Darryl Vaughn

Engineering

14 December, 16:08

A simple supported beam at x0 = 0 and xn = L with a uniform load w and the

vertical deflection v (x) is described by the boundary value problem

d

2

v

dx2

=

x-L

3EI

wx, v (0) = 5, v (L) = 100

where L is the length of the beam, E represents the Young's modulus of the material from which

the beam is fabricated and I is the second moment of area of the beam's cross-section. Suppose

L = 15 m, E = 210 kN/m

2

, I = 370.5 m2

and w = 9.8 kN/m. Use the Shooting method to

approximate the vertical deflection, v (x) with the step size, h = 3, the first guess, z0 = 10 and

the second guess, z0 = 5.