Let's break down the problem step by step: --- ## **Given:** - Diameter of bolt, d = 1.75 \) in - Force applied, \( P = 95 \) kip = \( 95,000 \) lb - You need to find the **shear strain \(\gamma\)** in the bolt. --- ## **Step 1: Find the Shear Stress (\(\tau\))** The shear **stress** on the bolt is: \[ \tau = \frac{P}{A} \] Where: - \( P \) = applied force - \( A \) = cross-sectional area of the bolt The **area** for a circular cross-section: \[ A = \frac{\pi}{4} d^2 \] Plug in the values: \[ A = \frac{\pi}{4} (1.75)^2 = \frac{\pi}{4} \times 3.0625 = 2.406 \text{ in}^2 \] So, \[ \tau = \frac{95000}{2.406} = 39,484 \text{ psi} \] --- ## **Step 2: Use the Material's Shear Stress-Strain Curve** The problem says the shear stress-strain diagram is "approximated as shown in Figure 2." You need the relationship between \(\tau\) and \(\gamma\) from that diagram. **Usually**, for the elastic region: \[ \tau = G \gamma \] Where \( G \) is the shear modulus. But since the diagram isn't shown here, **check your Figure 2** for the relationship. If it's linear, use the above. If it's a graph, find \(\gamma\) corresponding to \(\tau = 39,484\) psi. --- ## **Step 3: Final Answer (If Shear Modulus is Given/Implied)** Assume \( G \) is given or can be read from the graph. **If not specified, let's assume a typical value for steel: \( G = 12 \times 10^6 \) psi.** \[ \gamma = \frac{\tau}{G} = \frac{39,484}{12,000,000} \] \[ \gamma = .00329 \text{ radians} \] **Round to three significant figures:** \[ \boxed{.00329 \text{ rad}} \] --- ## **Summary of Steps:** 1. **Find area:** \( A = \frac{\pi}{4} d^2 \) 2. **Calculate shear stress:** \( \tau = \frac{P}{A} \) 3. **From the diagram (or using \( G \)), find \(\gamma\):** \( \gamma = \frac{\tau}{G} \) 4. **Express to three significant figures.** --- ### **You must check Figure 2 in your material for the exact relationship!** - If the diagram is nonlinear, interpolate. - If the value of \( G \) is different, use what is given. --- **If you upload Figure 2, I can help you read the value exactly!**