Deflection of a Simple Supported Beam

DEFLECTION OF BEAMS

Deflection of a Simple Supported Beam

OBJECTIVE :

1) To observe the deflection of a simple supported beam with variable loads.

2) To find the relationship between the deflection of a simple supported beam and the

variable length of the beam.

INTRODUCTION :

A beam is a length of material supported at its two ends, in such a way so as to bear loads. The load perpendicular to its longitudinal axis will result in bending and, in most cases, transverse shearing. In the simplest of situations, the beam is taken to have a rectangular cross-section and the loads and supporting reactions act in the vertical plane containing the longitudinal axis. The loads and the reactions at the supports are considered external forces and they must be in equilibrium for the entire beam to be in equilibrium. To study the strength of the beam, it is necessary to know how these external forces affect it. As in the theory appendix, the mathematical approach is to assume that an imaginary transverse section cuts the beam into two parts, and then to examine the equilibrium of each part. To maintain the equilibrium, certain forces must be introduced at the point of cut. When the cut is not present, these forces must continue to exist internally in the material of the beam. Before the slope or the displacement at a point on a beam (or shaft) is determined, it is often helpful to sketch the deflected shape of the beam when it is loaded, in order to "visualize" any computed result and thereby partially check these results. The deflection diagram of the longitudinal axis that passes through the centroid of each cross-sectional area of the beam is called the elastic curve. For most beams the elastic curve can be sketched without much difficulty. When doing so, however, it is necessary to know how the slope or displacement is restricted at various types of supports. In general, supports that resist a force, such as a fixed wall, restrict displacement, and those that resist a moment, such as a fixed wall, restrict rotation or slope. Due to the nature characteristic of the materials, when a force acting on a long beam, the force will cause the beam to bend. If the force is acting downwards, the moments at the two ends will act upwards and same for the opposite way.

THEORY :

In this experiment, we will examine the deflection of a simply beam subjected to an increasing point load. We will also vary the beam length by changing the distance between the supports. This means we can find out the relationship between the deflection and the length of the beam.