Deflection Equation and Components

4-term Equation

The program calculates the in-plane deflection of all shear resisting elements. Shearwalls implements the rigorous 4-term equation from SDPWS Commentary, Equation. C4.3.2-1

from SDPWS Commentary, Equation. C4.3.2-1:

Three-term Equation

Using a Design Setting, you can also choose to use tne 3-term equation given in SDPWS 4.3.2, Equation 4.3-1, in which the terms

are replaced by

where G_a is the effective shear stiffness calculated as described in Combined Shear and Nail Slip Deflection.

The meaning of the variables is given in the sub-topics under.Physical Parameters.

Meaning of Terms in Equation

The terms in the four-term equation give the contribution to deflection from the following sources, in order

• Bending: Bending of vertical shear wall chords (wall segment end studs)
• Shear: In-plane shear deformation of sheathing
• Nail slip: Slippage of nails fastening sheathing to top and bottom wall plates and to intermediate blocking
• Hold-down displacement: Shear wall rotation due to::
  • slippage of fasteners connecting hold-downs to studs,
  • elongation of hold-down brackets,
  • wood shrinkage within length of hold-down
  • wood crushing at compression force location at other end
  • oversized boltholes
  • additional displacement due to mis-cuts, gaps, etc.

In the three-term equation, the shear and nail slip values are combined into a single term.

Three-term vs. Four-term Equation

The three-term equation is a simplification of the four-term equation, using a linear approximation to the non-linear nail slippage effects, essentially by setting any terms that are non-linear in the shear force v to their value at shear wall capacity. This ensures that the equation is conservative in the amount of shear wall deflection for all shear walls that pass shear design, but it also has a significant impact on load and force distribution to wall segments using stiffness-based distribution, and this effect can be conservative or non-conservative.

Non-wood/Proprietary Walls

These calculations do not apply to Non-wood/Proprietary walls. Refer to Deflection of on-wood/Proprietary Walls for the procedure used for these walls.