As depicted in Fig. P1.24, the downward deflection y (m) of a cantilever beam with a uniform load w (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, w = 10,000 N/m, 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.

24EI dx 24E 0