Chapter 9 - Combined Bending & Axial Forces
© 2006, 2007, 2008, 2011, 2017 T. Bartlett Quimby
Introduction to Combined Effects
Last Revised: 07/08/2017
From statics and structural analysis engineers learn how to find forces on structural elements that can, at any given section, result in three translational forces and three rotational internal forces. These internal forces cause stress at points on a given section. As elastic behavior is assumed, the total normal stress at a point is the sum of the normal stresses at that point caused by the applicable internal forces. To be safe, the maximum total normal stress cannot exceed the capacity of the material to handle the stress.
Multiplying the material stress capacity by the appropriate section properties yields the strengths associated with each stress. The strengths must exceed the internal forces, as has been seen in the various strength based limit states considered to date. When combining forces, the ability to compute strengths associated with each internal forces is required. Consequently, considering combined effects will necessitate a good ability to compute axial (SCM Chapter E) and bending strengths (SCM Chapter F) in members.
The simultaneous combination of axial compression with bending creates what are known as "second-order" effects. The bending forces, alone, create deflections in the member. Adding axial force to the deflected member creates additional bending moment which, in turn, creates more moment, which creates more deflection, which creates more moment, which creates more deflection, etc until either the member either becomes unstable or the deflection/moment cycle converges.
The result of second-order effects is that the internal moments, in the presence of axial force, are actually larger that those predicted from structural analysis on the undeflected shape.
SCM Chapter H used to combine the effects of combined bending and flexure when determining if the member is adequate to support the loads. The equations used to check the adequacy of the members contain both the demand and capacity. The details are discussed in this chapter.
On of the big changes of the SCM 14th edition has been elevating the Direct Analysis Method to the preferred method for computing forces in members (i.e. the 'demand' or 'required strength') of frames subjected to combined bending and axial force. Both the Effective Length and First-Order Analysis methods can also be used, however those methods require modification of the internal forces to account for the second-order effects--the means for doing so have been moved to SCM Appendix 8.
The technique for accounting for second-order effects when using either the Effective Length or First-Order Analysis methods (Appendix 8) is covered in this chapter.
Finally, the SCM provisions for dealing with the total effect of combined axial and bending loads is covered.