Torsion of Bars Calculators

Torsion of Hollow Bar of Circular Cross Section

In this calculation, a circular bar of length L and an outer diameter D, with a hole of a diameter d displaced relative to the common axis by distance a 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.

Bar of circular with hole section under torsion

Calculation of Bar of circular with hole section under torsion

INITIAL DATA

D - Bar outer diameter;

d - Bar hole diameter;

a - Hole offset;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

τ - Maximum shear stress in the cross-section;

φ - Twist angle.

Metric Imperial

Outer diameter (D)

Inner diameter (d)

Hole offset (a)

Bar length (L)

Torque (Т)

Poisson's ratio (ν)

Young's modulus (Е )

Shear stress (τ)

Twist angle (φ)

BASIC FORMULAS

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

τ = 16TDK₂ / π(D⁴ - d⁴);

φ = TL / K₁G;

G - Shear modulus;

K₁, K₂ - coefficients, depending on d/D and d/a ratios.

INITIAL DATA

D - Bar outer diameter;

d - Bar hole diameter;

a - Hole offset;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

τ - Maximum shear stress in the cross-section;

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