$1\mathrm{.}11.$ For a long slender beam such as the one shown in the figure:

a$.$ The internal bending moment is essentially equal to zero.

b$.$ The internal strain energy due to transverse shear is negligible.

c$.$ All the above

d$.$ None of the above

$1\mathrm{.}12.$ To use Castigliano's Theorem to solve for the rotation, $0,$ at point B :

a$.$ Include a dummy horizontal force at point B

b$.$ Include a dummy moment at point B

c$.$ Include a vertical force at point B

d$.$ No dummy load is needed, only applied load

$1\mathrm{.}13.$ To use Castigliano's Theorem to solve for the vertical deflection, $\backslash (\backslash$delta $\backslash ),$ at point B :

a$.$ Include a dummy horizontal force at point B

b$.$ Include a dummy moment at point B

c$.$ Include a vertical force at point B

d$.$ No dummy load is needed, only applied load

$1\mathrm{.}14.$ In TORSION, the area$($s$)$ of maximum shear on a solid elliptical shaft are:

a

b

c

d