P ARAMETRIC S TUDY
5.3 R ESPONSE OF S HEAR W ALL - S LAB A SSEMBLAGE
5.3.3 Propagation of Crack and Damage
The variation of equivalent plastic strain in slab concrete with respect to the lateral drift is obtained at different locations along the wall-slab junction (Figure 5.4). Since the maximum equivalent plastic strain reflects the trend of crack formation, the tendency of crack formation in slab concrete in the different models is also obtained.
For WSC1, WSC2, WSC5 and WSC6 models (Figures 5.4a and 5.4b), almost similar cracking patterns are observed due to the same aspect ratios of the wall panels. The plastic strain values for 3% vertical reinforcement ratio are less as compared to the values obtained for 0.25% steel ratio, leading to less cracking in the junction region. The vertical reinforcement at the tension face of the shear wall starts yielding first resulting in the high plastic strain concentration.
It is observed that the plastic strain value reduces with increasing distance from the tension face of the wall. The web portion of the shear wall experiences less strain and the strain increases in small amount at the compression face. The plastic strain values increase with the drift as the cracks start propagating from the tension face of the shear wall. Cracking of concrete starts at the base of the shear wall and propagates up to the wall-slab junction. Due to the presence of the floor slab, a diagonal strut develops in the wall panel between two successive floor slabs, thus, the slender wall gets partitioned into a number of squat wall panels between the floor slabs.
Distance from the tension face of the wall Distance from the tension face of the wall (In Fraction of Lw) (In Fraction of Lw)
(a) (b)
Distance from the tension face of the wall Distance from the tension face of the wall (In Fraction of Lw) (In Fraction of Lw)
(c) (d)
Figure 5.3: Variation of minimum principal stress in shear wall: (a) WSC1 and WSC5; (b) WSC2 and WSC6; (c) WSC3 and WSC7; (d) WSC4 and WSC8.
For WSC3 and WSC7 (Figure 5.4c) models, squat wall behaviour is observed due to the low aspect ratio of those specimens. Maximum cracking is observed in the floor slab at the two ends of the wall-slab junction region. In this case also, the strut action spreads over a large region in the wall panel due to lower aspect ratio. Since the length of the shear wall is more, cracks do not propagate till the middle of the slab for low drift ratios. Though plastic strain values in the middle portion of the slab increase after 0.75% drift, the maximum values are observed at the two ends of the wall- slab junction.
Normalized minimum principal stress Normalized minimum principal stress
Distance from the tension face of the wall Distance from the tension face of the wall
(In Fraction of Lw) (In Fraction of Lw)
(a) (b)
Distance from the tension face of the wall Distance from the tension face of the wall (In Fraction of Lw) (In Fraction of Lw)
(c) (d)
Figure 5.4: Comparison of equivalent plastic strain in slab along the length of shear wall: (a) WSC1 and WSC5; (b) WSC2 and WSC6; (c) WSC3 and WSC7; (d) WSC4 and WSC8.
For WSC4 and WSC8 (Figure 5.4d), the plastic strain values are maximum as compared to the other models leading to a large number of cracks at the tension face of the wall and also in the floor slab.
It is concluded that the aspect ratio and the reinforcement ratio significantly affect the damage propagation and the load carrying capacity. Specimen with lower reinforcement ratio tends to develop more cracks in the junction region. After a drift level of 0.5%, the equivalent plastic strain in concrete at the shear wall-slab junction along the length of the wall exceeds the crushing strain of concrete (0.01). This may lead to the development of a major sliding shear crack across the wall- slab junction in the plane of the wall. The sliding cracks can further result in the formation of compressive strut in wall panel between the floor slabs.
