In the problem statement below, the question states to find the maximum load $\vec{P}$ that the truss can support. My method of approach was:
- Draw a FBD for the entire structure.
- Generally I would identify all external forces, however for this problem I felt it was unnecessary because I felt they weren't needed if I knew already the forces in each member.
- So I then dove straight into joint $D$, and assumed each member connected to $D$ was in tension and experienced the maximum tensile force $\vec{T} = 1500$ lb.
However, this led to the wrong answer when solving for $\vec{P}$. The solution manual instead found each external force in terms of $\vec{P}$ and started at joint $A$ to find $\overrightarrow{AD}$ and $\overrightarrow{AB}$ in terms of $\vec{P}$. In addition, in order to get numerical values, the solution manual assumed member $\overrightarrow{AB}$ was experiencing the maximum compression force of 660 lb. However, when I assume that member $\overrightarrow{AD}$ is experiencing the maximum tensile force, it doesn't work out the same.
My question is, conceptually, why must I find each each member's force in terms of $\vec{P}$, and why must one assume $\overrightarrow{AB}$ is experiencing maximum compression (but not $\overrightarrow{AD}$ in maximum tension)?
EDIT: I want to note that I do not need help with solving this problem, nor the math required. I simply am just looking for a conceptual answer as to why my approach did not work (i.e. only analyzing joint $D$).