Torsion of Bars Calculators

Torsion of a Bar of an Arbitrary Cross Section

In this calculation, a bar of length L, with the moments of inertia of a section I_x and I_y, area A and the maximum inscribed circle diameter D is considered.

The bar is under torque T, applied to the end. As a result of calculations, the total twist angle of the bar φ and the maximum shear stress τ at an arbitrary point with the radius of curvature of the section boundary r are determined. At that, shear stresses increase as the radius of curvature increases.

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

Torsion of Any Section Without Reentrant Angles calculation

Torsion of Any compact Section calculation

INITIAL DATA

I_x - Moment of inertia about any centroidal axis X;

I_y - Moment of inertia about centroidal axis Y, perpendicular to the axis X;

A - Area of the cross-section;

D - Diameter of largest inscribed circle;

r - Radius of curvarure of the section border at the calculation point;

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

Moment of inertia (I_x)

Moment of inertia (I_y)

Area of cross-section (A)

Diameter (D)

Radius (r)

Bar length (L)

Torque (Т)

Poisson's ratio (ν)

Young's modulus (Е)

Shear stress (τ)

Twist angle (φ)

BASIC FORMULAS

Maximum shear stress:

τ = 40*Т*(I_x + I_y) / A⁴*K₁;

Twist angle:

φ = 40*T*L*(I_x + I_y) / A⁴*G,

G - Shear modulus;

K₁ - Coefficient, depending on the cross-sectional dimensions.

INITIAL DATA

I_x - Moment of inertia about any centroidal axis X;

I_y - Moment of inertia about centroidal axis Y, perpendicular to the axis X;

A - Area of the cross-section;

D - Diameter of largest inscribed circle;

r - Radius of curvarure of the section border at the calculation point;

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