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The WLC model envisions a continuously flexible isotropic rod. [1] [2] [3] This is in contrast to the freely-jointed chain model, which is only flexible between discrete freely hinged segments. The model is particularly suited for describing stiffer polymers, with successive segments displaying a sort of cooperativity: nearby segments are ...
= [4] for four-point bending test where the loading span is 1/3 of the support span (rectangular cross section) = [5] for three-point bending test (rectangular cross section) in these formulas the following parameters are used:
The extension ratio λ is related to the engineering strain e by = This equation implies that when the normal strain is zero, so that there is no deformation, the stretch ratio is equal to unity. The stretch ratio is used in the analysis of materials that exhibit large deformations, such as elastomers , which can sustain stretch ratios of 3 or ...
For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller.
For thin beams (beam length to thickness ratios of the order 20 or more) these effects are of minor importance. For thick beams, however, these effects can be significant. More advanced beam theories such as the Timoshenko beam theory (developed by the Russian-born scientist Stephen Timoshenko ) have been developed to account for these effects.
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According to this formula, the graph of the applied force F s as a function of the displacement x will be a straight line passing through the origin, whose slope is k. Hooke's law for a spring is also stated under the convention that F s is the restoring force exerted by the spring on whatever is pulling its free end.