(Solved): 1. In the truss structure shown below, all members have the length 4000mm,yu=350MPa,E=200,00 ...

1. In the truss structure shown below, all members have the length $4000\mathrm{mm},{?}_{yu}=350\mathrm{MPa},\mathrm{E}=200,000\mathrm{MPa}$. a) Solve for member forces in all 9 members and identify the member with the largest tensile force and the largest compressive force. b) Multiply the largest force from part a) by the ${\mathrm{FOS}}_{\text{yituins }}=2$ and calculate the required cross-sectional area (A) such that yielding will not occur. Provide your answer for the required cross-sectional area $(A)$ in ${\mathrm{mm}}^2$. e) Multiply the largest compressive force from part a) by the ${\mathrm{FOS}}_{\text{turling }}=3$ and calculate the required second moment of area (I) such that buckling will not occur. Recall that the force required to cause a member in compression to buckle is: $P_{cr}=\frac{{?}^{2}EI}{L^2}$ Provide your answer for the required second moment of area (I) in $10^6{\mathrm{mm}}^4$. d) For the longest member in the structure, calculate the required radius of gyration ( $r$ ) such that the minimum slenderness ratio is less than 200 . Recall that the slenderness ratio is the ratio between the length the member and radius of gyration (L/r). Provide your answer for the required radius of gration $(r)$ in $\mathrm{mm}$. e) Using Appendix B from the course notes, pick the lightest square hollow structural section (HSS) designation such that the chosen HSS has a higher area (A), second moment of area (I), and radius of gyration ( $\mathrm{r}$ ), than those required in parts b) $\mathrm{c}$ ) d). (E.g., HSS $305\times 305\times 9.5$ has an area $\mathrm{A}=11000{\mathrm{mm}}^2$, a second moment of area $1=158\times 10^6{\mathrm{mm}}^4$, and a radius of gyration $\mathrm{r}=120\mathrm{mm}$. This choice will likely satisfy all three requirements from parts b), e), d), but it is also likely not the lightest choice since it weighs $86.5\mathrm{kg}/\mathrm{m}$.) 2. Consider the truss bridge shown below. The truss members identified as 1, II and III have the largest mernber forces and will hence govern how much load the bridge can carry. All members are made of steel which have ${?}_y,350\mathrm{MPa},\mathrm{E}=$ $200,000\mathrm{MPa},\mathrm{A}=2000{\mathrm{mm}}^2$ and $\mathrm{I}=5.6\times 10^6{\mathrm{mm}}^4$. All dimensions provided are in $\mathrm{mm}$. a) Solve for the forces in I, II and III using the method of joints (I) and method of sections (II and III) in terms of P. b) Calculate the value of $\mathrm{P}$ which would cause the bridge to fail. Failure may occur if the member stress exceeds the yield strength (in both tension or compression), or if a member in compression buckles. Factors of safery are ignored when the exact failure is to be determined. 3. Consider the following inverted Pratt truss. a) Choose one HSS designation that can safely resist the forces and satisfy slendemess requirements $(\mathrm{Lr}<200)$ for all truss members in the top chord (the 6 horizontal trusses at the top) b) Choose one HSS designation for all truss members in the bottom chord (the 4 horizontal trusses at the bottom) e) Choose one HSS designation for all diagonal truss members (6 total) d) Choose one HSS designation for all vertical truss members ( 5 total) 4. Consider the truss shown below. Assume all members shown in the elevation view are HSS $254\times 254\times 11$. The truss bridge has a $1.2\mathrm{m}$ tall railing. a) Calculate the applied joint loads due to a wind load of $2\mathrm{kPa}$ at each joint of the elevation view. b) Analyze the truss forces in the top braces and bottom braces. Present your final member forces on truss diagrams. Denote tension forees with $(+)$ and compression with $(?)$. Note: it is not necessary to solve for the forces in the horizontal members (when looking at the top/ bottom view) caused by the wind. c) Choose one HSS designation for both the top and bottom braces.