## How to Calculate and Solve for Performance Index | Material Selection

The image above represents performance index.

To compute for performance index, two essential parameters are needed and these parameters are Shear Stress at Fracture (τf) and Density (ρ).

The formula for calculating the performance index:

P = τf2/3 / ρ

Where:

P = Performance Index
τf = Shear Stress at Fracture
ρ = Density

Let’s solve an example;/
Find the performance index when the shear stress at fracture is 32 and the density is 10.

This implies that;

τf = Shear Stress at Fracture = 32
ρ = Density = 10

P = τf2/3 / ρ
P = 322/3/10
P = 10.079 / 10
P = 1.0079

Therefore, the performance index is 1.0079.

## 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.