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 δ 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
Figure 5.2.9 Deflection of vertical column in Problem 24
- (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.
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Chapter 5 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
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