Reference no: EM13561487

You need to compare measured and predicted deflections for the three situations described below. Comment on reasons for the differences between the predicted and measured values. Recall that E = 69 GN/m2, rho = 2700 kg/m3, and the beam cross-section is a rectangle with dimensions of 3 mm x 19 mm.

On three separate plots, for the three loading conditions described below, plot two curves: (1) the deflected shape from x = 0 to x = L as predicted by beam theory and (2) the measured deflected shape for the considered measurement locations. Comment on reasons for the differences between the predicted and measured values.

There were some problems with the measured values for the fixed-fixed loading condition. First, there was a 0.3 mm differential between the fixed ends and, second, at least one of the boundary conditions was imposing a non-zero rotation of the beam, causing upward deflections. As a way of sidestepping these issues, the measurements provided above are the difference between the measurements under self-weight plus 50 g load at x = 300 mm and the measurements under self-weight only. By principle of superposition, the difference is the deflection under only a 50 g load at x = 300 mm.

Note that a fixed-fixed beam is an indeterminate structure. Since we have not yet covered analysis of indeterminate structures, solutions for the moment and shear distribution of a fixed-fixed beam under a concentrated load are provided below.