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Question $3[22$ Marks$]$

A frame ABCDE is being designed to support a vertical load $P,$ as shown in Figure $2.$ The connection at $B$ is a fixed connection. The supports at $D$ and $E$ are pinned. Member $CE$ is a steel plate connected by a hinge to the frame. Your may neglect the self$-$weight of all members in your analysis.

$[3]$ a$)$ Determine if this structure is stable and statically determinate and, if so$,$ determine the magnitude and direction of all support reactions.

$[9]$ b$)$ Draw the free body diagrams and force effect diagrams $($axial$,$ shear and bending$)$ for each of members $AB,BCD$ and CE $.$

$[2]$ c$)$ If the specified live load $P=140kN,$ and assuming a load factor of $1\mathrm{.}5$ at ULS, determine the required width of plate for member $CE$ such that the member will not fail by yielding of the gross cross section. Assume the plate is CAN$/$CSA G$40\mathrm{.}21$ Grade $300$W steel, with a specified yield strength, $Fy,$ of $300$ MPa and a specified ultimate tensile strength, $F_u,$ of $450$ MPa $.$ The member will be fabricated from plate of $10$ mm thickness. The resistance factor for steel, $,$ is $0\mathrm{.}9$ and the resistance factor for fracture of the net section $u,$ is $0\mathrm{.}75$

$[4]$ d$)$ Assume that the connections at $C$ and $E$ will be made with ASTM $325$ bolts, $22$ mm in diameter, with a shear resistance of $140$ kN $.$ Design a suitable connection such that the member will not fail by fracture of the net cross section under the factored load used in part c$).$

$[4]$ e$)$ As the frame is being assembled, it is discovered that the specified load P used for design should have been $150$ kN $,$ rather than $140$ kN $.$ Is the current design sufficient? If not, what type of failure would occur under this higher load? If the plate to be used for member CE has already been delivered and is to be cut to length on site, what modification to your design might you make to accommodate the increased in specified load $($assume that ABCD remains unchanged and that the supports at D and E cannot move$)?$ Justify your answer with supporting calculations.