A Beginner's Guide to the Steel Construction Manual, 13^th ed. (old)

Chapter 9 - Combined Bending & Axial Forces

© 2006, 2007, 2008 T. Bartlett Quimby

Section 9.5

SCM Combined Force Equations

Last Revised: 11/04/2014

SCM H1 presents the combination equations to be used when determining the adequacy of steel members subject to both axial force and bending.  These equations take the general form of the combination equations presented in section 9.2, with some modifications.

Equations H1-1

SCM H1.1 presents two combination equations.  One is used for members that have a fairly significant axial force component (P_r/P_c > 0.2) and another to be used when axial force is not so significant.

The choice of equation to use follows this logic:

IF P_r/P_c > 0.2 THEN
     use equation H1-1a
ELSE
     use equation H1-1b

The numerator terms all have the subscript "r".  This denotes that these terms represent the required capacity of, or demand on, the member.  These are the internal forces modified for second order effects.  These values are determined by using analyses that utilize either LRFD or ASD load combinations.

If the axial force is tensile, there is, conservatively, no modification of the internal forces for second order effects.

The denominator terms all have the subscript "c".  This denotes that these terms represent the actual capacities of the members.  The capacities are determined using SCM chapters E and F as appropriate.  If LRFD load combinations were used to determine the required strengths, then capacities are the nominal capacities multiplied by their appropriate reduction factors, f.  If ASD load combinations were used to determine the required strengths, then capacities are the nominal capacities divided by their appropriate factors of safety, W.

The equations H1-1 combine items computed in SCM chapters C, D, E, and F.  By the nature of the equations, a single spreadsheet tool can be developed be used in the design of members subjected to axial tension, axial compression, strong axis bending, weak axis bending, and any combination of axial force and bending.  If equations H1-1 are satisfied, then the provisions of SCM chapters D, E, and F will also be satisfied. 

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