Problem No$.1$

This exercise will help you refresh your knowledge of statics and prepare you for future

exercises on Gerber girder and the project.

The figure above shows what is commonly known as Gerber girder ${?}^1,$ balanced$-$cantilever girder, or

sometimes simply cantilever girder. The small circles at $C$ and $D$ symbolize hinges, which means

that no bending moment is created at those points. This little detail ${?}^2$ allows you to determine

the internal forces and moments in the girder by using the knowledge you have so far acquired

from statics. The part CD can be taken as a separate beam that is simply supported at the

points C and D on the overhanging beams ABC and DEF $.$

There is a reason why the girder is built with these hinges, but you will learn that later. For

now, you need to do the following:

a$)$ Draw appropriate free$-$body diagrams for the structure.

b$)$ Derive the equations for shear force $($V$)$ and bending moment $($M$)$ in each free body.

c$)$ Draw the shear$-$force and bending$-$moment diagrams. In these diagrams, you must

show the values of V or M at key locations, and also the distances to the locations

wherever $V$ or $M$ changes sign.