Answer:
Width = Length = 1.148 inches
Step-by-step explanation:
We have been given the following data:
D = diameter = 2 inch = 0.0508m
P = Power = 100 HP = 74570 W
N = 500 rpm
Safety Factor = 2.5
Step 1:
We need to find yield strength which is represented by σ(y).
σ(y) for 1045 hot rolled steel = 330MPa
Step 2:
Find Shear Strength. Formula is given:
τ(y) = σ(y) / 2
τ(y) = 330 / 2
τ(y) = 165 MPa
τ(y) = 165 × 10⁶ Pa
τ(y) = 165 × 10⁶ kg.m⁻¹.s⁻²
Step 3:
Find Torque. Formula is given:
T = 60P / 2πN
T= (60)(74570) / 2π(500)
T = 1424.9 Nm
Step 4:
Find Shear Force. Formula is given:
F = 2T/d
F = 2(1424.9)/0.0508
F = 56098.43 N
F = 56098.43 kg.m.s⁻²
Step 5:
Find length by the given formula:
F/L² = τ(y)/Safety factor
Rearrange for L:
L = √(F· Safety factor / τ(y))
Substitute the values found in previous steps to calculate L.
L = 0.02915 meters
Convert it into inches:
L = 1.148 in
As it si a square key:
L = W
Width = 1.148 in