 # Bending of Beam Lab Report Essay

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1. Objective:
The objective of this experiment is to demonstrate the bending of a bean when loaded at the center of its length and examine its deflection when positioned in two different ways, when the flat side of the beam is support and when the thin side is supported. In addition, try to find linear relationship between the load applied and the deflection of the beam and comparing the experimental deflection with the theoretical deflection.
If the load is applied at the mid- length a=b=L/2 then mid span deflection is: δ = PL3/(48EI).
Where P is the applied force, L is the length of beam, E is the modulus of elasticity of aluminum, and I is the moment of Inertia.
For a beam of rectangular cross section, say of width w and
The beam was loaded the mid-length in 2.745 lbs. increments up to 6.745 lbs. The change in clearance of every load step was measured and data was recorded.

Case II: The beam was turned around in such way that the shortest side of the cross section is on the support. The steps described in Case I was repeated and data was recorded.

4. Results:
Following tables and graphs show the result of the experiment. The tables will demonstrate the experimental and theoretical deflection for each case. The graphs will show the relationship between the load applied and deflection, in addition to compare the experimental deflection and theoretical deflection.

Case I: Dimensions of the beam
Length (L)= 29.35 in., Width (w)= 1.008 in., Thickness (t)= 0.125 in.
Inertia (I)= wt3/12 = 0.000164063 in4.

TABLE I P (lbs.) | Initial Clearance (in) | New Clearance (in) | Experimental Deflection (in) | Theoretical Deflection (in) | 2.745 | 0.75 | 0.98 | 0.23 | 0.31092 | 3.745 | 0.75 | 1.13 | 0.38 | 0.47587 | 4.745 | 0.75 | 1.2 | 0.45 | 0.63011 | 5.745 | 0.75 | 1.31 | 0.56 | 0.79903 | 6.745 | 0.75 | 1.44 | 0.69 | 0.99236 |

Case II: Dimensions of the beam
Length (L)= 35.5 in., Width (w)= 1.008 in., Thickness (t)= 0.125 in.
Inertia (I)= w3t/12 = 0.010668672 in4.

TABLE II P (lbs.) | Initial Clearance (in) | New Clearance (in) | Experimental Deflection (in) | Theoretical Deflection | 2.745 | 1.973 | 2.051 | 0.086