Question

Problem 4. At one end of an elastic beam (length 2L, annular cross section with outer radius R, inner radius r, and planar moment of inertia z(R4- that is supported by a truss structure (cross-sectional area A), a vertical load P is applied, which results in a vertical deflection at that point that can be determined by 5PL 2PL3 EA 3EIz Two experiments with the same data but different inner radii r were conducted, and the deflections w were measured. For r = 9 in, the deflection was w 2.81 in, and for r-7 in, the deflection was w 2.64 in. Unfortunately, some data, more precisely L and R, got irretrievably lost. It was guessed that L 40 in and R-10 in. The remaining data are still known and given as follows: P-lbf, Young's modulus E-100 psi, and cross-sectional area A -1 in2 a) Derive two equations to find the values of L and R, and turn the problem into a rootfinding problem.

Answer 1

1,0-3): 축(R4-6561) 4 2401 千 uo(γ#9)-a.gl 20 3CR4-6561) + 2 L 3 26 30 4-2 2-4 しー -+ 813 2-64 7 L 2 K (024. 2401 15L CR4-240))13401)

The eichameas Fello k. R. -$2 CtO レ as inihal valus with L 10 2.