An Experimental Method for Determining Stress-Strain Relations with Strain Gages

Abstract

When a large force is applied to a rectangular beam two things may happen after the force is removed: the beam will recover from the bending moment; or, it may not recover from the bending force, and not return to its original shape. These two descriptions are characteristic of the beam, which are called the elastic and plastic properties, respectively. Once the theory of metals is clear, as stated from above, the mechanics for a cantilever beam can be considered. There are many laws in mechanics, which range from Newton's Second and Third Laws to Hooke's Law. From these Laws, stress and strain are determined by the mechanical equations of a cantilever beam. However, strain is determined by two methods: one is by the mechanics and deflection of the beam; the other is by the use of electrical foil resistance strain gages. From these two methods Young's modulus is determined. Both methods of strain determination, as well as stress, require rigorous mathematical proceedings. It would be very cumbersome and lengthy to include entire derivations in the body of the thesis. Thus, for convenience an Appendix is included which takes into full account of important derivations.