3.1 INTRODUCTION

In the earlier chapters, we have discussed about the internal stresses and strains developed in the members subjected to axial forces. The members subjected to transverse forces are referred as beams. In this chapter, we discuss the internal reactions in a member, as presented in Figure 3.1. Direction parallel to X axis is referred as longitudinal direction. Direction parallel to Y axis is referred as transverse direction. In addition, direction parallel to Z axis is referred as lateral direction. If the support in Figure 3.1 is along Z axis, the transverse direction will be parallel to Z axis and lateral direction will be parallel to Y axis.

The internal reactions at a section in beam, due to external forces or tractions or body forces, can be presented as shown in Figure 3.2. For clarity, internal moments are represented by double arrows, which follows right-hand thumb rule. As per right-hand thumb rule, thumb represents the axis of the couple and direction of four fi ngers represents the direction of the couple.

In case of planar members and coplanar loading, at any section in a member there exist three forces namely, moment, SF and normal force. Using three equilibrium equations, the three internal actions can be determined. Members are to be designed to resist these forces. The main objective of this chapter is to determine these forces.

3.2 DIFFERENT TYPES OF SUPPORTS AND BEAMS

The different types of supports are classifi ed based on the possible deformations (degrees of freedom allowed). The diagrammatic representation of these supports is shown in Figure 3.4.

Hinged support: At hinged support, the rotation in the XY plane, that is, about Z axis is allowed, whereas the linear displacement in X and Y directions is restrained. Hence, these two restraints generate two reactions in X and Y directions. The example of hinged support is the hinge used for connecting the doors to the door frames.

Roller support: At hinged support, the rotation in the XY plane, that is, about Z axis, as well as linear displacement along the support (X direction in the present case) is allowed and Y direction is restrained. Hence the single restraint generates single reaction in Y direction. The example of roller support is a plank resisting on smooth spherical rollers.