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For a stretched spring fixed at one end obeying Hooke's law, the elastic potential energy is Δ E p = 1 2 k ( r 2 − r 1 ) 2 {\displaystyle \Delta E_{p}={\frac {1}{2}}k(r_{2}-r_{1})^{2}} where r 2 and r 1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
Compression set A is defined as the percentage of original specimen thickness after the specimen has been left in normal (uncompressed) conditions for 30 minutes. C A, the compression set A is given by C A = [(t o - t i) / t o] * 100 where t o is the original specimen thickness and t i is the specimen thickness after testing. [2]
A spring with spaces between the coils can be compressed, and the same formula holds for compression, with F s and x both negative in that case. [4] Graphical derivation. 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.
The formulas are organized into tables in a hierarchical format: chapter, table, case, subcase, and each case and subcase is accompanied by diagrams. The main topics of the book include: • The behavior of bodies under stress • Analytical, numerical, and experimental methods • Tension, compression, shear, and combined stress
The parameters (,,,) obtained from a test result can be used with these formulas to calculate the equivalent true stress ´ at failure. Specimen shape effect The graph of specimen shape effect shows how the ratio of true stress to engineering stress (σ´/σ e ) varies with the aspect ratio of the test specimen ( d o / l o {\textstyle d_{o}/l ...
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
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The structure’s unknown displacements and forces can then be determined by solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method originated in the field of aerospace. Researchers looked at various approaches for analysis of complex airplane ...