The critical loads of thin columns depend on the end conditions of the column. The value of
Question:
The critical loads of thin columns depend on the end conditions of the column. The value of the Euler load P1 in Example 4 was derived under the assumption that the column was hinged at both ends. Suppose that a thin vertical homogeneous column is embedded at its base (x = 0) and free at its top (x = L) and that a constant axial load P is applied to its free end. This load either causes a small deflection d as shown in Figure 5.2.9 or does not cause such a deflection. In either case the differential equation for the deflection y(x) is
(a) What is the predicted deflection when δ = 0?
(b) When δ ≠ 0, show that the Euler load for this column is one-fourth of the Euler load for the hinged column in Example 4.
Figure 5.2.9
Step by Step Answer:
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill