A steel cantilever beam, of length $2L,$ has an I$-$section, see Figure Q$3.$ The cantilever beam is under

a uniformly distributed load $q=175k\frac{N}{m}$ applied in its vertical plane of symmetry at OA part of the

span. The yield strength of the steel is $[]=440$MPa; the Young's modulus $E=250$GPa.$L=1m$

and the coordinates of Point $H$ are $x=0mm,y=-80mm,z=0mm.$

a$)$

The factors of safety predicted at point $H$ by the maximum shear stress theory of failure $($Tresca

criterion$)$

b$)$

The von Mises equivalent stresses at point $H$ can be calculated as $,$MPa

C$)$

The factors of safety at point $H$ predicted by the maximum$-$distortion$-$energy theory $($von Mises

criterion$)$ can be calculated as

d$)$

By use of the virtual work method, determine the rotation and deflection at the end B$.$

Deflection $-,mm($ Downward deflection is negative $)$

Rotation $-,{10}^{-3}$ radians $($Positive rotation is in the anticlockwise direction$)$