Modulus of Rigidity Calculator
Calculate shear modulus, shear stress, strain, or deformation. Step-by-step formulas included for rods, shafts, beams, and elastic materials under torsion.
Modulus of Rigidity calculator:
This Modulus of Rigidity Calculator can be used to compute shear modulus, shear stress, strain, and torsional deformation of a rod, a shaft, or a beam. Modulus can be calculated by using enter applied shear force, area or deformation. Calculations are done stepwise and provide precise and clear results.
Modulus of Rigidity Tool Formula:
Modulus of Rigidity (G):
\[ G = \frac{T}{\Upsilon} \]
(where τ = shear stress, γ = shear strain)
The Modulus of Rigidity Calculator assists engineers, students, and designers to find out the shear modulus (G) of materials in torsional or shear load. Shear modulus, or the modulus of rigidity, is a basic property, which characterizes the correlation between shear stress (τ) and shear strain ( γ ). expressed as G = τ / γ.
The applied shear force, cross-sectional area, torsional deformation or measured shear strain can be keyed in by the users. The calculator determines the shear stress, shear strain, deformation and the modulus of rigidity. Formulas of torsion, shear stress, angular deformation, and shear modulus are demonstrated step by step, which is why it is easy to consider rods, shafts, beams and other structural members.
SI units are accepted: N, kN, mm, m, Pa, MPa, GPa. The tool is appropriate to mechanical engineers, civil engineers, design engineers, and learners who are tasked with determining the torsion of shafts, rods, or beams correctly to ensure that they make safe designs under shear loads by determining the shear modulus.
⚡ Work & Installation Input to Output:
Input:
- Applied shear force (F)
- Cross-sectional area (A)
- Measured torsional deformation / angle of twist (θ)
- Original length (L0)
- Shear strain (γ) if available
- Units: N, kN, mm, m, Pa, MPa, GPa
Processing:
- Compute shear stress: τ = F / A
- Compute shear strain: γ = θ × (radius / L0) or from measurement
- Compute modulus of rigidity: G = τ / γ
- Compute torsional deformation if unknown
- Validate input values and unit consistency
Output:
- Shear stress (τ)
- Shear strain (γ)
- Modulus of rigidity (G)
- Torsional deformation (θ)
- Step-by-step formulas and calculations
Testing and Final Adjustments
Test common scenarios:
- Shaft under F = 50 kN, A = 200 mm², L0 = 1 m, θ = 0.01 rad → compute G, τ, γ
- Beam with measured shear strain γ = 0.001, τ = 50 MPa → compute G
- Edge cases: very small or large cross-sections, high torsional loads
- Units validation: N ↔ kN, mm ↔ m, Pa ↔ MPa
- Step-by-step clarity for students and engineers
- Mobile/desktop UX: numeric keypad, labels, error messages
- Include material examples: steel (G ≈ 80 GPa), aluminum (G ≈ 26 GPa), brass (G ≈ 40 GPa)
- SEO metadata: "Modulus of Rigidity Calculator," "Shear Modulus Calculator," "Torsion Analysis," "Shear Stress-Strain," schema markup
Frequently Asked Questions - Modulus of Rigidity Calculator:
What is modulus of rigidity?
Modulus of rigidity (shear modulus, G) is the ratio of shear stress to shear strain in the elastic region of a material.
How do I calculate shear modulus?
G = τ / γ, where τ is shear stress and γ is shear strain.
How do I calculate shear stress?
Shear stress τ = F / A, where F is applied shear force and A is cross-sectional area.
How do I calculate shear strain?
Shear strain γ = θ × (radius / L0) or from measured angular deformation.
How do I calculate torsional deformation?
θ = γ × (L0 / radius), where L0 is length and radius is shaft radius.
Which units are supported?
Force in N or kN, length in mm or m, stress in Pa, MPa, or GPa.
Who should use this calculator?
Mechanical engineers, civil engineers, design engineers, and students analyzing torsion or shear in materials.
Why is modulus of rigidity important?
It helps predict material stiffness under shear and torsional loads, crucial for mechanical and structural design.
Can it be used for all elastic materials?
Yes, for metals, polymers, composites, and other materials within the elastic limit.
Does it show step-by-step calculations?
Yes, all formulas and intermediate steps are displayed for clarity and verification.
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