C ONNECTED W ITH F LOOR S LABS
6.3 R ESULTS OF N ONLINEAR A NALYSIS
6.3.1 Plastic Hinge Length
Based on the tensile damage at wall-slab junction region, possible extent of plastic hinge region are identified for different wall panel aspect ratios (Figures 6.10 and 6.11) during monotonic and cyclic analyses. Although conventionally inelastic curvature is directly used for expressing the plastic hinge length (Lp), the extent of tensile damage is also considered as a useful indicator for the present study. In case of monotonic pushover analysis, the curvature profile considering the strains at the extreme tension and compressive faces of the shear wall is obtained at the maximum damage level.
The curvature profile for cyclic loading is obtained at the maximum lateral load capacity of the shear wall. The variation in stress in the vertical reinforcement over the height of the wall and possible yielding of reinforcement at the wall-slab junction region are related to the maximum tensile damage at the wall-slab junction region. Although the observed maximum curvature reduces with increase in wall panel aspect ratio, the spread of tensile damage also decreases with the spreading out of strut-and-tie action in squat wall panels. This is observed for both monotonic and cyclic displacement-controlled nonlinear static analyses. It is observed that the spread of plasticity at the junction region reduces with an increase in the length of wall. Since the effect of axial compression is not contributing to the tensile damage and the compressive strains at the wall-slab junction region, the aspect ratio is considered as the key parameter affecting the extent of the zone showing inelastic behaviour.
For both monotonic pushover and cyclic pushover analyses, the identified Lp, normalized with respect to the length of the wall, is observed to increase with the wall panel aspect ratio (hs/Lw) (Figure 6.12). Considering Lp to be linearly varying with storey height and length of shear wall panel, the normalized plastic hinge length at the wall-slab junction is obtained using regression analysis and is expressed as,
0174 . 0 0546
.
, 0
w s w
cyclic p
L h L
L for cyclic loading, and (6.12)
tw hs floor slab
floor slab
floor slab
floor slab
roof slab Figure 6.9: Observation of plastic hinge region in specimen with wall panel aspect ratio of 1.67: (a) typical wall-slab assemblage, (b) variation in compressive strain, (c) tensile damge pattern, (d) variation in tensile damage and (e) variation in curvature profile.
(a) (b) (c) (d) (e)
Lp = 0.100Lw 0.06hs
hs/Lw = 1.67 Expected Plastic hinge region Lp = 0.069 Lw hs/Lw = 0.75 0.09hs Lp = 0.080 Lw hs/Lw = 1 0.08hs0.06h Lp = 0.030 Lw
hs/Lw = 0.5 Lp = 0.090 Lw
0.07hs
hs/Lw = 1.25
Figure 6.110: Comparison of possible plastic hinge length (Lp) for wall panels with different aspect ratios under monotonic nonlinear static analysis: (a) for aspect ratio of 1.67, (b) for aspect ratio of 1.25, (c) for aspect ratio of 1.0, (d) for aspect ratio of 0.75 and (e) for aspect ratio of 0.5. Figure 6.11: Comparison of possible plastic hinge length (Lp) for wall panels with different aspect ratios under cyclic nonlinear static analysis: (a) for aspect ratio of 1.67, (b) for aspect ratio of 1.25, (c) for aspect ratio of 1.0, (d) for aspect ratio of 0.75 and (e) for aspect ratio of 0.5.
hs/Lw = 1.25 Lp = 0.113 Lw
hs/Lw = 1 Lp = 0.090 Lw0.09hs0.09hs0.09hs
hs/Lw = 0.75 Lp = 0.070 Lw
0.14 hs Lp = 0.070 Lw
hs/Lw = 0.5 Lp = 0.150 Lw0.09hs
hs/Lw = 1.67 Expected Plastic hinge region (a) (b) (c) (d)(e) (a) (b) (c) (d)(e)
0234 . 0 0728
.
, 0
w s w
monotonic p
L h L
L for monotonic loading. (6.13)
From Eqs. (6.12) and (6.13), it is observed that Lp,monotonic1.34Lp,cyclic. To examine the accuracy of the proposed Eqs. (6.12) and (6.13), the plastic hinge length (Lp) at the wall-slab junction is estimated for five different lengths of shear wall and compared with the calculated values of Lp
proposed in the various past studies on RC walls (Table 6.1). In the past studies, it is mentioned that inelastic behaviour is observed mostly at the bottom of the isolated slender shear wall. However, the presence of slabs at every floor level in a multistoried building leads to inelastic behaviour at the wall-slab junction in addition to the inelastic behaviour at the base of the wall. The estimates of Lp, as per Eqs. (6.12) and (6.13), are obtained considering the possible zones of inelastic behaviour along the height of the wall and at wall-slab junction.
(a) (b)
Figure 6.12: Variation of normalized plastic hinge length with wall-panel aspect ratio for: (a) monotonic and (b) cyclic analysis cases.
Among the past studies, Panagiotakos and Fardis (2001) have proposed expressions for plastic hinge length under monotonic and cyclic loadings. Closed form equations were developed for the ultimate deformation capacity and for the deformation at yielding of RC members in terms of their geometric and mechanical characteristics. The database used for the study comprised of 1012 tests (mainly cyclic loading) of RC members in uniaxial bending, with or without axial compression. Out of these specimens, 61 specimens are walls with a rectangular, barbelled, or T-section. On comparing the estimated plastic hinge lengths under monotonic and cyclic loadings, it is observed that the analytical estimates using the equations of Panagiotakos and Fardis (2001) are slightly lesser than
Lp/Lw = 0.0728[hs/Lw]+0.0234 R2 = 0.9491
Lp/Lw = 0.0546[hs/Lw]+0.0174 R2 = 0.832
Lp/Lw Lp/Lw
hs/Lw hs/Lw
the estimated values as per the proposed equation (Table 6.1). However, the proposed expressions are applicable only for the plastic hinge region adjacent to the wall-slab junction region. Between the two parameters, hs and Lw, more weightage is given on hs which reflects the increase in plastic hinge length with more slender wall panel.
Table 6.1: Comparison of plastic hinge length for different lengths of shear wall