Torsion of Split Hollow Shaft | Online Calculator

Torsion of Bars Calculators







Torsion of Split Hollow Shaft

In this calculation, a split hollow shaft of a length L, outer diameter D, inner diameter d, and slot width H is considered.

The shaft is under torque T, applied to the end. As a result of calculations, the total twist angle φ and the maximum shear stress τ are determined. The shear stresses decrease as the D/d ratio increases.

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

Split Hollow Shaft under torsion
Calculation of Split Hollow Shaft under torsion

INITIAL DATA

D - Shaft outer diameter;


d - Shaft hole diameter;


H - Slot width;


L - Shaft length;


Т - Torque;


ν - Poisson's ratio;


Е - Young's modulus.


Calculation conditions:
0.2 < d/D < 0.6;
0.05 < H/d < 0.5.

RESULTS DATA

τ - Maximum shear stress in the cross-section;


φ - Twist angle.

Outer diameter (D)

Inner diameter (d)

Slot width (H)

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 = TK2 / D3;

φ = TL / K1G;

G - Shear modulus;

K1, K2 - coefficients, depending on the dimensions of the hole and slot.

INITIAL DATA

D - shaft outer diameter;


d - shaft hole diameter;


H - Slot width;


L - Shaft length;


Т - Torque;


ν - Poisson's ratio;


Е - Young's modulus.


Calculation conditions:
0.2 < d/D < 0.6;
0.05 < H/d < 0.5.

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)

-

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