Analytical Results of Bare Frame and Infilled Frames

M ASONRY I NFILLED RC F RAMES

5.3.3 Analytical Results of Bare Frame and Infilled Frames

The analytical model of the bare frame was first calibrated with the experimental results and it can be observed from Fig. 5.4 that the analytical response in terms of initial stiffness and the lateral load capacity matched very well with the experimental results. In the experimental study, it was noted that the bare frame failed by forming flexural plastic hinges in columns and no damage occurred in the beam due to the stiffening action provided by the slab.

Fig. 5.4. Comparison of analytical and experimental results for bare frame (BF) and infilled frames (IF-FB1 and IF-FB2).

In the analytical bare frame model also, flexural plastic hinges were formed in columns only and no hinges were formed in beams (Fig. 5.5). Initially, flexural yielding (stage I) was observed near the bottom portion of left and right columns. Later, as the

0 1 2 3 4

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Compressive Stress (MPa)

Compressive Strain

1:4 mortar grade

0 35 70 105 140

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Base Shear (kN)

Drift (%)

BF_Experiment BF_Analytical IF-FB1_Experiment IF-FB1_Analytical IF-FB2_Experiment IF-FB2_Analytical Infill Crack

Flexural Hinge Yielding Shear Hinge

Capacity 80% Capacity

Flexural Hinge Capacity

the columns (Stage II). After the lateral load capacity of the frame was attained, flexural hinge capacity was reached near the bottom (Stage III) and the top (Stage IV) of the columns. From Fig. 5.4 it can be observed that the post peak lateral load response of the bare frame was appropriately simulated by the analytical model. Therefore, it can be ascertained that global response of the bare frame can be evaluated analytically by modelling the frame elements as 2-noded elements and modelling the non-linear deformational properties by lumped plasticity approach.

Stage I Stage II Stage III Stage IV

Fig. 5.5. Stages of hinge formation for bare frame (BF) and infilled frames (IF-FB1 and IF-FB2) in pushover analysis.

The same analytical model was further used to predict the response of the infilled frames by modelling infill as an equivalent diagonal strut. The comparison of experimental and analytical response along with stages of hinge formation in the infilled frames is also shown in Figs. 5.4 and 5.5, respectively. From the analytical response, it was clearly observed that the analytical strut model fittingly simulated the experimental global response of both the infilled frame specimens (IF-FB1 and IF-FB2). From the experimental study, it was observed that initially most of the lateral force was resisted by masonry infills due to their high initial stiffness. As the lateral drift increased, cracking in infill was observed followed by the attainment of capacity of the infilled frame. In case of analytical model (IF-FB1 and IF-FB2), initial yielding of axial hinges was observed followed by flexural yielding in columns (Stages I and II); prior to the attainment of the lateral load carrying capacity (Fig. 5.5). With increase in lateral drift, axial strut failed along with yielding of flexural hinges at all the plastic hinge locations (Stage III). Later on, the ultimate moment capacity (Mu) of flexure hinges (Fig. 5.2) was reached in the post peak regime after the capacity of the infilled frame ceased to about 80% of the maximum

BF

IF-FB1 IF-FB2

(Stage IV). No shear hinges were formed in the analytical model, as the maximum shear force demand observed in the column was found to be far less than the shear capacity of the column. On the other hand, it was observed in the experimental study that the diagonal shear cracks were initiated in infilled frame at a lower drift level (0.77%) caused by the excessive shear demand on the column due to the frame-infill interaction. Even though the equivalent diagonal strut model was able to simulate the global response of the infilled frames, the model was unable to capture the local component failures, especially, the shear failure of the columns.

I

MPROVEMENT OF

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NALYTICAL

S

TRUT

M

ODEL

From the generalized design philosophy and from the prevailing simplified strut modelling analogy, it was clearly understood that the shear force and bending moment in columns follow constant and linear variation profiles, respectively, under lateral loads (Fig. 5.6). But the past and current experimental investigations revealed that the infill exerted concentrated forces along the compression zones near the loaded corners leading to linear shear and parabolic bending moment variations in the compression zones. It was also deduced that stronger the infill, larger is the magnitude of shear forces, and higher is the likelihood of column shear failure [Fig. 5.6(d)].

Fig. 5.6. Variation of internal force resultants for different analytical models: (a)Bare frame; (b) Infilled frame with single-strut model; (c) Infilled frame with double-strut model; (d) Shear failure of columns due to the effect of infill; and (e) Infilled frame modelled using the proposed improvement. (SFD-shear force diagram; BMD-bending moment

SFD BMD (a)

L R

SFD BMD (b)

L

R R

L

SFD BMD (c)

L R

L R L R

F

F

(e)

BMD lc

l_c

SFD

L R

L R L R

(d)

Similarly, it was observed that shorter the contact zone of the frame-infill interaction, higher the shear demand on the columns where it becomes difficult to verify the columns in shear. Therefore, to predict the seismic shear vulnerability of columns due to the local adverse effect of infill, the existing modelling analogy needs to be improved.

This was achieved in the current study by simulating the effect of infill by applying additional shear forces incrementally along the contact length of the column as shown in Fig. 5.6(e). Initially the nonlinear analysis of the equivalent strut frame was carried out to evaluate the global response and it was calibrated with the experimental response. Then additional shear forces, F [Fig. 5.6(e)] were applied along the contact length of the column. The nonlinear pushover analysis was repeated and the response evaluation was carried out by verifying the formation of shear hinges and global response.

In the current study, it was assumed that the shear failure of the column due to the effect of infill (F) occurs only when the infill exerts maximum force onto the column. In order to evaluate this maximum force exerted by the infill on to the columns, the maximum strength of masonry infill against two failure modes (crushing and shear) calculated using Eqs. (5.3) and (5.4) was considered. Both ASCE 41 (2013) and Al-chaar (2002) recommend considering the strength of infill to be the minimum of that corresponding to crushing and shear mode, but according to Flanagan and Bennett (19991, 2001) and Maidiawati and Sanada (2016), the final failure mode of infill is crushing even though other modes of failure were observed during lateral loading.

Therefore, the obtained horizontal component of the infill force (F) was applied as uniformly distributed load along the contact length (lc) of the column.