Problem $3$

Numerical Problem $(25$ points$)$: I feel that a HW is incomplete without a question which includes a pin$-$joint. More than $80$ percent of our real life structures have some kind of pin$-$joint $($our body has multiple pin joints in toes, feet, ankles, knees, hips, shoulders, elbows, hands and spine$)$ so I want you to feel confident in analyzing anything and everything related to them. Let's bring in a beam from previous $HW$ shall we$?$

For the beam shown below, please answer the following:

$(15$ points$)$ Draw the SFD$/$BMD for the beam on an engineering paper. Please make sure you provide numerical values of shear force and bending moment at locations where the loading changes $(0,4,6,9ft).$

$(5$ points$)$ What is the location and magnitude of the maximum positive bending moment anywhere along the beam?

$(5$ points$)$ Based on the SFD$/$BMD$,$ calculate the ratio of shear force and bending moment between a point at $2ft$ from A and a point at $7\mathrm{.}5ft$ from $A.$

Your diagrams$/$plots should be on an engineering paper or you can use the engineering paper template uploaded on Canvas. Unclear SFD$/$BMD$,$ or SFD$/$BMD not drawn on engineering paper, or SFD$/$BMD not drawn as per engineering specs will lose upto $-10$ points.Also, please make sure you box$/$highlight the various equations you created for various segments along the beam for us to give you partial points. Just creating SFD$/$BMD without laying down the steps$/$equations will get you only $5$ points. $($I know I am repeating this again and again but I want to make sure you understand the expectations which will be the same for the final exam.$)$

Remember due to positive bending moment sign convention for BMD the bending moment at fixed end will be negative. This convention is independent of the equilibrium convention that you draw at the start of every problem in this class.