SDPWS Deflection Equation

This setting allows you to choose between using the 3-term deflection equation from SDPWS 4.2-1 and the non-linear 4-term equation from C4.3.2-1.

The 3-term equation is a linearization of the 4-term equation, arrived at by combining the shear and nail slip equations in the 4-term equation using an "apparent" shear stiffness G_a. The linearization is achieved by setting the non-linear occurrences of shear force v in the 4-term equation to the shear capacity of the shear wall to render this value constant. It is therefore identical to the 4-term equation when the shear wall is at capacity, conservative when below capacity, and non-conservative for shear walls that are overstressed for design anyway. SDPWS Figure C4.3.2 shows this in graphical form.

The four-term equation was originally implemented in Shearwalls because it is more accurate and because the SDPWS does not publish G_a values for wind design. However, the process of equalizing deflections on the shear-resisting elements by adjusting the forces apportioned to each element converges more rapidly for the linear 3-term equation than the non-linear 4-term equation. Also, some users are more comfortable using the 3-term equation because it is in the main body of the SDPWS, whereas the 4-term equation is in the Commentary.

Note that sometimes neither equation converges because the solution lies in the discontinuity created at the point that the dead load force at a hold-down location equals the overturning force, and there is a jump in deflection due to the constant component of hold-down displacement from shrinkage, tolerance, and gaps. In this case, the program oscillates between two states that do not equalize deflections. The choice of 3-term vs. 4-term equation will not necessarily rectify this. We are working on a solution to this condition for a service release in the near future.