5.1 Axial Force, Shear, and Bending Moment
5.2 Shear and Bending Moment Diagrams
5.3 Qualitative Deflected Shapes
5.4 Relationships between Loads, Shears, and Bending Moments
5.5 Static Determinacy, Indeterminacy, and Instability of Plane Frames
5.6 Analysis of Plane Frames
Unlike trusses, considered in the preceding chapter, whose members are always subjected to only axial forces, the members of rigid frames and beams may be subjected to shear forces and bending moments as well as axial forces under the action of external loads. The determination of these internal forces and moments (stress resultants) is necessary for the design of such structures. The objective of this chapter is to present the analysis of internal forces and moments that may develop in beams, and the members of plane frames, under the action of coplanar systems of external forces and couples.
We begin by defining the three types of stress resultants axial forces, shear forces, and bending moments that may act on the cross sections of beams and the members of plane frames. We next discuss construction of the shear and bending moment diagrams by the method of sections. We also consider qualitative deflected shapes of beams and the relationships between loads, shears, and bending moments. In addition, we develop the procedures for constructing the shear and bending moment diagrams using these relationships. Finally we present the classification of plane frames as statically determinate, indeterminate, and unstable; and the analysis of statically determinate plane frames.
