# beam

**Topics:**Beam, Second moment of area, Solid mechanics

**Pages:**2 (538 words)

**Published:**October 31, 2014

Bending of a Beam

Senior Freshman Engineering Laboratories

Lab: 2E4A

Coordinator: Asst. Prof. Bidisha Ghosh

Demonstrator:

Concept

A transverse load is applied to a beam. The beam changes its shape and experiences bending moment. Internal stresses (bending stress) develop in the beam. In the bent or curved shape, the material on the inside of the curve experiences compression and material on the outside of the curve experiences tension. In pure bending, the transverse planes in the material remain plane and parallel during bending. Objectives

1. To measure deflections and strains in a simply supported steel beam. 2. To compare the analytical and experimental values of strains in the beam. 3. To use measured deflections and theory to evaluate the Young’s modulus of the material. 4. To note the source of errors in a typical simply supported beam experiment. Theory

Please refer to the beam bending lecture notes as provided by Dr A. O’Connor in 2E4 class. A steel I-beam is subjected to a point load in the middle. The beam is loaded within the elastic limit.

Figure 1: Bending of a Beam

Beam deflection :

The deflection, can be computed for general loading situation by integrating the moment curvature equation. For Fig. 1, the theoretical value of beam deflection can be determined as follows: where, P is the applied load and l is the length of the beam. Bending Stress: For a given beam the stress experienced due to bending is dependent on the bending moment and geometrical characteristics of the beam: σ=My/I, where y is the distance from the neutral axis.

Bending stress distribution for a beam in pure bending:

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