Which theory of failure will you use for aluminium components under steady loading? 

Explanation:-

Maximum Shear Stress Theory ( MSST )

• According to this theory, failure occurs when maximum shear stress at any point reaches the yield strength. 
• Condition for safe design:

\({\tau _{max}}\; \le \;\frac{{{S_{ys}}}}{N} = \frac{{{S_{yt}}}}{{2N}}\)

For tri-axial state of stress,

\(Max\left\{ {\left| {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right|\;,\left| {\frac{{{\sigma _2} - {\sigma _3}}}{2}} \right|,\;\left| {\frac{{{\sigma _3} - {\sigma _1}}}{2}} \right|\;\;} \right\}\; \le \;\frac{{{S_{yt}}}}{{2N}}\)

For bi-axial state of stress,

\(\;Max\left\{ {\left| {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right|\;,\left| {\frac{{{\sigma _2}}}{2}} \right|,\;\left| {\frac{{{\sigma _3}}}{2}} \right|\;\;} \right\}\; \le \;\frac{{{S_{yt}}}}{{2N}}\)

• This theory is well suitable for ductile materials.
• MSST is not suitable for hydrostatic loading.

Important Points

For brittle material

For Ductile material