In Example 4 of Section 5.2 we saw that when a constant vertical compressive force, or load, P was applied to a thin column of uniform cross section and hinged at both ends, the deflection y(x) is a solution of the BVP:

(a) If the bending stiffness factor EI is proportional to x, then EI(x) = kx, where k is a constant of proportionality. If EI(L) = kL = M is the maximum stiffness factor, then k = M L and so EI(x) = Mx L.

Use the information in Problem 37 to find a solution of

if it is known that √xY₁(2√λx) is not zero at x = 0.

(b) Use Table 6.4.1 to find the Euler load P₁ for the column.

(c) Use a CAS to graph the first buckling mode y₁(x) corresponding to the Euler load P₁. For simplicity assume that c₁ = 1 and L = 1.

Table 6.4.1

Transcribed Image Text:

d²y EI + Py = 0, y(0) = 0, y(L) = 0. dx %3D