Shear Stress in Roller Pin of Forked End of Rocker Arm Given Force on Roller Pin Calculator

Formula Used:

\[ \tau_r = \frac{2 \times P_c}{\pi \times d_2^2} \]

Shear Stress in Roller Pin (τr):

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1. What is Shear Stress in Roller Pin?

Shear stress in roller pin is the stress induced into the pin when subjected to forces that cause deformation by slippage along parallel planes. It represents the force per unit area acting tangentially to the cross-section of the pin.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_r = \frac{2 \times P_c}{\pi \times d_2^2} \]

Where:

\( \tau_r \) — Shear stress in roller pin (Pa)
\( P_c \) — Force on roller pin (N)
\( d_2 \) — Diameter of roller pin (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the shear stress distribution in a cylindrical roller pin subjected to transverse loading, assuming uniform stress distribution across the cross-section.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress is crucial for ensuring the structural integrity of roller pins in mechanical systems. It helps determine if the pin can withstand applied loads without failure and ensures proper safety margins in design.

4. Using the Calculator

Tips: Enter force on roller pin in Newtons and diameter of roller pin in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of shear stress values for roller pins?
A: Shear stress values depend on material properties, but typically range from 50-400 MPa for steel pins, depending on the application and safety factors.

Q2: Why is the factor of 2 used in the formula?
A: The factor of 2 accounts for the double shear condition where the pin is subjected to shear forces at two cross-sections simultaneously.

Q3: What materials are commonly used for roller pins?
A: Common materials include carbon steel, alloy steel, stainless steel, and sometimes bronze, chosen based on strength, wear resistance, and corrosion requirements.

Q4: How does pin diameter affect shear stress?
A: Shear stress is inversely proportional to the square of the diameter. Doubling the diameter reduces shear stress by a factor of four.

Q5: When should this calculation be used in mechanical design?
A: This calculation is essential during the design phase of any mechanical system involving pinned connections, such as rocker arms, linkages, and pivot joints.