Q$1.$ A thin rectangular plate of dimensions $75mm200mm$ is formed by welding two triangular plates $($see Fig Q$1).$ The plate is subjected to a compressive stress of $3\mathrm{.}0$ MPa in the long direction and a tensile stress of $10\mathrm{.}0$ MPa in the short direction.

$($a$)$ Determine the normal stress ${}_w$ acting perpendicular to the line of the weld and the shear stress ${}_w$ acting parallel to the weld.

$($b$)$ Calculate the principal stresses and maximum shear stress in the plate.

$($c$)$ Make a rough sketch of Mohr's Circle of stress for the plate.

$($d$)$ Locate the weld on your circle.