Deflection of a Beam Under Axial Force. A uniform beam

Chapter 6, Problem 14E

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Deflection of a Beam Under Axial Force. A uniform beam under a load and subject to a constant axial force is governed by the differential equation where y(x) is the deflection of the beam, L is the length of the beam, k2 is proportional to the axial force, and q(x) is proportional to the load (see Figure 6.2).(a) Show that a general solution can be written in the form (b) Show that the general solution in part (a) can be rewritten in the form where (c) Let q(x)=1. First compute the general solution using the formula in part (a) and then using the formula in part (b). Compare these two general solutions with the general solution which one would obtain using the method of undetermined coefficients.(d) What are some advantages of the formula in part (b)? Figure 6.2 Deformation of a beam under axial force and load 6.4 EXERCISES