Simply Supported Beam Deflection equation solution

A structural member that is capable of resisting the bending load (load applied perpendicular to concerned axis) is called beam. In order to study about beams the two main point’s one where load is being applied and other where support is being provided must be studied. Based on the types of support beam has there is three basic types of beam.

1.      Simply supported beam

2.      Overhanging beam

3.      Cantilever beam

Simply supported beam is one in which there two supports present at the both ends of the beam. Cantilever beam is one in which there is only one support present at any one of the ends a beam have. Overhanging beam also have two supports just like simply supported beam but some part of beam is extended further from one end.

Young Modulus of beam

When a load is applied on beam then as a result of that load beam show some deflection in its shape. This deflection in beam is the function of its material young modulus and this young modulus can be finding out by the following formula

Now in the above formula

I is the symbol of second moment of the inertia

 is the symbol of deflection

E the symbol of modulus of elasticity

F is the symbol of force applied

Pre Test data

·         Length = 1.198 m

·         Length between pivot points = 1.08 m

·         Average thickness = 0.00354 m

·         Width = 0.02522 m

Procedure

1.      First step is the setting up of the apparatus for the experiment which involve placing the apparatus on horizontal place, attaching the beam, hanger and dial gauge.

2.      Second step is to add the weight in hanger to apply weight on beam. As the result beam will deflect from its position

3.      Record the deflection by noticing the dial gauge attached to the beam

4.      Repeat the step 2 and 3 for different weights

load(n)	deflection(mm)			Average deflection
	1	2	3
1	1.72	1.71	1.71	1.71
2	3.53	3.48	3.56	3.52
3	5.43	5.47	5.38	5.43
4	7.29	7.34	7.21	7.28
5	9.13	9.1	9.13	9.12
6	11.21	11.09	11.09	11.13

Graph between Displacement and load

Based on the graph shown above it can be sad that there is linear relationship between displacement and load because it is shown in graph that when load on the beam is increase the deflection produce by the beam has also increased. From this it can also be said that higher the load more will be the displacement.

Modulus of elasticity