The strength of ‘strut’ depends on

Concept:

Struts:

These are long and slender structural members in an assembly that are subjected only to an axial compressive force.

They predominantly fail by buckling but sometimes the yielding failure occurs in compression before buckling.

These members are structurally analogous to columns. So, the buckling strength of struts is similar to that of the column and can be taken as,

\({{\rm{P}}_{{\rm{buck}}}} = {\rm{K}}\frac{{{{\rm{\pi }}^2}{\rm{EI}}}}{{{\rm{L}}_{\rm{}}^2}},{\rm{\;K\;}}\)is a factor depending upon the end conditions.

\(\therefore {\rm{\;}}{{\rm{P}}_{{\rm{buck}}}} \propto \frac{{{\rm{EI}}}}{{{\rm{L}}_{\rm{e}}^2}} \propto \frac{{{\rm{EA}}{{\rm{r}}^2}}}{{{\rm{L}}_{\rm{e}}^2}} \propto \frac{{{\rm{EA}}}}{{{{\left( {\frac{{{{\rm{L}}_{\rm{e}}}}}{{\rm{r}}}} \right)}^2}}} \propto \frac{{{\rm{EA}}}}{{{{\left( {\rm{\lambda }} \right)}^2}}}{\rm{\;\;}}\;\;\)

\(\therefore {{\rm{P}}_{{\rm{buck}}}} \propto \frac{1}{{{{\left( {\rm{\lambda }} \right)}^2}}}\;\) where λ is the slenderness ratio.

where,

P_buck is the buckling strength of the strut,

E is the modulus of elasticity of the strut,

I is the moment of inertia, 

A is the cross-section and

L_e effective length of the strut respectively.

Note: The net area of the strut is mainly the deciding factor in case for yielding failure but not for the buckling strength failure.