The objective of the experiment was to determine the existence of stress and strain concentrations on a cantilever beam, approximate the value of the stress concentration factor, K_t, and compare to the published value of 1.2 Theory: The presence of any discontinuity such as holes, notches, or grooves, in a machine part of a structural member can alter the stress distribution in the vicinity of that discontinuity. Such discontinuities are called stress raiser, and the regions in which they occur are called areas of stress concentrations. The stress concentrations factor, K_t, used to measure the ratio of the maximum stress at the stress-raiser to the nominal stress at the respective point.^(2) In this experiment, the discontinuity was a circular hole drilled through the depth of the beam on its centerline. Four strain readings were obtained one at a time using a strain indicator. A gage factor correction was made for the strain indicated by Gage 4, since it was different from gage factor of Gages 3, 2, and 1 using the equation: epsilon\'_4.^(3) The result of this calculation was the nominal strain at the respective point. Then three coefficients, A, B, and C were determined from the measured strains using the equations: respectively.^(4) The summation of the A, B, and C equations yielded the maximum strain, epsilon_0 at the respective point. Finally, the stress concentration factor, K_t was obtained by dividing epsilon\'_0 over epsilon\'_7. Results: The computations of the four strains, the gage factor correction (epsilon\'_7), the three coefficients (A, B, and C), the maximum strain (epsilon_0), and the measured stress concentration factor (K_t) were recorded and presented in Table 1. Conclusion: The experiment outcomes were 2242 mu epsilon, 1918 mu epsilon, 1821 mu epsilon, and 2000 mu epsilon for strain, 1967 mu epsilon for gage factor correction, 1377 mu epsilon, 518 mu epsilon, and 1868 mu epsilon for coefficients A, B, and C respectively. The maximum strain was found to be 2727 mu epsilon and the stress concentration factor was found to be 1.386. Finally, the difference between the measured and the published stress concentration factor was 15.5%.
Objective:
To determine stress concentration, strain concentration and the value of stress concentration factor on cantilever beam
Theory:
The presence of discontinuities such as holes, notches or grooves on the surface of machine parts of structural members may alter the distribution of stress. These discontinuities are called as stress raisers and the region in which they occur are called stress concentration.The stress concentration factor, Kv is the ratio of the maximum stress at streass raiser to the nominal stress at respective point. In this experiment, the discontinuity is a circular hole drilled through the depth of the beam on its centerline. Using strain indicator,four strain readings are obtained one at a time. Gauge factor correction is made for the strain indicated by gauge 4, since it is different from gauge factor of gauges 1,2 and 3 using the equations. Thus, we get nominal strain at the respective point. Now, the three coefficients A,B and C are determined from the measured strains using the following equations respectively. The summation of A,B and C equations yielded the maximum strain at the respective point. Finally, the stress concentration factor (Kv) is obtained by dividing E\'0 over E\'7
Result:
The computations of four strains, the gauge factor correction, the three coefficients (A.B.C), the maximum strain and the measured stress concentration factor Kv are recorded and presented in the Table 1
Conclusion:
The experiment outcomes are
Four Strains: 2242,1918,1821 and 2000
Gauge factor Correction:1967
Coefficients A,B and C:1377,-518 and 1868
The maximum strain is found to be 2727 and the stress concentration factor was found to be 1.386.
Finally, the difference between the measured and the published stress concentration factor is -15.5%
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