The problem you provided is about calculating the maximum load $P$ that can be applied to a truss structure, given the cross-sectional area of the truss members and a maximum allowable normal stress.

Here's a step-by-step explanation of how to solve it:

Problem Details:

• The truss members have a cross-sectional area of $A = 8 \, \text{mm}^2$.
• The maximum allowable normal stress in members $AB$ and $CB$ is $\sigma_{\text{max}} = 140 \, \text{MPa}$.
• We need to calculate the maximum load $P$ that can be applied, while ensuring the stress in the members $AB$ and $CB$ does not exceed the limit.

Approach:

1. Convert stress and area to consistent units: $A = 8 \, \text{mm}^2 = 8 \times 10^{-6} \, \text{m}^2$ $\sigma_{\text{max}} = 140 \, \text{MPa} = 140 \times 10^6 \, \text{Pa}$

2. Force in members $AB$ and $CB$: The normal stress $\sigma$ in any member is given by: $\sigma = \frac{F}{A}$ Rearranging for $F$ (the force in a truss member): $F = \sigma \cdot A = (140 \times 10^6) \times (8 \times 10^{-6}) = 1120 \, \text{N}$

3. Using Method of Joints: You can now analyze the forces in the truss members by using the Method of Joints. At joint $B$, you'll have vertical and horizontal components of forces. The trigonometry and geometry of the structure (not fully visible in the image) will help break the forces into components and solve for the external load $P$ in terms of these forces.

4. Find maximum $P$: Using equilibrium equations $\Sigma F_x = 0$ and $\Sigma F_y = 0$, the relationship between $P$ and the forces in $AB$ and $CB$ will allow you to determine the maximum $P$.

Would you like a full solution with detailed equilibrium equations, or do you have any specific part you'd like help with?

Related Questions:

1. What is the role of normal stress in structural design?
2. How does the method of joints help in analyzing trusses?
3. How do you convert between units of stress (MPa to Pa)?
4. What are common methods to analyze trusses besides the method of joints?
5. How does cross-sectional area affect the strength of a structural member?

Tip:

Always ensure that units are consistent when solving stress-related problems, particularly converting mm² to m² and MPa to Pa.