A cantilever beam: under the action of a concentrated load applied at its free end the beam will deflect. Provided the applied load acts in the XY plane and deflection occurs in this same plane, the elastic modulus can be derived from the equation. In the case of a beam of rectangular cross-section, the second moment of area with respect to the axis m is given.
The end of a steel beam was clamped to an aluminium extrusion frame. The free end of the beam had been drilled to allow a set of nine weights to be hanged from that. The critical dimensions of the beam (L, X, b and h) were measured and the uncertainty associated with those estimates arising from the instrument used for measurement was noted. Nine weights (99.6 g, 99.3 g, 99.5 g, 99.2 g, 103.1 g, 100.1 g, 98.3 g, 103.2 g and 99.7 g) were used. The deflection of the beam under these weights was measured using two sensors – a dial gauge and a potentiometer, which was wired to a digital display. The dial gauge and the potentiometer were zeroed while the beam was unloaded. The weights were added one by one to the free end of the beam and at each stage the mass added to the free end of the beam. The deflection readings obtained from both the potentiometer and the dial gauge were recorded. After adding all the masses to the free end of the beam, slowly the masses were removed one by one until the beam was subjected to no external loads. The experiment was repeated five more times and the data were recorded at each stage in the same manner as the previous step.
From the set of data recorded from the dial gauge which represent the beam deflection better the Young's modulus (E) of the beam and the standard error of Young's modulus were calculated for each experiment. From the recorded data and the calculated values, the true value of Young's modulus is calculated to be 191.9 GPa and the standard error associated with this is calculated to be 0.