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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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