4.1. Strength of Masonry Infills
In ASCE 41 [
25], which is a representative standard used for the seismic performance evaluation of buildings, the shear strength of masonry was defined as the sum of cohesion and friction.
where
is the friction coefficient,
is the horizontal cross-sectional area of an infill, and
is cohesion of the brick–mortar interface, which is equal to the shear strength when no axial stress is applied.
is the axial load supported by the infill caused by gravity distributed between the infill and the columns based on their relative axial stiffnesses assuming full contact between the infill and the beams.
In the case of the specimen in this paper,
was ignored as the masonry wall was constructed after the frame was completed so that no vertical load was applied. Therefore, the strength of the masonry wall is determined by the cohesion only. The strength of the specimen calculated using only the adhesive strength obtained through material testing is 270.3 kN for single wythe and 371.9 kN for double wythe.
Table 5 shows a comparison between the calculated strength and the strength from the tests. It can be seen that the prediction for IFS-0.5, which has a single wythe wall with a gap, was accurate, but predictions for the rest of the specimens were underestimated. This result implies that frictional force should be considered.
In FEMA 306 [
24], the masonry shear strength
is described as the sum of the bond strength
between the masonry unit and the mortar, and the frictional force, which is the product of the friction coefficient and normal stress applied to the masonry, as shown in Equation (4). Here, the normal stress
can be calculated from the curvature shortening associated with lateral displacement of the frame, as shown in Equation (5).
where
is the friction coefficient,
is the modulus of elasticity of the masonry, and
is the rotation angle of the column in radians.
Therefore, the shear force carried by the masonry infill wall can be estimated by multiplying the shear strength by the area of the masonry, as shown in Equation (6). However, if there is a gap, no normal force can be developed by curvature shortening, and the shear strength of the masonry depends on bonding strength only.
As shown in
Figure 4, the shear strength of masonry of 0.462 MPa and the friction coefficient of 1.564 were obtained from the material test. To obtain the frictional force, the normal stress
was calculated via Equation (5) using the rotation angle when the specimen exhibits the maximum lateral force (
in
Figure 9). However, in the case of IF-0.5, the difference between the maximum strength of the first cycle and that of the second cycle at 1.5% drift was very large, as shown in
Figure 9b. It was observed that the maximum strength was reached before the 1.5% drift; thus, a drift angle of 1.0% was used for the estimation of the normal force.
Table 6 shows the predicted strength for each specimen. The values of
are the sum of the predicted strength masonry infill (
) and expected lateral strength of the frame when flexural failure occurs at both columns (2
) using an actual yield strength of a SD300 rebar (367.6 MPa; see
Table 2). A lateral load of 89.4 kN for a column was obtained from the calculation using Equation (1).
In IF-0.5 and IFS-0.5, in which single wythe masonry walls were used, the predicted values in
Table 6 are very close to the test results. However, for IF1.0 and IFS-1.0, in which the double wythe masonry wall was used, the predictions underestimate the test results by 79% to 93%.
4.2. Frame Strength Accounting for Interaction with the Masonry Infill Wall
The strength prediction in
Table 6 underestimates the strength of specimens with double wythe (IF-1.0 and IFS-1.0). It should be noted that strength prediction was made based on the flexural failure strength of the columns, although the actual failure mode of the two specimens was the shear failure of columns rather than flexural failure. The reason for such change in failure mode is presumably the existence of an interaction between the masonry infills and the surrounding frame. It is generally assumed that, in a masonry-infilled frame, the infill walls and frame resist lateral loads by formulating a diagonal compression strut, as shown in
Figure 10b. The horizontal component of this strut force will be applied to the upper part of the windward column and the lower part of the leeward column.
Figure 10a is the free body diagram of the windward column when it was assumed that both ends of the column yield by flexure.
Figure 11 shows the shear force diagram and bending moment diagram for the free body diagram in
Figure 10a. It was assumed that plastic hinges were formulated at both ends, and the reactive force from the masonry wall acts as a triangular distributed load at the top of the column. If
, which represents the shear force at the top of the column, is lower than the shear strength of the column section
, flexural yielding will occur as assumed. However, as shown in the figure, if
exceeds the shear strength of column
, shear failure will occur before flexural yielding at both ends of the column.
In the IF-1.0 and IFS-1.0 specimens, in which the double wythe masonry wall was used, shear failure occurred. Therefore, the contribution of the lateral-load capacity of a frame part was adjusted considering the difference in the failure mode as follows.
First, as shown in
Figure 10a, when flexural yielding occurs at both ends, the equilibrium moment equation centered on the lower part of the column can be established as shown in Equation (7).
where
is the clear height of the column,
is the plastic moment capacity of a column section, and
is the contact length between the masonry infill and the frame. In this study,
was estimated according to ASCE 41 [
25] as
, with
being the equivalent strut width.
Solving for
in Equation (7) yields Equation (8), which shows that
is the increase in nodal force at the top of the column due to reaction from the masonry infill wall, considering that
is the shear strength when flexural yielding occurs at both ends of a column in a bare frame.
For the IF-1.0 specimen, the strength of the masonry infill wall, including the frictional force, was 306.3 kN.
, calculated using Equation (8), was 384.7 kN, and the shear strength of column
was 175.3 kN. Since
exceeds
, it is expected that the column will fail due to shear failure, and the maximum load that can be applied to a windward column will be 175.3 kN, which is the nodal load at the top of the column member when any of the column sections reaches shear failure. Strictly speaking, if yielding does not occur at the end of the column, the magnitude at both ends and concentrated load at the top of the column
should be determined from the solution of an indeterminate structure. However, simple proportionality was assumed for brevity to obtain
. A similar procedure can be applied to the leeward column to obtain the applied load at the top of the column. Total horizontal force is determined by summing the load carried by the windward column, leeward column, and masonry infill. Strength predictions for IF1.0 and IFS-1.0 by the procedure above are summarized and compared with test results in
Table 7. Predictions became closer to the test results, ranging from 95% to 106% in the case of IF-1.0 and from 96% to 113% in the case of IFS-1.0.
Compared with the average values of the peak force in the positive and negative directions, the predictions showed an almost perfect match. However, the predictions in this study were made based on observations of test specimens, especially observed failure mode and the drift angle at the maximum load. In order for the proposed method to be used practically, the failure mode and the deformation angle at the maximum load must be theoretically determined. In addition, a method for discriminating the various destruction modes of masonry is required. Additionally, it is necessary to check whether the proposed method is effective in other failure modes of masonry walls.