This problem is a classic truss analysis question for a bridge structure that can be loaded at two different points, either Pin E or Pin F, with a total of nine members. Here is a breakdown of how we might approach each part:

1. Part (a):

   • Use either the Method of Joints (MoJ) or Method of Sections (MoS) to find tensile/compressive forces in each member when $P_1 = 3000 \, \text{lb}$ and $P_2 = 0 \, \text{lb}$.
   • Begin by solving for the reactions at the supports, then analyze each joint to determine forces.
   • Each member’s force is calculated as a function of $P_1$, allowing you to substitute $P_1 = 3000 \, \text{lb}$ later.

2. Part (b):

   • With a computational tool, plot the tension/compression in each member as a function of $P_1$ (setting $P_2 = 0$).
   • This graph will help visualize how each member's force changes as $P_1$ varies.

3. Part (c):

   • Given that a member will fail if its tensile force exceeds 6000 lb or if its compressive force exceeds 4000 lb, check the plot from Part (b) to determine which member would fail first if $P_1$ is loaded and $P_2$ is not.
   • This part involves interpreting the plot to find the critical member.

4. Part (d):

   • Repeat the calculation, but now for $P_1 = 0$ and $P_2 = 3000 \, \text{lb}$.
   • This time, compute the tensile/compressive forces in all members as a function of $P_2$.

5. Part (e):

   • Again, use a computational tool to plot the forces in each member as a function of $P_2$ (with $P_1 = 0$).
   • This will allow you to observe the changes in member forces with varying $P_2$.

6. Part (f):

   • Analyze the results to determine which member would fail first if Pin E is loaded while Pin F is unloaded, and vice versa.
   • This involves comparing the load-bearing capacities to decide if Pin E or Pin F can support a larger load.

Recommendations

For computational solutions (Parts (b) and (e)), software such as MATLAB, Python, or structural analysis software (like SAP2000) would be ideal. These tools can automate the repetitive calculations and allow you to plot the forces across a range of loads.

Would you like detailed steps on any specific part, or help with setting up calculations for plotting in a computational tool?

Related Questions:

1. How do you determine support reactions for a truss with given external loads?
2. What is the Method of Joints and how does it apply to truss analysis?
3. How do tension and compression affect the stability of truss members?
4. How can failure thresholds (tensile and compressive limits) influence truss design?
5. How would the angle of members, like the 30° angle in this truss, affect force distribution?

Tip:

When solving for forces in a truss, start by isolating the equilibrium equations at each joint and solve systematically to prevent overlooking critical members.