Combined Lateral Bending and Axial Load

Sizer implements interaction equations for combined axial and bending resistance from O86 6.5.9 for sawn lumber, 7.5.12 for glulam, 8.4.6 for CLT, and 15.3.3.10 for SCL, respectively, for both axial tension and axial compression loads. For compressive axial load, this equation is of the form

(P_f/P_r)² + (M_f/M_r) [ 1 / (1-P_f/P_E) ] < = 1

where

• P_f is the axial load
• M_f is the maximum applied moment
• P_r is the axial resistance
• M_r is the bending moment resistance
• P_E is the Euler buckling load, which is an expression that takes into account the the length between lateral supports, end fixity, section moment of intertia and modulus of elasticity.

Refer to Axial Design for CLT Wall Panels for a detailed description of the CLT procedure, which differs from the others.

For tensile axial load, the expression is

(T_f /T_r)² + (M_f/M_r) < = 1

where

• T_f is the axial load
• T_r is the axial resistance

Negative Bending Moment Factor

Note that the expression 1 - P_f / P_E that is used to divide the bending moment design ratio can be negative, leading to a more favorable combined ratio. However, as it approaches this condition, it becomes infinitely large, so Sizer considers a negative condition to be a failed design ratio, arising from a weak Euler buckling resistance P_E when compared with the compressive force P_f.

Load Combinations In Each Direction

Sizer constructs load combinations for both directions of loading, axial and lateral, using all the load types on the member, even if some of those load types do not apply to that direction of loading. It relies on both the K_D factor and the fact that some loads will be of zero magnitude in one direction or the other, to discard load combinations during design that are not appropriate to the direction of loading. The complete analysis is too complex to present here.

Load Duration Factor K_D

Refer to Combined Axial and Bending KD Factor for an explanation of the KD factor used int the calculation of axial resistanced Pr and Mr for this purpose

Eccentric Effects

The effects on moment and shear in the lateral direction due to eccentric axial loading are considered in both the creation of load combinations and the calculation of the permanent load factor using 5.3.2.2.