Modulus Of Rigidity Of Material Of Shaft Using Shear Stress-Induced At Surface Of Shaft Calculator

Formula Used:

\[ G_{Torsion} = \frac{\tau \times L_{shaft}}{R \times \theta_{Torsion}} \]

Shear Stress in Shaft (τ):

Pascal

Length of Shaft (L_shaft):

Meter

Radius of Shaft (R):

Meter

Angle of Twist (θ_Torsion):

Radian

Modulus of Rigidity (G_Torsion):

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1. What is the Modulus of Rigidity Formula?

The Modulus of Rigidity (also known as shear modulus) is a measure of a material's rigidity, given by the ratio of shear stress to shear strain. It represents the material's resistance to deformation under shear stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ G_{Torsion} = \frac{\tau \times L_{shaft}}{R \times \theta_{Torsion}} \]

Where:

\( G_{Torsion} \) — Modulus of Rigidity (Pascal)
\( \tau \) — Shear Stress in Shaft (Pascal)
\( L_{shaft} \) — Length of Shaft (Meter)
\( R \) — Radius of Shaft (Meter)
\( \theta_{Torsion} \) — Angle of Twist (Radian)

Explanation: This formula calculates the modulus of rigidity by considering the shear stress applied to a shaft, its dimensions, and the resulting angle of twist.

3. Importance of Modulus of Rigidity Calculation

Details: The modulus of rigidity is a fundamental material property that helps engineers design structures and components that can withstand shear forces without excessive deformation. It's particularly important in torsion applications and mechanical design.

4. Using the Calculator

Tips: Enter shear stress in Pascal, length and radius in meters, and angle of twist in radians. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of rigidity values?
A: Modulus of rigidity values vary by material. For steel, it's typically around 79 GPa, for aluminum about 26 GPa, and for rubber it can be as low as 0.0003 GPa.

Q2: How does modulus of rigidity relate to other elastic moduli?
A: For isotropic materials, modulus of rigidity (G) is related to Young's modulus (E) and Poisson's ratio (ν) by the formula: G = E / [2(1 + ν)].

Q3: What factors affect the modulus of rigidity?
A: Temperature, material composition, and processing methods can all affect the modulus of rigidity. Generally, it decreases with increasing temperature.

Q4: Why is modulus of rigidity important in shaft design?
A: In shaft design, the modulus of rigidity helps determine the amount of twist a shaft will experience under torsional loads, which is critical for ensuring proper operation and avoiding failure.

Q5: Can this formula be used for non-circular shafts?
A: This specific formula is derived for circular shafts. Different formulas are needed for shafts with non-circular cross-sections.