This topic was chosen from the mechanical engineering profession. The goal of this experiment was to measure strain from an externally loaded beam and utilize it to measure experimental stress values at various loads in order to establish the link between theoretical stress values and experimental stress values [1]. When a beam is loaded with external loads, shear force and moment are usually built up at each strain [4].
The internal stress resists bending, but the bending moment at a cross-section of the beam deflects it. The theory of simple bending is based on the assumption that the beam material has been stressed up to its elastic limit hence it will follow the hooks law [1].
The young’s modulus value was assumed to remain the same throughout the experiment [3]. The material of the beam was assumed to have homogeneous elastic properties in all directions. The strain gauge was used to measure the strain in static conditions of the beam [3]. The experimental readings showed no deviation from the entire test at each load, which indicates the highest degree of accuracy in the calibration of the strain gauge transducer. From the results obtained, stress values obtained from the theoretical analysis for each load are much less than the experimental values obtained from the strain values for each load. The experimental values of stress are 1000 times greater than the theoretical values.
2. Technological significance
The experiment measured strain from an externally loaded beam and used it to measure the experimental values of stress at different loads to establish the relationship been theoretical stress values and experimental stress values. Based on the results of the experiment, it was discovered that the theoretical values should not be used as a baseline for ascertaining the strength of the beam.
3. Discussion
The difference between the experimental value and the theoretical values was brought by a number of inconsistencies mainly the arrangement of the experimental setup and non-uniformity of beam properties in various directions. Some loads might not have stressed the beam material up to the maximum limit hence hooks law was not followed accurately.
The rate of plastic material loading is a significant component of how the world perceives the material performance [1]. High strain rates tend to favor the elastic properties of materials. Elasticity is associated with load-bearing performance as embodied in properties such as strength and stiffness [2]. However, low strain rates favor the energy-damping aspects of material behavior. This comparison is significant when selecting the nature of the material to use in beam construction and mechanical designs.
4. Conclusion
The values of stress in experimental data entirely depend on the strain gauge readings and the young’s modulus of the beam . Ensuring uniformity of the young’s modulus of the beam and calibrating the strain gauge accurately are the major elements that can yield accurate results in this experiment.
The maximum stress level experienced at the measured point can be reduced in future experiments by increasing the length of the load from the neutral axis and reducing the moment of cross-sectional area of the beam.
References
[1] Khan, A. S., & Wang, X. Strain Measurements and Stress Analysis. Upper Saddle River: New; Jersey: Prentice Hall, 2001
[2] Dally, J. W., & Riley, W. F. Experimental Stress Analysis: Third Edition. Boston, Massachusetts: Mcgraw-Hill, 1991
[3] Hazel M, Comparing Strain Gage Measurements to Force Calculations in a Simple Cantilever Beam, 2016
[4] Popov E.P, Engineering Mechanics of Solids, 2nd ed. Chap. 20, Prentice Hall (Singapore), 1999
Appendix
Experimental results for, the strain gauge
Reading in mv/V
Load in N
Test 1
Test 2
Test 3
Average
Standard Deviation
1.0
-0.033
-0.033
-0.033
0.033
0.00
2.0
-0.067
-0.067
-0.067
0.067
0.00
3.0
-0.101
-0.101
-0.101
0.101
0.00
4.0
-0.135
-0.135
-0.135
0.135
0.00
5.0
-0.170
-0.170
-0.170
0.170
0.00
6.0
-0.204
-0.204
-0.204
0.204
0.00
Calculated strain from the average values
Load/N
Average(mv/V)
Strain
1.0
0.033
0.016
2.0
0.067
0.022
3.0
0.101
0.049
4.0
0.135
0.066
5.0
0.170
0.083
6.0
0.204
0.099
Calculated stress from experimental data
Load/N
Average(mv/V)
Strain
Stress(Nmm-2)
1.0
0.033
0.016
210x103x0.016= 3360
2.0
0.067
0.022
210x103x0.022=4620
3.0
0.101
0.049
210x103x0.049=10290
4.0
0.135
0.066
210x103x0.066=13860
5.0
0.170
0.083
210x103x0.083=17430
6.0
0.204
0.099
210x103x0.099=20790
Calculated stress from theoretical data
Load(N)
Calculated stress From experimental data (N/mm2)
Calculated stress from theoretical data (N/mm2)
1.0
3360
3.366
2.0
4620
6.732
3.0
10290
10.098
4.0
13860
13.464
5.0
17430
16.830
6.0
20790
20.197
