# Beam Deflection Lab work equation solution

Beams are the structural members which are designed to take load applied laterally to beam axis. Load applied to the beam try to produce deflection in beam whose magnitude vary along the length of the beam. There are many different types of the beam available like simply supported beam, cantilever beam and overhanging beam. Reaction of a beam when external load is applied on it depends on the type of beam, shape of beam and material from which beam is being is made.

For a simply supported beam reaction or the deflection of the beam can be calculated by the help of following formula
δ=-(FL^3)/48EI

In above equation
δ is the reaction or deflection of beam
F is force applied to the beam
E the modulus of elasticity of material
I is second moment of the inertia of the beam

According to the experimental data collected, if the load applied is 6 N then the deflection in beam is about -11.13 mm. As the length of beam is 300 mm = 0.3 m and cross section of 10*10 mm.

Simply supported beam are those which have support present at both ends of the beam and when external force is applied on the beam both supports have reaction forces against the applied load. Sum of both of the reaction is always equal to the magnitude of the external force applied to the beam.

When an external force is applied on the beam whose ends are fixed then that externa force will produce moment at the ends of the beam that moment can be calculated by the following equation

Show above is the graph between displacement and load and according to this graph it is clear that there is liner relation between load and displacement because in graph with the increase in load the displacement of the beam is also increasing and with decreasing the load the displacement of the beam is decreasing. So from this it can be concluded that the displacement of beam is directly proportional to the applied load on the beam.