Analyze a beam (EA, EI, L) with one end fixed and the other end vertically supported by a linear elastic spring with spring constant k (lb/in), as shown in Fig. P5.12. The beam is subjected to...

Analyze a beam (EA, EI, L) with one end fixed and the other end vertically supported by a linear elastic spring with spring constant k (lb/in), as shown in Fig. P5.12. The beam is subjected to uniformly distributed transverse load of intensity q0 (lb/in). Use the Euler–Bernoulli beam element with Newton’s iteration method. Use eight elements in the beam (1 × 1 in2 cross section, E = 30 × 106 psi, and L = 100 in) and k = 0, 25, and 250 (i.e. three different cases). Tabulate and plot the deflection w(L) versus the load q0, with maximum load of q0 = 10 (lb/in), for two separate cases: (a) horizontal movement of the free end is not restricted, and (b) the horizontal movement of the free end is restricted to zero. A load increment of ∆q0 = 0.5 (lb/in) is suggested. Use a convergence tolerance of = 10−3 and the maximum number of iterations to be ITMAX = 25.