**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

**Unit :**Beam and Trusses

## Beams: Type of Beams

**Beams:**** **Beams are structural members which offer resistance to bending due to applied loads. The cross- section of beams is much smaller compared to its length. Generally the largest dimension of the cross- section is less than 1/10th of the length. Loads are generally applied normal to the axes of the beams.

**Types of Beam: **

Beams supported such that their external support reactions can be calculated by the methods of statics alone are called statically determinate beams. A beam which has more supports than needed to provide equilibrium is statically indeterminate. To determine the support reactions for such a beam, compatibility of deformation is to be considered.

Three different types of statically determinate beams are shown in the next page. First is the simply supported beam. The left support can provide only vertical and horizonal reactions. The right support can provide only vertical reactions. Thus, there are three unknown reactions, which can be determined by the balancing vertical and horizontal forces and a moment.

The second beam is a cantilevered beam. Here, the beam is fixed at one end and free at the other end. Fixed support offers vertical and horizontal reactions as well as a moment.

The third beam is an over hanged beam, similar to simply supported beam. Only difference is that right support is not at the end.

Three examples of statically indeterminate beams are shown beside. In this case compatibility conditions have to be used for finding out the reactions. In the first beam, left support can offer horizontal and vertical reactions, middle support can offer only a vertical reaction and the right support can offer only a vertical reaction. Thus, there are 4 unknowns and three equations of equilibrium for a plane. Thus, to solve for support reactions, one compatibitity equation has to be used. Similarly, in the second beam which is also called propped cantilever beam, there are 4 unknown support reactions to be determined. Here, the left support offers vertical and horizontal reactions as well as a moment reaction. The right support offers a vertical reaction. In the third beam, six unknowns have to be determined. Each support is capable of offering a vertical and horizontal reactions and a moment.