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Shear force distribution to the piers in force-transfer walls is described in APA T555 as a sequence of numerical calculations in a design example of a wall with two openings of the same size. The following gives an algebraic formulation of the general procedure used by Shearwalls; it corresponds to the calculations in the T555 example.
V – Total shear force on wall (lbs)
– Unit shear force in the opening piers
– Unit shear force in central piers
– Unit shear force in corner piers
– Distance from top of opening to the top of the wall
– Distance from bottom of opening to bottom of the wall
– Height of wall
– Length of wall
– Length of opening
– Length of opening to the right of pier under consideration
– Length of opening to the left of pier under consideration
– Length of pier under consideration
– Length of central pier to the left of the pier under consideration
– Length of central pier to the right of the pier under consideration
Opening Piers
The total shear force in a vertical line on the wall is equal to the hold-down force VH / L (neglecting hold-down offsets), so the unit shear force in the upper and lower piers is that force divided by the length of the combined height of the piers:
Central Piers
The force in the central piers is the unit diaphragm shear force over the wall segment with the central pier plus the portion of diaphragm shear force over the openings on either side of the pier transferred to the pier via straps and blocking. This portion is determined by multiplying the unit diaphragm force by the ratio of the adjacent opening lengths to the combined length of the central piers on either side of these openings.
Corner Piers
The unit force in the corner pier is the unit force in the central pier minus the strap/blocking forces from each side divided by the length of the pier. This works out to
