steps action

of actuator is only about YJ of calculation steps. Obviously, this method is

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econmical and available.

7. REFERENCE

1. Tang Daixin: "Reinforced Concrete Structure and Masonry Structure" Chi­

nese Building Industry Press. 1992.

2. Tang Daixin: "Sub-structure Pseudodynamic Test Method" Journal of

Harbin Architecture University. 1991. No. (6)

3. Zhu Benquan: "The Study on Sub-structure Pseudodynamic Test Method

Accounting for Bending Deformation Effects" Engineering

Mechanics Supplement. 1996. 12

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