Problem $3$

The continuous beam shown below is supported by columns at $B$ and $C($both pin$-$connected$)$ and

attached via a shear$-$connection $(=$ pinned$)$ to a strong column at $A.$ The owner of the structure

needs to replace the middle column because it was damaged during a recent forklift accident.

The plan is to install a hydraulic jack $($see photo in Appendix, Page $3)$ next to support $B$ and push

the beam upward by $1\mathrm{.}0$ in so that the column can be replaced.

Perform the following using the force method:

$($a$)$ Calculate the bending moment, $M_{B,J}$ due to jacking alone. Draw the shear force and bending

moment diagrams for the beam.

$($b$)$ Draw the shear force and bending moment diagrams for the beam due to $w_D,$ which includes

$2000l\frac{b}{f}t+$ self$-$weight of the W$12$x$170$ section. Your colleague has determined the bending

moment, $M_{B,D}=-191$ kip$*$ft$.$

$($c$)$ Compare the shear force and bending moment diagrams for $($a$)$ and $($b$)$

$($d$)$ Will the jack shown in the Appendix be sufficiently strong for this work?

Context note: The internal forces you computed here are unfactored. To verify that the planned

jacking operations are safe, an ultimate limit strength check $($as discussed in Module $1)$ would

be performed. Essentially, what you would do is factor these internal forces with appropriate

load factors, making them $V_u$ and $M_u,$ and then compare these against the design strength, $M_n$

of the W$12170$ beam section.