AN ESTIMATION METHOD FOR SEISMIC EFFECTS OF REINFORCED CONCRETE NON-STRUCTURAL WALLS TO STRUCTURAL FRAME MEMBERS

To resolve the undesirable effects of reinforced concrete non-structural walls to the earthquake behaviour of structural members, weak points (called "Structural Slits") are intentionally provided at the connection between structural members and non-structural walls. This paper presents an estimation method for the stress developed in the "Structural Slits" which are applied to the non-structural walls of reinforced concrete high-rise residential buildings.


INTRODUCTION
and ductility to the resisting mechanism planned.To respond to such principles, a beam-yield type's frame structure which has strong columns and ductile beams is planned.However, as various shapes of reinforced concrete non-structural walls are constructed with structural members using the same concrete materials, the clear resistingmechanism often is not realized by the effects of such non-structural walls.Each small exterior wall shown in Figure 1, which represents part of a typical elevation of high-rise residential buildings developing Recently in Japan, many high-rise buildings have been constructed for redevelopment in cities to use sites effectively and to deal effectively with the problems of land cost skyrocketing.Reinforced concrete frame type structures are very often adopted as the structural system for high-rise residential buildings, because of the low construction cost and the inherent high-stiffness for lateral forces.
In seismic design for high-rise buildings, two basic principles are required: 1) to clear the resisting mechanism to earthquake forces and (2) to provide sufficient strength

Non-structural Walls (spandrel)
Model-A in Japan, is also one of the non-structural walls.Such non-structural walls generate secondary stress into the frames subjecting them to lateral deformation.Figure 2 Non-structural Wall (mullion) Model-B Consequently, the frame may become a different mechanism from the original one planned.
The beam becomes more susceptible to brittle shear-failure.If it is possible to remove such non-structural walls from the frame, the problem may be cleaned up.However, they are provided for such reasons as fire protection, sound insulation, construction cost, design of facade, etc., so it is not so easy to remove them for only a structural assertion.
To resolve comprehensively such problems as earthquake related problems and other requirements, weak points (called "Structural Slits") to break intentionally in times of severe earthquake have been thought out and provided at the connections between structural members and non-structural walls.
Figure 3 shows typical shapes of "Structural Slits".w t'

Wall j_t_j_
Single-Shear Slit As "Structural Slits" are planned to break themselves, it is necessary to know the possible maximum failure-capacity for their use.This paper presents an estimation method for the stress and capacity developed in "Structural Slits".The equations for the estimates were based on the results from twelve tests in which the parts surrounded by broken lines in Figure 1 were modelled.

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TEST PROGRAMS The Objectives of the Tests Two typical reinforced concrete nonstructural walls which form the exterior walls of high-rise residential buildings were modelled to test: Model-A combines a mullion type wall with a half-height spandrel; the other is the mullion type wall, Model-B.
The objective of the tests for Model-A is to determine a reasonable location for setting "Structural Slits".The objective of the tests for Model-Bis to obtain data for stress developed in "Structural Slits".

Test Specimens
The In general, a reinforced concrete member shows the characteristics of longitudinal elongation which occurs by the development of cracks.The non-structural walls in a frame also must have such elongation, if there is little restriction for it.However, in the non-structural walls as shown in Figure 1, the development of longitudinal elongation due to lateral deformation may be restricted by the surrounding frame with strong columns.The arrangement of non-structural walls with the multi-storied condition may also restrict each elongation by itself.The thin flexible steel plates in either side of the specimen and the steel rod at the center of the specimen as shown in Figure 4 are set to restrict the longitudinal elongation in consideration of the condition mentioned above.
Two types of "Structural Slits" are provided : the concave type (called Rectangular Slits") and the single shear type (called "Single Shear Slits") shown in Figure 3. Normal stress is transmitted through the "Structural Slits" in the case of "Rectangular Slits".Shearing stress is trans-

Loading and Measuring
Both supports of the bottom beam, assuming the inflection points of the frame, were provided for the condition of simplesupport.Lateral load-reversals for positive and negative loading were applied alternately from one side of the top beam.
The loads and the displacement during tests was controlled on the basis of the horizontal displacement at the top beam corresponding to a story-drift.
The data concerned with lateral loads, displacements, strains of side-plates, forces of the steel rod for longitudinal restriction to the non-structural wall, strains of reinforcing bars and the surface concrete, etc., were measured at each loading step.
TEST RESULTS

The Forces Developed in Non-Structural Walls
The relation between the lateral loads (Q) and the drift angles (R) of each specimen are shown in Figure 5 by the enveloped curves for cyclic loading.The failure modes after the test in each specimen are shown in Figure 6.The failure mode of the opposite wall not presented here was similar to Figure 6 in each specimen, respectively.
No. 1 specimen, in which the "Structural Slits" were not provided, failed by brittle behaviour due to diagonal tension.The diagonal tension cracks occurred at about 0.004 radian of drift-angles.In No. 2 specimen with "Rectangular Slits of 30% offset" at the top of the wall, the "Structural Slits" crushed in overall width by diagonal compression and simultaneously slipped horizontally.In No. 3 specimen with "Rectangular Slits of 60% offset", the "Structural Slits" crushed partially only near the corner.Diagonal tension cracks occurred, and covered concrete of the top beam fail~d by splitting.

