Bending Moment Given Bending Stress In Hollow Shaft Calculator

Formula Used:

\[ M_{b_h} = \sigma_{b_h} \times \frac{\pi \times d_o^3 \times (1 - C^4)}{32} \]

Bending Moment in Hollow Shaft (M_{b_h}):

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1. What is Bending Moment in Hollow Shaft?

Bending Moment in Hollow Shaft is the reaction induced in a structural shaft hollow element when an external force or moment is applied to the element, causing the element to bend. It represents the internal moment that resists the bending deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_{b_h} = \sigma_{b_h} \times \frac{\pi \times d_o^3 \times (1 - C^4)}{32} \]

Where:

\( M_{b_h} \) — Bending Moment in Hollow Shaft (N·m)
\( \sigma_{b_h} \) — Bending Stress in Hollow Shaft (Pa)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the bending moment based on the bending stress, shaft geometry, and the ratio of inner to outer diameter.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for structural design and analysis of hollow shafts, ensuring they can withstand applied loads without failure or excessive deformation.

4. Using the Calculator

Tips: Enter bending stress in Pascals, outer diameter in meters, and the diameter ratio (0-1). All values must be valid positive numbers with ratio between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the (1-C⁴) term?
A: This term accounts for the hollow nature of the shaft, where C is the ratio of inner to outer diameter. It reduces the moment of inertia compared to a solid shaft.

Q2: What are typical values for the diameter ratio C?
A: Typical values range from 0.5 to 0.9, depending on the application and required strength-to-weight ratio.

Q3: How does hollow shaft compare to solid shaft in bending?
A: Hollow shafts provide better strength-to-weight ratio but may have different stress distributions and buckling characteristics.

Q4: What are the limitations of this formula?
A: This formula assumes linear elastic material behavior, uniform cross-section, and applies to pure bending conditions.

Q5: Can this calculator be used for dynamic loading?
A: For dynamic or cyclic loading, additional factors like fatigue strength and stress concentrations must be considered.