Project #$6$

For the frame below, please answer the following questions $($all members are A$-36$ steel$).$ Take ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=9$MPa and ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=0\mathrm{.}6$MPa. Neglect the weight of all members. The connection at $B$ is a pinned connection. If you need any additional information, make assumptions, but make sure to include your assumptions in your final report and your presentation.

Determine all reactions. Note that for member $AB,$ joint $A$ is fixed while joint $B$ is pinned. For member $BCD,B$ is pinned and $D$ is a roller support.

Determine the internal forces for all members. Draw the axial, shear and moment diagrams for each member.

Considering the types of internal loads in the members, describe the different types of stress that can occur in each element.

If all members have a rectangular cross$-$section with a height$-$to$-$width ratio of $1\mathrm{.}5,$ determine the minimum member size $($height and width$)$ to the nearest $cm$ for each member.

Using the member size determined in $4,$ determine the state of stress that the loadings produce at points $M$ and $N.$

For the member sizes determined in part $4,$ determine the total weight of the structure.

We are considering building this structure out of steel or wood $({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=9$MPa and ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=0\mathrm{.}6$MPa $).$ Which would be the least cost option $($only considering the purchase price of the members$).$

For questions $4$ and $7,$ provide a discussion regarding the selected sections and the total costs.