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
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
L is the length of the beam
Total Length of the beam is 119.8 cm or 1198 mm but the length of the beam which is between the pivot points is 108 cm or 1080 mm. Three different thicknesses for the beam were recorded and they are 3.24 mm, 3.46 mm and 3.92 mm whose average is 3.54 mm. Like thickness three different widths were recorded and they are 24.56 mm, 25.59 mm and 25.50 mm whose average is 25.22 mm.
Recording the deflection
Following is the procedure to experimentally find the deflection of beam under a certain load
1. First of all setup the apparatus and fix the both ends of beam at the pivot point of the apparatus
2. Attach the weight pan at the center of the beam and apply the load of 1 N by adding the some weight in hanger.
3. Record deflection of the beam. Take three different readings and then use their average value
4. Repeat the step 2 and 3 for loads of 2 to 6 Newton
According to above 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