Ratio of Diameters given Principle Stress Calculator

Formula Used:

\[ C = \left(1 - \frac{16 \cdot \left(Mb_h + \sqrt{Mb_h^2 + Mt_{hollowshaft}^2}\right)}{\pi \cdot d_o^3 \cdot \tau}\right)^{1/4} \]

Bending Moment in Hollow Shaft (Mb_h):

N·m

Torsional Moment in Hollow Shaft (Mt_hollowshaft):

N·m

Outer Diameter of Hollow Shaft (d_o):

Maximum Principle Stress in Hollow Shaft (τ):

Ratio of Inner to Outer Diameter of Hollow Shaft (C):

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1. What is the Ratio of Diameters given Principle Stress?

The ratio of inner to outer diameter of a hollow shaft is a critical parameter in mechanical engineering that determines the optimal cross-sectional geometry when subjected to combined bending and torsional loads under maximum principle stress constraints.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = \left(1 - \frac{16 \cdot \left(Mb_h + \sqrt{Mb_h^2 + Mt_{hollowshaft}^2}\right)}{\pi \cdot d_o^3 \cdot \tau}\right)^{1/4} \]

Where:

\( C \) — Ratio of Inner to Outer Diameter of Hollow Shaft
\( Mb_h \) — Bending Moment in Hollow Shaft (N·m)
\( Mt_{hollowshaft} \) — Torsional Moment in Hollow Shaft (N·m)
\( d_o \) — Outer Diameter of Hollow Shaft (m)
\( \tau \) — Maximum Principle Stress in Hollow Shaft (Pa)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the optimal diameter ratio that ensures the maximum principle stress does not exceed the specified limit under combined loading conditions.

3. Importance of Diameter Ratio Calculation

Details: Calculating the proper diameter ratio is essential for designing hollow shafts that can withstand combined bending and torsional loads while maintaining structural integrity and preventing failure due to excessive stress.

4. Using the Calculator

Tips: Enter bending moment and torsional moment in N·m, outer diameter in meters, and maximum principle stress in Pascals. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for diameter ratio in hollow shafts?
A: The diameter ratio typically ranges from 0.5 to 0.9, depending on the application and loading conditions.

Q2: Why is this calculation important in shaft design?
A: This calculation ensures that the hollow shaft can withstand combined loading conditions without exceeding the material's maximum allowable stress.

Q3: What units should be used for input values?
A: Use Newton-meters (N·m) for moments, meters (m) for diameter, and Pascals (Pa) for stress to maintain consistency.

Q4: Can this formula be used for solid shafts?
A: No, this formula is specifically derived for hollow shafts where the inner diameter is a significant fraction of the outer diameter.

Q5: What factors affect the optimal diameter ratio?
A: The optimal ratio depends on the magnitude of bending and torsional moments, the outer diameter constraint, and the maximum allowable stress of the material.