Tip Deflection of a Cantilever Beam - Coursework Example

Insert Tip deflection of a cantilever beam Objective The objective of this experiment was to determine the tip deflections of I and T section cantilever beams when subjected to increasing point loads and relate the values obtained with the theoretical values. Apparatus The experiment was conducted with the following equipments I and T section beams Rule Micrometre Vernier Calliper Dial Test Indicator Procedure The dimensions for both I and T section beams were measured and recorded Both beams were weighed and their weights recorded in kilograms The second moment of area for each beam was calculated and recorded A mass of 0.5 kg was loaded at the tip of each beam and the deflection measured using the Dial Test Indicator. The procedure was repeated by adding a mass of 0.5 kg up to 4 kg and each deflection recorded. Results Beam dimensions I section T section Rectangular section b1 32.08 b1 12.16 a 31.83 b2 8.28 b2 31.84 b 31.93 b3 32.17 d1 21.92 L2 d1 8.12 d2 10.11 d2 4.33 L1 1010 d3 2.72 L 1000 L1 Density of beams Density of I section beam Density of T section beam Deflection results, I section Mass(kg) Force, F (N) Experimental Deflection, y (mm) Theoretical Deflection, y(mm) % Error Increasing F Decreasing F Average 0.5 -4.905 -0.10 -0.10 -0.10 -0.0005 199 1 -9.81 -0.21 -0.22 -0.215 -0.094 128.7 1.5 -14.715 -0.32 -0.32 -0.32 -0.141 127 2 -19.62 -0.42 -0.42 -0.42 -0.187 124.6 2.5 -24.525 -0.52 -0.53 -0.525 -0.234 3 -29.43 -0.63 -0.64 -0.635 -0.281 3.5 -34.335 -0.74 -0.74 -0.74 -0.328 4 -39.24 -0.84 -0.84 -0.84 -0.375 T section Mass(kg) Force, F (N) Experimental Deflection, y (mm) Theoretical Deflection, y(mm) % Error Increasing F Decreasing F Average 0.5 -4.905 -0.17 -0.18 -0.175 -0.166 1 -9.81 -0.34 -0.36 -0.35 -0.332 1.5 -14.715 -0.52 -0.52 -0.52 -0.497 2 -19.62 -0.69 -0.70 -0.695 -0.663 2.5 -24.525 -0.86 -0.87 -0.865 -0.829 3 -29.43 -1.03 -1.04 -1.035 -0.995 3.5 -34.335 -1.21 -1.21 -1.21 -1.160 4 -39.24 -1.37 -1.37 -1.37 -1.326 Second moment of area I section beam F=force L=length of beam E=modulus of elasticity I=second moment of area All other values of theoretical deflection shall be calculated using the equation T section Graphs I section, experimental values Theoretical values T section beam Experimental values Discussion From the experiment, the experimental values for deflection are higher than the theoretical values. The difference in both values is due to errors in estimation of the readings with more than two decimal points. Also, the residue stress in both beams resulted in the variations of experimental and theoretical values. The percentage error in the values of Length, the second moment of area and the modulus of elasticity led to abnormal errors in the values of experimental and theoretical deflection (Nageim, 2003) The errors in the experiment could be reduced by using more accurate values of length, modulus of elasticity and the second moment of area. The readings should be taken more than once and by more than one student to obtain more accurate results. In conclusion, the experiment was conducted equally with the highest accuracy as possible. Errors were expected since the values for Length, modulus of elasticity and second moment were not accurate, and the standard procedures were not followed. The experiment also requires to be conducted by experienced personnel. Read More