In Exercise 7 of Section 11.3, the deflection of a beam with supported ends subject to uniform loading was approximated. Using a more appropriate representation of curvature gives the differential equation
[1 + (w'(x))2] ˆ’3/2w" (x) = S / EI w(x) + qx / 2EI (x ˆ’ l), for 0 Approximate the deflection w(x) of the beam every 6 in., and compare the results to those of Exercise 7 of Section 11.3.
In exercise
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.

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al- w