Analysis of Beams in Bending

Three methods of solving viscoelastic boundary value problems were given early in the Fundamental Concepts section of this chapter. The development of the beam equation serves as a simple method to illustrate these various techniques. Before proceeding with this section, the reader is advised to review the procedure for developing the deflection equation for linear elastic prismatic beams given in elementary texts on solid mechanics. 

It may be well to note that while the deflection derivations shown in this section are for pure bending, the equations developed are valid for general loadings (i.e., point, distributed, etc.) as long as shear deformations are negligible as in elastic beams. 

If a step bending moment is input such that, M,(t) = M,H(t) = Mo integration of Eq. 8.31 yields, 

Equilibrium of forces in the axial direction on any cross-section gives. 

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