## S3

Horizontal shear deformation A, ft 0.1 0.2 0.3 0.4

Ground surface

Horizontal shear deformation A, ft 0.1 0.2 0.3 0.4

Ground surface

Soil deformation profile Racking deformation of a box structure

FIGURE 28.20 Racking deformation for a box structure (© Parsons Brinckerhoff, Inc. 1993, with permission).

Soil deformation profile Racking deformation of a box structure

FIGURE 28.20 Racking deformation for a box structure (© Parsons Brinckerhoff, Inc. 1993, with permission).

Determine the racking stiffness, Ks, of the structure from a structural frame analysis. For practical purposes, the racking stiffness can be obtained by applying a unit lateral force at the roof level, while the base of the structure is restrained against translation, but with the joints free to rotate. The structural racking stiffness is defined as the ratio of the applied force to the resulting lateral displacement. In performing the structural frame analysis, it is important to use the appropriate moment of inertia, taking into account the potential development of the cracked section, particularly for the vertical walls.

Determine the flexibility ratio, Frec, of the proposed design of the structure using the following equation:

Frec jr 1

where w is the width of the structure and Gm is the average strain-compatible shear modulus of the surrounding ground.

The flexibility ratio is a measure of the relative racking stiffness of the surrounding ground to the racking stiffness of the structure.

Based on the flexibility ratio obtained from Step 3, determine the racking reduction ratio, Rr< structure using Figure 28.21 or the following expression [17]:

for the

The triangular points in Figure 28.21 correspond to published results [12]. The data in [12] were generated by performing a series of dynamic finite element analyses on a number of cases with varying soil and structural properties, structural configurations, and ground motion characteristics. As indicated in the figure, if Frec = 1, the structure is considered to have the same racking stiffness as the surrounding ground, and therefore the racking distortion of the structure is about the same as that of the ground in the free field. When Frec approaches zero, representing a perfectly rigid structure, the structure does not rack regardless of the distortion of the ground in the free field. For Frec > 1.0 the structure becomes flexible relative to the ground, and the racking distortion is magnified in comparison to the shear distortion of the ground in

0 0