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Stiffness used for Deflection Calculations
The value of EIapp from Equation 10.4-1 using the shear deformation factor Ks = 11.5 value for uniformly distributed loads and simple-span pinned pinned conditions is currently applied for all loading, fixity, and span conditions. This can create inaccurate shear deflection for some loading conditions, and WoodWorks is developing a rigorous implementation of shear deflection to be integrated into our matrix stiffness loads analysis.
The calculation of the effective bending stiffness (EI)eff used in this equation is given in CLT Handbook 3.3.1 and O86 8.4.3.2 - Effective Stiffness.
Stiffness Used for Buckling Calculations (EI) app-min’
(EI) app-min’ is the factored effective stiffness modified for shear deflection. Although the E for pure bending is used to derive Emin for other materials, NDS Commentary C10.3.7 refers to “significant shear deformation that can occur between the parallel and perpendicular CLT laminations”.
EIapp is determined from EIeff using NDS Equation 10.4-1, then the formula from NDS Appendix Eqn. D-4 and Commentary Eqn. C4.2.4-1, is applied to get (EI) app-min. Finally the adjustment factors from NDS Table 10.3.1 ( or Table 16.2.2. for fire design) are applied to get EIapp-min’.
Note that Eqn. D-4 that is ordinarily applied to E to determine Emin includes a 1.03 factor to convert to pure bending, that is, to factor out the decrease in the published E from the true E to account for shear deflection. This factor has been included in (EI)app-min even though it is intended to include shear deflection.
Examples in the CLT Handbook and the AWC Technical Report 10 for fire design include the 1.03 factor, so it is retained in Sizer as well even though it is contrary to the intention of C10.3.7. Note that the lamination E values used to create EIeff include the 1/1.03 factor for shear deflection, so this just serves to eliminate this redundancy for buckling design.
Ks Factor for Column Buckling
The Ks factor in Table 10.4.1.1 used to determine EIapp for column buckling is derived using the following expression
and then substituting the expression for PcE given earlier; i.e. PcE-app = π2 (EI)app / (KeL) 2 and PcE-eff = π2 (EI)eff. / (KeL) 2 . κ is a standard factor for section shape, which equals 1.2. for rectangles.
If you then isolate EIapp on the left-hand side, and compare with NDS Equation 10.4-1, which is
you find that
Ks = κ ( π / Ke )2
The values 11.8 and 47.4 for Ks in Table 10.4.1 are derived using the "recommended design" row from NDS Table G1 for Ke , for pinned-pinned and fixed-fixed columns, respectively.
Sizer allows pinned-fixed, pinned-pinned, and fixed-free columns, and allows you to enter your own Ke value, so Ks is calculated with the above formula and the Ke values that you input. The default values Ke of 0.8, 1.0, and 2.1, respectively, yield Ks values of 18.50, 11.84, and 2.68.