The basic differential equation of the elastic curve for a simply supported, uniformly
Chapter 24, Problem 24.16(choose chapter or problem)
The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam (Fig. P24.16) is given as E I d2 y dx2 = wLx 2 wx2 2 where E = the modulus of elasticity, and I = the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using (a) the finite-difference approach (x = 0.6 m) and (b) the shooting method. The following parameter values apply: E = 200 GPa, I = 30,000 cm4 , w = 15 kN/m, and L = 3 m. Compare your numerical results to the analytical solution: y = wLx3 12E I wx4 24E I wL3x 24E I
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