Torsion of Bars Calculators

Torsion of a Bar of Triangular Cross Section

In this calculation, a triangular bar of length L and isosceles cross-section with base size a and lateral side size b is considered.

The bar is under torque T, applied to the end. Following the calculations, the total twist angle φ and the maximum shear stress τ in the section are determined. The shear stresses in the section take their minimum values at a = b.

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

Bar of triangle section under torsion

Calculation of Bar of triangle section under torsion

INITIAL DATA

a - Base of the triangular cross-section;

b - Side length of the triangular cross-section;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

Calculation condition:
40° < α < 120°.

RESULTS DATA

τ - Maximum shear stress in the cross-section;

φ - Twist angle.

Metric Imperial

Base (a)

Side length (b)

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 = T / K₂;

φ = TL / K₁G;

G - Shear modulus;

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

INITIAL DATA

a - Base of the triangular cross-section;

b - Side length of the triangular cross-section;

L - Bar length;

Т - Torque;

ν - Poisson's ratio;

Е - Young's modulus.

Calculation condition:
40° < α < 120°.

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