As depicted in Fig. P1.23, the downward deflection, y (m), of a cantilever beam with a uni...

As depicted in Fig. P1.23, the downward deflection, y (m), of a cantilever beam with a uniform load, w = 10,000 kg/m, can be computed as

where x = distance (m), E = the modulus of elasticity = 2 × 10¹¹ Pa, I = moment of inertia = 3.25 × 10^–4 m⁴, and L = length = 4 m. This equation can be differentiated to yield the slope of the downward deflection as a function of x

If y = 0 at x = 0, use this equation with Euler’s method (Δx = 0.125 m) to compute the deflection from x = 0 to L. Develop a plot of your results along with the analytical solution computed with the first equation.

Figure P1.23: A cantilever beam.