Spring Work

Spring Work occurs when force is applied to a spring and the length of the spring changes.

 

·         When the length of the spring changes by a differential amount dx under the influence of a force F, the work done. That work is calculated as,  δWspring = F*dx                                (2-27)

·         To determine the total spring work, we need to know a functional relationship between F and X. 

·         For linear elastic springs, the displacement x is proportional to the force applied. That is  f=kx  (kN)                                                                                                                                    (2-28)

o   Where K is the spring Constant and has the unit (kN/m). The displacement x is measured from the undisturbed position of the spring (that is, x = 0 whenever F = 0). Substituting Eq. 2-28 into Eq. 2-27 and integrating yields

Wspring= 1/2 k{(x^2final)-(x^2initial)} (kJ) (2-29)

xinitial and xfinal are the initial and final displacements of the spring respectively, measured from the undisturbed position of the spring.

 Example: The force F required to compresss a spring x is given by F-F0 = kx Where k is the spring constant and F0 is the preload.Determine the work required to compress a spring whose spring constant is k=200 lbf/in in a distance of one inch starting from its free length where F0 =0 lbf. Express your answer in both lbf*ft and Btu.

=8.333 lbf*ft

=.0107 Btu