Define the term load-displacement relations?

Load displacement relations give the relationship between the displacement caused by any load on any member. Load displacement relations are very Important and is they are studied before design of any mechanical member.

Some of the load displacement relations are:

1.

$$\begin{gathered} \mathrm{Elongation} (\mathrm{dispalcement} \mathrm{of} \mathrm{bar} ) \mathrm{under} \mathrm{self} \mathrm{weight} \mathrm{W} \mathrm{is} \mathrm{given} \mathrm{by}; \\ \to \mathrm{\delta }=\frac{1}{2}\times \frac{\mathrm{WL}}{\mathrm{AE}} \\ \mathrm{where}, \\ \mathrm{A}=\mathrm{area} \mathrm{of} \mathrm{cross} \mathrm{section} \mathrm{of} \mathrm{bar} \\ \mathrm{E}=\mathrm{modulus} \mathrm{of} \mathrm{elasticity} \mathrm{of} \mathrm{bar} \\ \mathrm{L}=\mathrm{length} \mathrm{of} \mathrm{bar} \end{gathered}$$

2.

$$\begin{gathered} \mathrm{Maximum} \mathrm{displacement} \mathrm{or} \mathrm{deflection} \mathrm{of} \mathrm{a} \mathrm{simply} \mathrm{supported} \mathrm{beam} \mathrm{under} \mathrm{point} \mathrm{load} \\ \mathrm{W} \mathrm{at} \mathrm{its} \mathrm{middle} \mathrm{is} \mathrm{given} \mathrm{by}: \\ \to \mathrm{\delta }=\frac{1}{48}\times \frac{{\mathrm{WL}}^3}{{\mathrm{EI}}_{\mathrm{NA}}} \\ \mathrm{Where}, \\ \mathrm{L}=\mathrm{length} \mathrm{of} \mathrm{beam} \\ \mathrm{E}=\mathrm{Modulus} \mathrm{of} \mathrm{elasticity} \mathrm{of} \mathrm{beam} \mathrm{material} \\ {\mathrm{I}}_{\mathrm{NA}}=\mathrm{Moment} \mathrm{of} \mathrm{inerta} \mathrm{of} \mathrm{beam} \mathrm{about} \mathrm{neutral} \mathrm{axis}. \end{gathered}$$

3.

$$\begin{gathered} \mathrm{Similarly},\mathrm{for} \mathrm{a} \mathrm{cantilever} \mathrm{beam} \mathrm{with} \mathrm{point} \mathrm{load} \mathrm{at} \mathrm{its} \mathrm{free} \mathrm{end} ,\mathrm{the} \mathrm{maximum} \mathrm{displacement} \mathrm{of} \mathrm{the} \mathrm{beam} \\ \mathrm{is} \mathrm{given} \mathrm{by}: \\ \to \mathrm{\delta }=\frac{1}{3}\frac{{\mathrm{WL}}^3}{{\mathrm{EI}}_{\mathrm{NA}}} \end{gathered}$$