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 $BCD$ as shown in Figure Q$2.$ The rigid body is also supported by a cable $AB$ and pin connection at point $C.$ The yield stress under shearing and the safety factor for the pin $C$ are $300$ MPa and $2\mathrm{.}5,$ respectively. Cable $AB$ has a diameter of $30$ mm with Young's modulus of $200$ GPa $.$

i$)$ Calculate the normal stress in cable $AB$

ii$)$ Calculate the normal strain in cable $AB$

iii$)$ Determine the allowable diameter of pin $C$

$[7$ marks$]$

Figure Q$2$