Lateral Load Distribution

The program performs the distribution of lateral loads among the shear walls in a structural floor, taking into account the torsional moment generated due to an eccentricity between the center of mass and the center of rigidity.

The following assumptions have been made:
a) The horizontal diaphragm is infinitely rigid in its plane, so all the walls deflect the same amount and the forces are distributed in proportion to their rigidities.
b) The walls are assumed to be fixed at its base, and either fixed or pinned at its top.
c) Wall deformations are computed as the sum of the bending and shear effects.
d) All the walls are oriented in such a way that the principal axes are parallel to the coordinate axes.

Input Data

The input data required by this program include the floor dimensions in plan, the applied horizontal loads in two perpendicular directions, and its position with respect to an arbitrary origin of coordinates. The point of application of the external loads must be the geometric centroid or the center of mass of the structure in plan.

If the structure is not rectangular in plan, the required dimensions are the maximum and minimum dimensions in plan. The program computes an accidental torsional moment as the larger applied force by an eccentricity of 5% of the longer plan dimension.

In addition to the (x, y) position of its centroid, its dimensions in X and Y directions, and its height are required for each individual wall. The program also considers whether the wall is fixed or cantilevered at top. The required input data is shown schematically in the figure to the right.

Example

As an example, consider the structure subjected to a lateral load of 500 plf along the long side, whose plan view is shown in the figure to the left.

All the walls are 12" thick and 12'-0" high. Find the loads resisted by each wall.

Output

When the data is entered, the program automatically computes the wall rigidities, the position of the rigidity center, and performs the distribution of the lateral loads showing the contribution of the direct load and the torsional effect separately. As recommended by most of the building codes, when the torsional moment reduces the load taken by a wall, this effect is neglected.

Figure above shows the template related to this program with the structure analyzed in the example.