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A $28-$in$.-$wide by $0\mathrm{.}105-$in$.-$thick by $110-$in$.-$long steel sheet is to be formed into a hollow section by being bent through $360$ and having

the long edges welded $($i$.$e$.,$ butt$-$welded$)$ together. Assume a cross$-$sectional medial length of $28in.($no stretching of the sheet due to

bending$).$ If the maximum shear stress must be limited to $10$ ksi $,$ determine the maximum torque that can be carried by the hollow

section if

$($a$)$ the shape of the section is a circle.

$($b$)$ the shape of the section is an equilateral triangle.

$($c$)$ the shape of the section is a square.

$($d$)$ the shape of the section is a rectangle measuring $8\mathrm{.}45\mathrm{.}6$ in$.$

Answers:

$($a$)T_{\text{m}\text{a}\text{x},\text{c}\text{i}\text{r}\text{c}}=$

kip$-$in$.$

$($b$)T_{\text{m}\text{a}\text{x},\text{t}\text{r}\text{i}}=$

kip$-$in$.$

$($c$)T_{\text{m}\text{a}\text{x},sq}=$

kip$-$in$.$

$($d$)T_{\text{m}\text{a}\text{x}\text{,}\text{r}\text{e}\text{c}\text{t}}=$

i

kip$-$in$.$