3.0 Overview
3.1.1 Analytical Idealization of the Generic Buildings
An internal frame (Fig. 3.1) of a three-bay, four-storey (3B-4S) RC building, designed and detailed for the highest seismic zone as per the relevant Indian Standards (BIS 2016a, BIS 2016b), is considered. Three structural configurations representing both regular and irregular frames are considered for the 3B-4S RC frame as listed below:
a. Bare Frame (BF): Masonry infill walls are not provided in any storey (regular frame).
b. Open Ground Storey (OGS) Frame: Masonry infill walls are provided in all the stories except the ground storey (vertically irregular frame).
c. Fully Infilled (FI) frame: Masonry infill walls are provided in all the stories (regular frame).
Different number of bays (NB) and stories (NS) are considered for the building typologies intended to cover low- to mid-rise buildings, and with varying sizes of central opening in infill walls (Op). The openings considered account for the door and window openings present in the buildings. All the frames have a bay width of 3 m and a ground storey height of 4.4 m; all upper stories are 3.2 m high. Though ductile detailing is provided in the RC frame members, the frame is designed as a weak column-strong beam frame system to reflect the current design practice adopted by designers in India as well as in many other countries (Kaushik et al. 2009). The bare frame is modelled as per general design criteria of considering only the weight of masonry infills on the frame members.
For the OGS frame, stiffness and strength of masonry infills are considered in the upper stories; however, the ground storey of the frame is kept open, i.e., without masonry infills.
3.1 Details of Structural Systems
The fully infilled (FI) frames are provided with masonry infills at all stories uniformly.
Thus, both the strength and stiffness of masonry infill walls are considered while modelling for nonlinear analyses of FI frame. Typical structural plan, elevation, and member cross-sectional details of a 3 bay-4 storey (3B-4S) frame are shown in Fig. 3.1.
Figure 3.1 (a) Structural elevation of the considered frame – bare, OGS, and FI, (b) Building floor plan, and detailed sectional properties of (c) columns and (d) beams for the frames.
The RC frame is assumed to be fixed at the base and soil-structure interaction effects are not considered in the study. Columns and beams of the frame are modelled using two-noded frame elements with three degrees of freedom at each node. The mean compressive strength of concrete cubes of 150 mm size is considered as 25 MPa (Elastic Modulus: 25000 MPa), and the reinforcing bars have expected yield stress of 450 MPa (Elastic Modulus: 200 GPa). Poisson’s ratio for concrete is taken as 0.15, and modulus of elasticity Ec of RC members of the frame is calculated using IS 456 (BIS 2000) as:
c 5000 ck
E = f (MPa) (3.1)
where, fck is the characteristic cube strength of concrete in MPa.
Monolithic beam-column joints in RC frames are generally rigid (with some finite strength) as compared to columns and beams of the frame. This effect is simulated in the analytical models by defining end offsets in the RC joints with 50% rigidity (semi-rigid
joints) because of smaller size of joints. Infill walls are modelled as equivalent diagonal struts using two-noded beam elements. Several additional strut models have been proposed in the literature for infills; however, only single strut model is chosen in the present study because of its simplicity. The diagonal struts for masonry walls are modelled such that transfer of bending moments from RC frame elements to masonry is prevented. This is achieved by specifying moment releases at both ends of the strut elements. Therefore, in the plane-frame analysis, strut elements have only two degrees of freedom at each node: translations along two directions. Weight density and Poisson’s ratio for masonry are taken as 18.0 kN/m3 and 0.20, respectively. Modulus of elasticity of masonry Em is taken from Kaushik et al. (2007) as:
550 '
m m
E = f (MPa) (3.2)
where, fm' is the compressive prism strength of masonry in MPa. In the present comparative study, weak masonry with fm' as 4.1 MPa is used in the analyses; therefore, the modulus of elasticity of masonry comes out to be 2255 MPa.
An average value of strut width equal to one-fourth of the diagonal length of infill is used in the present study; this was also suggested by Paulay and Priestley (1992).
4
w s
w = d
(in m) (3.3)where, dw is the diagonal length of masonry wall. The thickness of strut is taken as the actual thickness of masonry walls (220 mm). The reduced width of the strut elements due to the presence of central opening in masonry infill walls is obtained using Eq. (3.4) (Surendran 2012), where r0 is the ratio of opening area to the total area of the wall panel.
Eq. (3.4) was developed based on experimental results of several frames with different opening sizes in masonry infill walls.
(
0) ( )
0.675
Reduced strut width = 1 –r × original strut width (3.4) Beams and columns of the frames are detailed to exhibit ductile response.
Therefore, shear failure of the columns is not expected and not considered in the present study. There is a possibility of shear failure of the columns due to frame-infill interaction.
However, this is a complex phenomenon, which is not taken care of by the simplified
3.1 Details of Structural Systems
diagonal strut modelling used in the present study. The masonry infill panels can fail in several failure modes under seismic action, for example, diagonal compression, crushing in the corners in contact with the frame, sliding shear along horizontal joints and diagonal tension. The present study, however, considers only the diagonal compression as the failure mode in infill panels that can be captured by the simplified equivalent diagonal strut model.
For the frames, first gravity load analysis, as a combination of dead and live loads (DL + 0.25×LL), is carried out before nonlinear static or dynamic analysis. P-delta effects are not included in the analyses, as the frames are not expected to undergo large deformations. Rayleigh damping (CR) is assumed based on a modal damping ratio of 5%
(Wilson 1996) and calculated using Eq. (3.5).
C = M +βK
Rα
(3.5)where, α and β are scale factors calculated using Eq. (3.6).
( - )
-
i j j i i j
2 2
j i
ξ ω ξ ω ω ω
ω ω
α =2
, ( j - i)
-
j i
2 2
j i
ξ ω ξ ω β=2 ω ω
(3.6)
Here, ωi and ωj are two of the Eigen frequencies of the system and ξi and ξj are their corresponding damping ratios, approximately equal to 0.05. The damping ratio for each mode i can thereafter be calculated using Eq. (3.7).
i i
i
ξ + ω β
= 1ω α
2 2
(3.7)