ABSTRACT
Apart from trusses discussed in the previous chapter, members of which are always subjected to axial forces only, 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 analysis and determination of these internal forces and moments are necessary for the design of such structures. The aim of this chapter is to gain a deeper understanding of the analysis of internal forces and bending moments that develop in beams, and the members of plane frames, under the action of coplanar systems of external forces and moments. We start by defining the three types of internally induced forces and moments – axial forces, shear forces, and bending moments – that will act on any arbitrary cross sections of beams and the members of plane frames. Then, we will discuss the construction of shear and bending moment diagrams by the method of sections. We will also discuss qualitatively the deflected shapes of beams and the relationships between loads, shears, and bending moments. Also, we will develop the methods for constructing the shear and bending moment diagrams using these relationships and equations. Finally, we will introduce the concept of classification of plane frames as statically determinate, indeterminate, and unstable; and last but not least, analysis of statically determinate plane frames.
