Diameter of Shaft given Principle Shear Stress Calculator

ASME Shaft Diameter Formula:

\[ d_{ASME} = \left( \frac{16}{\pi \cdot \tau_{max_{ASME}}} \cdot \sqrt{(M_t \cdot k_t)^2 + (k_b \cdot M_b)^2} \right)^{1/3} \]

Maximum Shear Stress in Shaft from ASME:

Torsional Moment in Shaft:

N·m

Combined Shock Fatigue Factor of Torsion Moment:

Combined Shock Fatigue Factor of Bending Moment:

Bending Moment in Shaft:

N·m

Diameter of Shaft from ASME:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the ASME Shaft Diameter Formula?

The ASME (American Society of Mechanical Engineers) shaft diameter formula calculates the minimum required shaft diameter based on maximum shear stress theory. It considers both torsional and bending moments with appropriate shock and fatigue factors for safe shaft design.

2. How Does the Calculator Work?

The calculator uses the ASME shaft diameter formula:

\[ d_{ASME} = \left( \frac{16}{\pi \cdot \tau_{max_{ASME}}} \cdot \sqrt{(M_t \cdot k_t)^2 + (k_b \cdot M_b)^2} \right)^{1/3} \]

Where:

\( d_{ASME} \) — Diameter of shaft (m)
\( \tau_{max_{ASME}} \) — Maximum allowable shear stress (Pa)
\( M_t \) — Torsional moment (N·m)
\( k_t \) — Combined shock fatigue factor for torsion
\( k_b \) — Combined shock fatigue factor for bending
\( M_b \) — Bending moment (N·m)
\( \pi \) — Mathematical constant (≈3.1416)

Explanation: The formula combines torsional and bending stresses using the maximum shear stress theory, incorporating safety factors for shock and fatigue loading conditions.

3. Importance of Shaft Diameter Calculation

Details: Proper shaft sizing is crucial for mechanical system reliability. Undersized shafts may fail under load, while oversized shafts increase cost and weight unnecessarily. The ASME formula provides a standardized approach for safe shaft design.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Maximum shear stress should be the allowable value from material properties. Shock and fatigue factors depend on application conditions (typically 1.0-2.0).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for shock and fatigue factors?
A: For steady loading: 1.0, for minor shocks: 1.0-1.5, for heavy shocks: 1.5-2.0 or higher depending on application severity.

Q2: How do I determine maximum allowable shear stress?
A: Typically 0.3 × yield strength or 0.18 × ultimate tensile strength for ductile materials, but consult specific material standards.

Q3: Can this formula be used for hollow shafts?
A: This formula is specifically for solid circular shafts. Different formulas apply for hollow shafts.

Q4: What safety factors are included in this calculation?
A: The shock and fatigue factors (k_t and k_b) incorporate safety considerations for dynamic loading conditions.

Q5: When should I use this vs other shaft design methods?
A: The ASME method is widely accepted for general machinery applications. For highly specialized applications, other standards or finite element analysis may be appropriate.