Torsion of Bars Calculators

Torsion of Thin-walled Bar of Rectangular Cross Section

In this calculation, a rectangular thin walled bar of length L with the cross-sectional dimensions a × b and wall thicknesses s₁ and s is considered.

The bar is under torque T, applied to the end. Following the calculations, the total twist angle φ and the maximum shear stresses τ in the section are determined.

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

Thin walled bar of rectangular section under torsion

Calculation of Thin walled bar of rectangular section under torsion

INITIAL DATA

a - Cross-section width;

b - Cross-section height;

s - Wall thickness on "b" side;

s₁ - Wall thickness on "a" side;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

τ - Maximum shear stress in the cross-section on "b" side;

τ₁ - Maximum shear stress in the cross-section on "a" side;

φ - Twist angle.

Metric Imperial

Width (a)

Height (b)

Thickness (s)

Thickness (s₁)

Bar length (L)

Torque (Т)

Poisson's ratio (ν)

Young's modulus (Е)

Shear stress (τ)

Shear stress (τ₁)

Twist angle (φ)

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BASIC FORMULAS

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

τ = T / 2s(a - s)(b - s₁);

τ₁ = T / 2s₁(a - s)(b - s₁);

φ = TL / K₁G;

G - Shear modulus;

K₁ - coefficient, depending on dimensions of the rectangle.

INITIAL DATA

a - Cross-section width;

b - Cross-section height;

s - Wall thickness on "b" side;

s₁ - Wall thickness on "a" side;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

τ - Maximum shear stress in the cross-section on "b" side;

τ₁ - Maximum shear stress in the cross-section on "a" side;

φ - Twist angle.

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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