Crushing

The amount that the wall bottom plate crushes due to the combined overturning and dead force in the end chord studs contributes to the rotational deflection of the wall segment. Shearwalls implements the calculation for this crushing described in the American Wood Council's Special Design Provisions for Wind and Seismic (SDPWS), Example C4.3.4-2.

The expression for deformation Δ_C in the bottom plate under the compression-end end post, otherwise known as "crushing", is parameterized by the ratio r_f = s_cp/ F_cp⊥ where s_cp is the compressive stress perpendicular to the grain and F_c⊥ is the specified resistance perpendicular compression resistance. There are three intervals in the relation between r_f = s_cp/ F_cp and bottom plate deformation:

Linear from (0,0) to Δ_C= 0.02" when r_f = 0.73 : Δ_C = (0.02 / 0.73) r_f

Linear from r_f = 0.73 to Δ_C = 0.04" when r_f = 1.0 : Δ_C = 0.02" ( 1 + ( r - 0.73 ) / 0.27 )

Cubic when r_f > 1.0: Δ_C = 0.04 r_f³

Factored vs. Unfactored Resistance

The SDPWS does not address whether the resistance F_cp is factored for moisture and other conditions. However if failure is defined as the force at which there is 0.04" deflection, and factors are applied to that failure strength for member design, the wood must deform more at lower stress levels if subject to moisture, etc.

Therefore, the factored resistance is used:

F_cp = f K_D K_Scp K_Zcp K_B f_cp, where

f = 0.8

F_cp is the specified compressive resistance perpendicular to the grain of the wall framing material grade

K_D is the load duration factor = 1.15 for wind and seismic

K_Scp is the wet service factor from O86 Table 6-10 = 0.67 for in-service moisture greater than 15%

K_Zcp is the size factor from 6.5.6.4 which we can assume will be 1.15 for all bottom plates

K_B is the bearing factor from O86 6.5.6.5

All factors except K_B are given in the notes to the Framing Materials table.

The bearing area factor is applied only to those force locations that are under openings and the opening does not extend to the bottom of the wall. Otherwise it is at the end of the member where the bearing area factor does not apply.

Refer to Design for Compression Forces for more details about these factors.

Wind Load Combinations

The SDPWS example is for seismic design, which in Canada has the same load combination factor for ultimate limit states (ULS), used for shearwall design and for serviceability limit states (SLS) used for deflection. However however for wind design the ULS factor is 1.4 and the SLS factor is 1.0. Therefore the crushing component of deflection will only reach 0.0285" rather than 0.04" when the bottom plate fails for compression design.