QUESTION $2$

a$)$ What the difference between statically determinate and statically indeterminate problems? Give only ONE example of structure for each case.

$[3$ marks$]$

b$)$ A force of $80$ kN is applied to a rigid body $\backslash ($ B C D $\backslash )$ as shown in Figure Q$2.$ The rigid body is also supported by a cable $\backslash ($ A B $\backslash )$ and pin connection at point $\backslash ($ C $\backslash ).$ The yield stress under shearing and the safety factor for the pin $\backslash ($ C $\backslash )$ are $300$ MPa and $2\mathrm{.}5,$ respectively. Cable $\backslash ($ A B $\backslash )$ has a diameter of $30$ mm with Young's modulus of $200$ GPa $.$

i$)$ Calculate the normal stress in cable $\backslash ($ A B $\backslash )$

ii$)$ Calculate the normal strain in cable $\backslash ($ A B $\backslash )$

iii$)$ Determine the allowable diameter of $\backslash (\backslash$mathrm$\{$pin$\}$ C $\backslash )$

$[7$ marks$]$