How to Calculate and Solve for Mass of Cylindrical Shaft | Material Selection

The image above represents mass of cylindrical shaft.

To compute for mass of cylindrical shaft, five essential parameters are needed and these parameters are Factor of Safety (N), Twisting Moment (M), Length of Shaft (L), Density (ρ) and Shear Stress at Fracture (τf).

The formula for calculating mass of cylindrical shaft:

m = (2NM)2/31/3L)(ρ/τf2/3)

Where:

m = Mass of Cylindrical Shaft
N = Factor of Safety
M = Twisting Moment
L = Length of Shaft
ρ = Density
τf = Shear Stress at Fracture

Let’s solve an example;
Find the mass of cylindrical shaft when the factor of safety is 4, the twisting moment is 2, the length of shaft is 7, the density is 6 and the shear stress at fracture is 10.

This implies that;

N = Factor of Safety = 4
M = Twisting Moment = 2
L = Length of Shaft = 7
ρ = Density = 6
τf = Shear Stress at Fracture = 10

m = (2NM)2/31/3L)(ρ/τf2/3)
m = (2(4)(2))2/3 (π1/3(7)) (6/102/3)
m = (16)2/3 ((1.46)(7)) (6/4.64)
m = (6.349) (10.25) (1.29)
m = 84.14

Therefore, the mass of cylindrical shaft is 84.14 kg.

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How to Calculate and Solve for Shear Stress | Material Selection

The image above represents shear stress.

To compute for shear stress, three essential parameters are needed and these parameters are Twisting Moment (M), Radius (r) and Polar Moment of Inertia (J).

The formula for calculating shear stress:

τ = Mr/J

Where:

τ = Shear Stress
M = Twisting Moment
r = Radius
J = Polar Moment of Inertia

Let’s solve an example;
Find the shear stress when the twisting moment is 12, the radius is 8 and the polar moment of inertia is 14.

This implies that;

M = Twisting Moment = 12
r = Radius = 8
J = Polar Moment of Inertia = 14

τ = Mr/J
τ = (12)(8)/14
τ = 96/14
τ = 6.85

Therefore, the shear stress is 6.85 Pa.

Calculating the Twisting Moment when the Shear Stress, the Radius and the Polar Moment of Inertia is Given.

M = τJ / r

Where;

M = Twisting Moment
τ = Shear Stress
r = Radius
J = Polar Moment of Inertia

Let’s solve an example;
Find the twisting moment when the shear stress is 10, the radius is 6 and the polar moment of inertia is 4.

This implies that;

τ = Shear Stress = 10
r = Radius = 6
J = Polar Moment of Inertia = 4

M = τJ / r
M = 10 x 4 / 6
M = 40 / 6
M = 6.67

Therefore, the twisting moment is 6.67.

Continue reading How to Calculate and Solve for Shear Stress | Material Selection