Different plastics have a homogenous behavior when unstressed, but may change into being optical whenever stressed. The alteration of index of refraction involves a function of the stress that is applied in a similar manner to the change in resistance in a gage strain. According to Brewster’s law, the relative alteration in the refraction index is directly proportional to principal strains. Objectives The targets of this experiment involved using the photoelastic methods of measuring stress in obtaining the normal stress values in a beam and comparing the measured values of stress that were computed from the strength elementary of theory of material.
The study compared the theoretical and measured values of the beam deflection. The study demonstrated the Maxwell’s law of reciprocal deflections Scope of Work The experiment covered the analysis of the beam using photoelastic methods. The cantilever beam was tested by being fixed on one end and set free on the other side. The deflections were measured using the dial gage and the stress determined using Photoelasticity. The dimensions of the beam were measured and mounted to the required fixed support with the help of the ‘C’ clamp.
One dial indicator was placed at the centre of the beam and the other close to the free end giving room for enough space for the load applied, After this the weight was applied at the free beam fails to exceed the required range of the gage dial and at the same time observation made in three full-color cycles colors of the polariscope. Whenever necessary, one load was used in measuring the observed deflections. The heavier load, on the other hand was used in measuring the stresses.
The distance was measured from the load of each gage dial and to an end that is fixed to the beam. Different measurements of length were made from the point where the load was applied. The distance from each dial gage load and the beams fixed end of beam. Beginning with the dial indicators the measured deflections of the beam were read and recorded for the provided load. It was prudent to ensure that the weighing was done accurately before the completion of the laboratory work. In order to measure stresses, the polariscope reflection was utilized in a circular mode.
The polariscope reflection as set up for the circular operation through engagement of the pin in the lettered hole (M). The quarter wave plates were placed at forty five degrees to the analyzer polarizer axes. The polariscope was converted into a circular operation.
Davis, Troxell, & Hauck, The Testing of Engineering Material, 4th Ed., McGraw-Hill, 1982, Chapter 11 and Section 16.9.
Calculation and Formula
Moment of Inertia
I = (1/12)wt3
I = (1/12)(3.1552)(0.249)3
I = 4.05 x 10-3 lb in
Deflection at DG1
Subtract the readings on the strain gages during loading from the initial values:
ΔDG = (-PL3)/3EI
Percent Error for Deflections
Divide the difference between the theoretical an experimental deflections, by the theoretical deflections. Then multiply by 100 to convert to a percent
σ = [(CbEf)/1+v] N
σ = Mc/I