Question: The basic differential equation of the elastic curve for a uniformly loaded beam (Figure) is given as El d 2 y / dx 2 =

The basic differential equation of the elastic curve for a uniformly loaded beam (Figure) is given as

El d²y/dx² = wLx/2 – wx²/2

where E = the modulus of elasticity and l = the moment of inertia. Solve for the deflection of the beam using

(a) The finite-difference approach (Δx = 2 ft) and

(b) The shooting method. The following parameter values apply; E = 30,000 ksi, l = 800 in⁴, w = 1 kip/ft, L = l0 ft. Compare your numerical results to the analytical solution,

w Lx3 y = 12 EI wx* 24 EI 24 EI

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