$4$ For a cantilever z$-$section with off$-$center transverse load shown in $($a$)$ derive

i$.$ the normal stress distributions due to bending $(\backslash ($ b $\backslash ))$

ii$.$ the shear stress distributions due to bending $($c$)$

iii. the shear stress distributions due to torsion with free warping.

iv$.$ the shear stress distributions due to torsion with the warping constrained at the fixed$-$end $($d$)$

v$.$ the maximum normal stress due to constained warping $($f$)$

vi$.$ the maximum shear stress due to constained warping $(\backslash ($ g $\backslash ))$

vii. compare normal and shear stresses calculated in v $.$ and vi$.$ to those due to bending, i$.$ and ii$,$ and draw conclusions.

Take $\backslash ($ v$=1/4\backslash )$