I
No .8 No .9 No .10 No .11was remarkably small compared to the No.4 and No. 5 specimens.Although the "Single-Shear Slits" has difficulties for construction and for rainproofing, it offers excellent performance for mitigation of forces developed in non-structural walls and also for control of damage in non-structural walls.
The Forces Exerted on Beams From Nonstructural Walls Figure 7 illustrates the vertical forces exerted on the upper half of the specimen.The force (C) of compression zone at the corner is expressed by Eg. (1).
where, Tp and T' are the restrictive force in each side of i::'ne steel plates, Ts is the tensile force of reinforcing bars in the wall, and Nr is the external restriction force by steel rod without prestress.
In the specimens with "Structural Slits", the compressive forces ~re mitigated by the effects of "Structural Slits".If the compressive forces are estimated originally, they could be projected to the seismic design of beams with non-structural walls.Figure 9 shows the distribution of longitudinal strains along the connection between the wall and the beam.As shown in the figure, the strain distribution is approximately linear in each range of drift-angle.
Figure 10 shows the relation between the drift-angle (R) and the rotation angle (8 -) which is measured at the end of the wall J with "Structural Slits".It is observed that ej is approximately the same as R in the range before the failure of "Structural Slits".This seems to indicate that the non-structural wall between the top and the bottom almost behaves as a rigid body.

ESTIMATION OF COMPRESSION FORCE DEVELOPED IN "STRUCTURAL SLITS" Assumptions to Express the Equation of Compression Force
The following is assumed to precede the equation for estimation of the compression force (C) in "Structural Slits".

1)
The distance between top and bottom beam, h 0 is kept constant during loading.

2)
The non-structural wall behaves as a rigid body.The drift angle (R) is the same as the rotation angle (0i) at the end of the wall with "Structural Slits".
3) The triangular compressive strain-zones are formed at the top and the bottom end of the wall.

4)
The ratios of the strains at both compression fibres (a= Ew/E•) are proportional to the offset ratio~ of wall thickness.(See Figure 12).

5)
The nominal deformations sunk into beams is O.lh 0 times the fibre strain in each compression zone.ej (x O. 001 rad.) 2 0 , ----------r -------, ~ The relation between the drift-angle (R) and the compression fibre strain (£j) in the "Structural Slits" is expressed in Eq. ( 2) from the geometric deformation on the above assumptions.where, £w and h 0 are the width and the height of the non-structural wall, respectively.The length of compression zone in the "Structural Slits", (Xr,l is expressed by Eq. (3), see Figure 11.

Comparison of Estimated Values with Test Results
Applying the "e-function expression" proposed by Dr. H. Umemura [l] for the stress-strain relationships of concrete in compression, the maximum compressive resultants (Cmaxl developed in the zone (Xnl were calculated for each specimen.The results calculated are presented in Table 3 compared with the test results.The estimated values for the specimens in which concretecrushing occurred in "Structural Slits" are comparatively close to the measured values. In No. 1 specimen, in which the shear failure occurred prior to the concrete-crushing, and in No. 12 specimen, in which the failure of covered concrete occurred without any crushing in "Structural Slits", the measured values are lower than the estimation.~he effects of compression forces developed in non-structural walls which were arranged with the multi-storied condition could be dealt as a coupled moment, as shown in Figure 13, and could be expressed by Eq. ( 4).The secondary moments and shear forces due to Figure 13 should be added to the original frame-stresses analysed for the frame without non-structural walls. (4) where, C is the resultant compressionforce, and Jw is the distance between the coupling forces (C}.

FIGURE 13
Additional stress by non-structural walls COUPLING FORCE EXERTED ON BEAMS FROM NON-STRUCTURAL WALLS

FIGURE 1 :
FIGURE 1: ILLUSTRATION OF NON-STRUCTURAL WALLS IN HIGH-RISERESIDENTIAL BUILDINGS

FIGURE 3 :
FIGURE 3 : TYPICAL STRUCTURAL SLITS FIGURE 4 SHAPE AND SIZE OF TEST-SPECIMENSin Figure4.Two same non-structural walls are opposite in a specimen.The adoption of the opposite-walls-system reflects consideration for stability of the specimen during tests.
FIGURE 5 : ENVELOPED CURVES OF RELATION BETWEEN LATERAL LOAD (Q) AND DRIFT-ANGLE (R) FIGURE 6 : FAILURE MODES OF EACH SPECIMEN AFTER TEST FIGURE 9 FIGURE 12

TABLE 1 :
THE LIST OF SPECIMENS