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A Beginner's Guide to the Steel Construction Manual, 14th ed. Chapter 9 - Combined Bending & Axial Forces © 2006, 2007, 2008, 2011, 2017 T. Bartlett Quimby |
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Section 9.5 SCM Combined Force Equations Last Revised: 08/16/2017 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 BGSCM 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 (Pr/Pc > 0.2) and another to be used when axial force is not so significant. Another way to look at the equations is that one applies to members which are primarily axial compression members (columns) and the other to members which are primarily bending members (beams). The choice of equation to use follows this logic:
The numerator terms all have the subscript "r". This denotes that these terms represent the required strength of, or demand on, the member. These are the internal forces either from a numeric second-order analysis or from a first-order analysis 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. Unlike compressive axial forces, tensile axial forces tend to reduce internal moment. The denominator terms all have the subscript "c". This denotes that these terms represent the actual capacities or available strengths of the members. The available strengths are determined using SCM chapters E and F as appropriate. If LRFD load combinations were used to determine the required strengths, then the capacities are the nominal capacities multiplied by their appropriate reduction factors, f. If ASD load combinations were used to determine the required strengths, then the 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 and Appendices 7 and 8. 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. |