Abstract
In Chapter 8 we discussed an approximation for trusses. The elastic deformations were lumped in springs. We may apply a similar model to beams in bending as a first step to a discrete model for plate bending. A rigid element that has rotational springs at its ends replaces a beam element of length a. This model is depicted in Figure 9.1. The rotational spring is considered to be composed of two parallel springs, for the compression and tension zones, respectively. The rotational rigidity at each end is D. It is required that the beam-ends in both the model and the actual beam have the same rotation e for a constant moment M. This requirement is met if D = 2EI/a. When two beam elements are linked together, the two rotational end springs are connected in series. The rigidity of the resulting rotational spring is D = EI/a.
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