Higher values of compressive stresses are observed at the wall-slab junction as compared to those observed at the base of the wall. Similar results were observed in the experimental study carried by Ile and Reynouard (2004). Deformation of individual bar at wall-slab junction also leads to
Equivalent plastic strain Equivalent plastic strain
concentration of stresses. Stresses in the longitudinal reinforcement of the slab reach the yield values starting from the face of the wall and extend linearly to the edge support. In the shear wall-slab junction region, most of the vertical reinforcing bars get yielded. The maximum tensile damage is observed in the shear wall-slab junction region and spreads diagonally between two consecutive floor slabs concentrating the stresses at the corners. Flexural shear cracks are formed in the slab at the connection with the shear wall (Pantazopoulou and Imran, 1992). In addition, major cracks develop in the slab at the tension face of the wall-slab junction.
Figures 5.5 and 5.6 show the propagation of cracks from the initial cracking to the crushing of concrete up to the final displacement. The cracks in the shear wall start from the bottom and propagate to the shear wall-slab junction region. However, at wall-slab junction, first cracking starts at the first floor slab and then in the shear wall. The vertical bars on the tension side at the bottom of the wall start yielding for all the models. Also at the same displacement level, some of the vertical bars at the first floor shear wall-slab junction region start yielding. Since the yielding of reinforcement in the shear wall and floor slab starts at a very low drift ratio, significant nonlinear behavior is observed in wall and slab well before the code specified elastic drift of 0.4% (BIS, 2016b). The crushing of concrete is observed to initiate in wall-slab junction at a lateral drift of 1.47% for WSC1 and WSC2 and at 1.6% for WSC5 respectively. Due to the presence of floor slab, a diagonal compressive strut develops in the wall panel between two successive floor slabs similar to squat wall behaviour. Thus, the floor slab significantly modifies the behavior of the slender wall by partitioning it into squat wall panels.
Comparing WSC1, WSC2 and WSC5 models at different drift ratios, it is observed that with higher reinforcement in WSC5, the patterns of cracking and tensile damage are completely different as compared to the other two models. The damage does not spread significantly in the floor slab for WSC5, whereas, in case of WSC1 and WSC2, diagonal struts tend to concentrate the damage at the wall-slab junction regions along with considerable propagation of damage in the slab panel (Figure 5.5). These models are compared since the length of the wall is same in all of them.
Lateral drift (%)
Tensile damage pattern
WSC1 WSC2 WSC5
0.5
1.0
1.5
2.0
3.33 (Final Stage)
Figure 5.5: Variation of tensile damage with lateral drift level in WSC1, WSC2 and WSC5 models.
Comparing the pattern in WSC2, WSC3 and WSC4 models, it is observed that the formation of strut is more prominent in case of WSC2. All these models are compared as they are having the same reinforcement ratio but different aspect ratios. WSC3 model is more squat and WSC4 model is more slender than WSC2 model. Comparing the propagation of damage in the slab and the wall at different drift levels, it is observed that the maximum level of damage is attained faster in case of slender wall model (WSC4). Less damage propagation is observed in squat wall model (WSC3). It is observed that the slab reinforcement connected to the shear wall, along the length of wall, yields first, while the reinforcement in the extended slab region remains unyielded. The vertical reinforcement in the wall yields mostly at the wall-slab junction region.
Also, it is observed from the cracking pattern and tensile damage pattern that maximum cracks are developed in the slab panels connected with shear wall. The extended part of floor slab panels, not connected with shear wall, experiences less cracks and very less damage. Conventionally, slender shear wall in multi-storied buildings is designed in the same way as an isolated shear wall. However, due to the presence of slabs, lateral stiffness of wall tends to increase at each wall-slab junction.
Thus, the slender wall gets partitioned into a number of smaller panels between successive floor slabs. Each such panel behaves as a squat wall with the formation of diagonal strut between two successive wall-slab junctions as observed for WSC1 and WSC2 models. Thus, the design methodology for slender walls in multistoried buildings with floor slabs need to consider strut formation and the associated failure modes in the partition wall panels.
Lateral drift (%)
Tensile damage pattern
WSC2 WSC3 WSC4
0.5
1.0
1.5
2.0
3.33 (Final stage)
Figure 5.6: Variation of tensile damage with lateral drift level in WSC2, WSC3 and WSC4 models.