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Torsion Bar Spring

In this calculation, a torsion spring representing a round bar of length L with an outer diameter D and inner diameter d is considered. A lever of length L is attached to the bar being under the action of a load F perpendicular to its axis.

As a result of calculations, the spring stiffness C, lever deflection from the initial position Y, and maximum shear stresses τ in the rod are determined.

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

Torsion bar spring calculation
Torsion bar calculation

INITIAL DATA

D - Bar outer diameter;


d - Bar inner diameter;


L - Bar length;


R - Lever radius;


E - Young's modulus;


ν - Poisson's ratio;


F - Load.

RESULTS DATA

Y - Deflection of spring lever under load F;


C - Spring stiffness;


τ - Maximum shear stress under load F.

Diameter (D)

Diameter (d)

Length (L)

Lever (R)

Young's modulus (Е)

Poisson's ratio (ν)

Spring load (F)

Deflection (Y)

Stiffness (C)

Shear stress (τ)

BASIC FORMULAS

Deflection:

Y = 32F*R2*L / π*G*(D4 - d4);

Stiffness:

C = F / Y;

Maximum shear stress:

τ = 16R*F*D / π(D4 - d4).

INITIAL DATA

D - Bar outer diameter;


d - Bar inner diameter;


L - Bar length;


R - Lever radius;


E - Young's modulus;


ν - Poisson's ratio;


F - Load.

RESULTS DATA

Y - Deflection of spring lever under load F;


C - Spring stiffness;


τ - Maximum shear stress under load F.

MATERIAL PROPERTIES

Steel

Tensile strength, depending on tempering temperature

MPa (psi)

Yield strength, depending on tempering temperature

MPa (psi)

1050

738÷979 (107*103÷142*103)

469÷724 (68*103÷105*103)

1080

889÷1310 (129*103÷190*103)

600÷979 (87*103÷142*103)

4150

958÷1931 (139*103÷280*103)

841÷1724 (122*103÷250*103)

5160

896÷2220 (130*103÷322*103)

800÷1793 (116*103÷260*103)

6150

945÷1931 (137*103÷280*103)

841÷1689 (122*103÷245*103)

9255

993÷2103 (144*103÷305*103)

814÷2048 (118*103÷297*103)

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