Indicate with arrows $(n$ a rotation; $$ a translation$)$ on each structure and list

beside each structure the number of structural degrees of freedom, $k,$ that are

required to do an analysis by the slope$-$deflection method. In each case, use the

minimum number of structural degrees of freedom; where they occur, take into

account symmetry, anti$-$symmetry and joints that are known to have zero moments.

$($a$)$

TYPICAL HINGE.