Shear wall frame

Shear wall frame

Without question this system is one of the most, if not the most, popular systems for resisting lateral loads. The system has a broad range of applications and has been used for buildings as low as 10 storeys to as high as 50 storeys or even taller buildings. With the advent of haunch girders the applicability of the system is easily extended to buildings in the 70–80 storey range.

1  Shear wall frame interaction

This interaction has been understood for quite some time. The classical mode of the interaction between a prismatic shear wall and a moment frame is shown in Fig. 21.3. The frame basically deflects in a so-called shear mode to which the shear wall predominantly responds by bending as a cantilever.

Compatibility of horizontal deflection produces interaction between the two. The linear sway of the moment frame, when combined with storey sway of shear walls, results in enhanced stiffness because the wall is restrained by the frame in the upper floor while at lower levels the frames restrained by the wall, resulting in deflected shape in the form of a ‘lazy S’ curve.

However, it is always easy to differentiate between modes. A frame with closely spaced columns with deep beams tends to behave more or less like a shear wall in bending mode, while the wall weakened by large openings tends to act more or less like a frame deflecting in shear mode. The combined structural action therefore depends on the relative rigidity of the two and their modes of deformation.

The simple interaction diagram shown in Fig. 21.3 is valid only:

•       if the shear wall and frame have constant stiffness throughout the height;

•       if stiffness varies, the relative stiffness of the wall and the frame remains unchanged throughout the height.

First consider an example of shear wall with moment resisting frame analysed by the Khan and Sbarounis (1964) method.

Example 21.1

Analyse the building shown in Fig. 21.4 for a uniform lateral load of 1.5 kN/m2 which is the result of earthquake motion. All girders are 300 Ã— 500 mm.

Solution

IG = 8.859 Ã— 109 mm4 (includes slab) except 3 m link beam (250 Ã— 400 mm size). ILB = 3.25 Ã— 109 mm4 (link beams are assumed to be hinged). E (concrete) = 20 GPa.

=1.6 Ã— 1012 mm4

=1.6 m4

Lateral load due to earthquake (for the whole frame)

On the nodes 2, 3, 4, 5 = 1.5 Ã— 4 Ã— 12

= 72 kN

On node 1 = 1.5 Ã— 4.5 Ã— 12

= 81 kN

Step 1 Estimate wall deflections. For the approximate analysis, compute deflection of the wall having I = Iw + Ic (1.6 + Ic) loaded with full lateral load. The deflection is computed using Newmark’s method. Ic is comparatively smaller and hence need not be taken into account. The calculations are shown in Fig. 21.5.

Step 2 For the frame to fit the wall and compute the moments by using anti-symmetric loading on a symmetrical structure to reduce the frame to single column frame. Distribution factors are given in Table 21.2 and shown in Fig. 21.6.

Beam stiffness = 1.5 ( S b + Sb′ ) = 0.0168 m3

Fixed end moment in columns due to 0.001 drift

The fixed moments due to drift are shown in Table 21.3. Moment distribution is carried out as shown in Table 21.4. Now the wall has to be analysed for the loading condition as shown in Fig. 21.7. The convergence characteristics are given in Fig. 21.8. The free body diagram is shown in Fig. 21.9.