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)

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)	-

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER