Torsion of Bars Calculators

Torsion of Shaft with Keyway

In this calculation a shaft of length L, diameter D, with keyway dimensions K × H is considered.

The shaft is under torque T, applied to the end. As a result of calculations, the total twist angle φ and the maximum shear stress τ are determined.

For the calculation, the elastic modulus E and Poisson's ratio ν of the bar should be specified.

Torsion of Shaft with Keyway

Calculation of Torsion of Shaft with Keyway

INITIAL DATA

D - Shaft outer diameter;

H - Keyway width;

K - Keyway depth;

L - Keyway length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

Calculation conditions:
0.1 < K/D < 0.25;
1 < H/K < 3.

RESULTS DATA

τ - Maximum shear stress in the cross-section;

φ - Twist angle on the keyway length.

Metric Imperial

Outer diameter (D)

Keyway width (H)

Keyway depth (K)

Keyway length (L)

Torque (Т)

Poisson's ratio (ν)

Young's modulus (Е)

Shear stress (τ)

Twist angle (φ)

BASIC FORMULAS

Shear stress and angle of twist are determined by parametric equations of the form:

τ = TK₂ / D³;

φ = TL / K₁G;

G - Shear modulus;

K₁, K₂ - coefficients, depending on the dimensions of keyway.

INITIAL DATA

D - Shaft outer diameter;

H - Keyway width;

K - Keyway depth;

L - Keyway length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

Calculation conditions:
0.1 < K/D < 0.25;
1 < H/K < 3.

RESULTS DATA

τ - Maximum shear stress in the cross-section;

φ - Twist angle on the keyway length.

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

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