Problem $2$: Use the force method to analyze the structure. Both the cable and the beam are made of the same material $($E is the same$).$ Solution for $2\mathrm{.}4$: $35\mathrm{.}6$ kN$.$

C

$3$ m

Cable Ac $=300$ mm$^2$

$12$ kN$/$m

A

B

Beam

IB $=200(106)$ mm$48$ m

E $=$ constant

$2\mathrm{.}1)$ Select the tension in the cable as the redundant. Determine the deflection at A in the primary structure due to the distributed load.

$2\mathrm{.}2)$ Determine the deflection at A due to the redundant force acting on the primary structure.

$2\mathrm{.}3)$ Construct the compatibility equation for the deflection at A$.$

$2\mathrm{.}4)$ Determine the magnitude of the tension force in the cable. Hint: Remember that the cable can stretch. Try to find another expression for the deflection at A$.$

$2\mathrm{.}5)$ Determine the vertical deflection at A in millimeters. Assume the material of the structure is steel $($E $=200$ GPa$).$