Use the Force Method to determine the vertical reaction at Joint $B$ and the

reactions at Joint A$.$ Follow steps a through d$.$

E and I are constant.

A is a fixed support and $B$ is a roller.

Real Structure

$1=\frac{\text{D}\text{e}\text{g}\text{r}\text{e}\text{e}\text{I}\text{n}\text{d}\text{o}\text{t}\text{o}\text{r}\text{m}\text{i}\text{n}\text{a}\text{t}\text{e}}{?}$

Reduced Structure $1$

Removed Reaction @ B

Reduced Structure $2$

Unit Load @ B

$($Problem $1,$ Continued$)$

a$.$ Using Reduced Structure $1,$ determine the deflection at $B({}_B)$ due to the $4$

kip applied load.

Notes:

$(1)$ the given deflection equation assumes positive deflections is up

b$.$ Using Reduced Structure $2,$ determine the flexibility coefficient $f_{BB}.$

Notes:

$(1)f_R=$ deflection at $B$ due to a unit load applied at $B$

$(2)$ The unit load is applied down to match the given deflection equation

c$.$ In the real structure the deflection at $B$ is zero. Use the compatibility

equation below to determine $B_y.$

By $f_{gs}+B=0$

Notes:

$(1)$ Be sure to keep the correct signs from parts a and $b.$

$(2)$ The sign of By will be relative to the direction of the unit force in Reduced Structure $2.$

d$.$ Now that $B_{}$ is known, use statics to find the reactions at A $.$