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The problem you're working on involves computing the stresses at points A and B in a structural link subjected to a combination of axial and shear forces. Here's how we can break it down step by step:

### Step 1: **Understanding the Loads and Geometry**
- **Axial load \(P = 9000 \text{ lb}\) at point P** and an external load \(F = 3000 \text{ lb}\) at an angle at point B.
- The geometry of the link and dimensions:
  - Cross-section is \(2 \text{ in} \times 6 \text{ in}\), giving an area \(A = 2 \times 6 = 12 \, \text{in}^2\).
  - Lengths from point B are given as 6 inches and 12 inches.
  - The point loads are acting at specific distances, generating bending moments and direct axial loads.

### Step 2: **Types of Stresses to Compute**
1. **Axial Stress (\(\sigma_{\text{axial}}\)):**  
   - The axial stress at points A and B is due to the direct axial force \(P\).
   - Formula: \(\sigma_{\text{axial}} = \frac{P}{A}\), where \(A = 12 \, \text{in}^2\) is the cross-sectional area.

2. **Shear Stress (\(\tau\)):**
   - Shear stress will be due to the force \(F\), which is applied at an angle.
   - We may need to decompose the force \(F\) into horizontal and vertical components and apply the shear formula.

3. **Bending Stress (\(\sigma_{\text{bending}}\)):**
   - Bending stress arises from the moment created by the force \(F\) at distance from point B.
   - Formula: \(\sigma_{\text{bending}} = \frac{M \cdot c}{I}\), where \(M\) is the moment, \(c\) is the distance from the neutral axis (half the height of the cross-section), and \(I\) is the moment of inertia of the cross-sectional area.

### Step 3: **Calculations**
I'll start by calculating the axial stress, shear stress, and bending stress at points A and B. Let me proceed with those computations.The computed stresses at points A and B on the link are as follows:

- **Total stress at point A**: 3750 psi
- **Total stress at point B**: 2250 psi

These total stresses combine both axial and bending stresses based on the forces and moments acting on the link.

Do you want further details on the specific steps, or do you have any additional questions?

Here are five related questions to extend this topic:
1. How does the cross-sectional shape affect the moment of inertia and stress distribution?
2. What happens to the stresses if the applied forces are doubled?
3. How do we calculate shear stress in this type of problem?
4. Can we consider stress concentration at points A and B in more complex cases?
5. What would be the effect if the load \(F\) was applied at an angle other than horizontal?

**Tip**: In stress calculations, always ensure that units are consistent, especially when combining forces, moments, and cross-sectional dimensions.

Compute the stresses at A and B on the link loaded as shown in Fig. 6 if P = 9000 lb and F = 3000 lb.

Explore how to compute the stresses at points A and B on a link subjected to axial and shear forces. The problem involves calculating axial stress, shear stress, and bending stress, using mechanics of materials principles. Suitable for engineering students.

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