Question $1$: $(50$ Points$)$

The shear stress in the beam under transverse loading is given by an expression,

$=\frac{VQ}{It}$

Where V is the shear force, Q is the first moment of area, I is the second moment of area, and t is

the thickness.

Derive a shear stress distribution in a rectangular solid cross$-$section and find the maximum and

average shear stress.

${}_{xy}=\frac{3V}{2A}(1-\frac{y^2}{(\frac{h}{2}{)}^2})$

Compare the above shear stress distribution with any thin$-$walled cross$-$section of your choice.

Discuss which cross$-$section generates lower maximum and average shear stresses under a similar

applied shear force $($considering bending only$).$

Question $1$: $(50$ Points$)$

The shear stress in the beam under transverse loading is given by an expression,

$=\frac{VQ}{It}$

Where V is the shear force, Q is the first moment of area, I is the second moment of area, and t is

the thickness.

Derive a shear stress distribution in a rectangular solid cross$-$section and find the maximum and

average shear stress.

${}_{xy}=\frac{3V}{2A}(1-\frac{y^2}{(\frac{h}{2}{)}^2})$

Compare the above shear stress distribution with any thin$-$walled cross$-$section of your choice.

Discuss which cross$-$section generates lower maximum and average shear stresses under a similar

applied shear force $($considering bending only$).$