Bending Stress in Roller Pin of Forked End of Rocker Arm given Bending Moment Calculator

Formula Used:

\[ \sigma_{bp} = \frac{32 \times M_b}{\pi \times d_2^3} \]

Bending Stress in Roller Pin (σ_bp):

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1. What is Bending Stress in Roller Pin?

Bending Stress in Roller Pin is the amount of bending stress in the roller pin used with a roller joint to allow freedom of turning. It represents the internal stress caused by bending moments applied to the pin.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_{bp} = \frac{32 \times M_b}{\pi \times d_2^3} \]

Where:

\( \sigma_{bp} \) — Bending Stress in Roller Pin (Pa)
\( M_b \) — Bending Moment in Roller Pin (N·m)
\( d_2 \) — Diameter of Roller Pin (m)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: This formula calculates the maximum bending stress in a circular cross-section pin subjected to a bending moment.

3. Importance of Bending Stress Calculation

Details: Calculating bending 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 or excessive deformation.

4. Using the Calculator

Tips: Enter bending moment in Newton-meters (N·m) and diameter in meters (m). Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the 32/π factor in the formula?
A: The factor 32/π comes from the section modulus formula for a solid circular cross-section, which is πd³/32 for bending about a diameter.

Q2: What are typical bending stress limits for roller pins?
A: Bending stress limits depend on the material properties. Typically, pins are designed to keep bending stress below the material's yield strength with an appropriate safety factor.

Q3: How does pin diameter affect bending stress?
A: Bending stress is inversely proportional to the cube of the diameter. Doubling the diameter reduces bending stress by a factor of 8.

Q4: Can this formula be used for hollow pins?
A: No, this formula is specifically for solid circular pins. Hollow pins require a different section modulus calculation.

Q5: What units should be used for input values?
A: Bending moment should be in Newton-meters (N·m) and diameter in meters (m) to get bending stress in Pascals (Pa).