Youngs Modulus
Solid Mechanics Lab Report
Measurement of Young’s Modulus
Sherin Joseph
00549618
Measurement of Young’s Modulus of Aluminium using Cantilever loading
Abstract
The Young’s modulus of Aluminium was calculated using the measurements of the cantilever deflections. A beam of aluminium was clamped on one end and the other end was loaded with different weights, ranging from 1 to 15N. The deflection was then measured using a dial gauge. The slope of a load (abscissa) vs. deflection (ordinate) graph was then substituted into,
E=4L3bd3(Slope). The Young’s modulus was calculated to be 67.3 GPa. The results were then compared with known Young’s Modulus value of Aluminium, 72.6 GPa.
A supplementary experiment was carried out to measure the deflection of a cantilever at different distances along the beam (from the origin) using a constant load. Measures were taken at regular intervals of 100mm from the origin when loaded with 15N. A deflection (ordinate) vs distance from origin (absicca) graph was then plotted. The known values of Young’s modulus and dimensions of the beam were used to deflection values at each interval, using the following formula yx= PL32EI xL2- 13xL3 .Both the curves were then plotted on the same graph to compare the uncertainties in the measured value.
Introduction
Young’s Modulus is a measure of the stiffness of a material. By Hooke’s law Young’s modulus is the ratio of stress to strain [where stress = forceCross sec. area and Strain =change in lengthinitial length ]. The beam is clamped to form a cantilever (fixed at one end). At the clamped end, there is no moment on the beam. When a load is applied to free end, it causes stress in the material, which leads to bending. The degree of bending is proportional to the load applied. As the load increases above the ultimate tensile strength the beam experiences plastic deformation (cannot go back to initial dimensions). When the load is increased further the material breaks.
Measurement of Young’s Modulus
Sherin Joseph
00549618
Measurement of Young’s Modulus of Aluminium using Cantilever loading
Abstract
The Young’s modulus of Aluminium was calculated using the measurements of the cantilever deflections. A beam of aluminium was clamped on one end and the other end was loaded with different weights, ranging from 1 to 15N. The deflection was then measured using a dial gauge. The slope of a load (abscissa) vs. deflection (ordinate) graph was then substituted into,
E=4L3bd3(Slope). The Young’s modulus was calculated to be 67.3 GPa. The results were then compared with known Young’s Modulus value of Aluminium, 72.6 GPa.
A supplementary experiment was carried out to measure the deflection of a cantilever at different distances along the beam (from the origin) using a constant load. Measures were taken at regular intervals of 100mm from the origin when loaded with 15N. A deflection (ordinate) vs distance from origin (absicca) graph was then plotted. The known values of Young’s modulus and dimensions of the beam were used to deflection values at each interval, using the following formula yx= PL32EI xL2- 13xL3 .Both the curves were then plotted on the same graph to compare the uncertainties in the measured value.
Introduction
Young’s Modulus is a measure of the stiffness of a material. By Hooke’s law Young’s modulus is the ratio of stress to strain [where stress = forceCross sec. area and Strain =change in lengthinitial length ]. The beam is clamped to form a cantilever (fixed at one end). At the clamped end, there is no moment on the beam. When a load is applied to free end, it causes stress in the material, which leads to bending. The degree of bending is proportional to the load applied. As the load increases above the ultimate tensile strength the beam experiences plastic deformation (cannot go back to initial dimensions). When the load is increased further the material breaks.