I need to calculate transverse shear force on 1inch dia X 3inch Long pin.

Pin is supported at fixed at both ends, cannot use Beam formulae since L<8D. The location of force is 1.86 inches from left end. There is direct single shear of this pin due to vertical load falling on it. Need to give the allowable veritcal shear load at distance of 1.86 from left support. Yield strength is 75 ksi, factor of safety - 1.5. As per my calculation allowable shear force is 7528 lbf. Please suggest, will be great help for me.

To determine the allowable vertical shear load on a pin with the given specifications, we need to consider the shear strength of the material and the geometry of the pin. Since the pin is fixed at both ends and subjected to a vertical load, we will calculate the shear force based on the yield strength and the factor of safety you've provided.

Understanding Shear Force Calculation

The first step in calculating the allowable shear force is to determine the shear area of the pin. For a circular pin, the shear area can be calculated using the formula:

• Shear Area (A_v): A_v = π/4 × D²

Where D is the diameter of the pin. In your case, the diameter is 1 inch. Plugging in the values:

• A_v = π/4 × (1 inch)² ≈ 0.7854 in²

Calculating Allowable Shear Force

Next, we need to calculate the allowable shear force using the yield strength and the factor of safety. The formula for allowable shear force (V_allowable) is given by:

• Allowable Shear Force (V_allowable): V_allowable = (Yield Strength / Factor of Safety) × Shear Area

Substituting the values you provided:

• Yield Strength = 75 ksi = 75,000 psi
• Factor of Safety = 1.5

Now, we can calculate:

• V_allowable = (75,000 psi / 1.5) × 0.7854 in²
• V_allowable = 50,000 psi × 0.7854 in² ≈ 39,270 lbf

Verifying Your Calculation

Your calculation of 7528 lbf seems to be significantly lower than what we derived. It’s important to double-check the calculations to ensure that the shear area and the yield strength were applied correctly. Based on the provided yield strength and factor of safety, the allowable shear force should be approximately 39,270 lbf.

Considerations for Shear Force Application

Since the load is applied at a distance of 1.86 inches from the left support, it is crucial to ensure that the shear force does not exceed the calculated allowable shear force at that point. The maximum shear force will be influenced by the distance from the supports and the applied load. If the load is within the allowable limits, the pin should perform adequately under the given conditions.

Final Thoughts

In summary, based on the yield strength of 75 ksi and a factor of safety of 1.5, the allowable shear force for your pin is approximately 39,270 lbf. If your calculations yielded a different result, I recommend reviewing the steps to ensure that all parameters were correctly applied. If you have any further questions or need clarification on any specific part of the calculation, feel free to ask!