The lead example of this chapter concerned the deflection of a beam with supported ends subject to uniform loading. The boundary-value problem governing this physical situation is

with boundary conditions w(0) = 0 and w(l) = 0.
Suppose the beam is a W10-type steel I-beam with the following characteristics: length l = 120 in., intensity of uniform load q = 100 lb/ft, modulus of elasticity E = 3.0×107 lb/in.2, stress at ends S = 1000 lb, and central moment of inertia I = 625 in.4.
a. Approximate the deflection w(x) of the beam every 6 in.
b. The actual relationship is given by
w(x) = c1eax + c2eˆ’ax + b(x ˆ’ l)x + c,
where c1 = 7.7042537×104, c2 = 7.9207462×104, a = 2.3094010×10ˆ’4, b = ˆ’4.1666666× 10ˆ’3, and c = ˆ’1.5625 × 105. Is the maximum error on the interval within 0.2 in.?
c. State law requires that max0

al- w