Answer:
The maximum shear stress in shaft AB, is 15 MPa
The maximum shear stress in shaft CD, is 45.9 MPa
Explanation:
The formula for a shaft polar moment of inertia, J is given by
J =
Therefore, we have
Where:
D = Diameter of shaft AB = 30 mm = 0.03 m
r = Radius of shaft AB = 15 mm = 0.015 m
∴ = 7.95 × 10⁻⁸ m⁴
and
Where:
D = Diameter of shaft CD = 36 mm = 0.036 m
r = Radius of shaft CD = 18 mm = 0.018 m
Therefore,
= 1.65 × 10⁻⁷ m⁴
Given that the shaft AB and CD are rotated 1.58 ° relative to each other, we have;
1.58 °= rad = 2.76 × 10⁻² rad.
That is = 2.76 × 10⁻² rad.
However
Where:
and
and
= Torque on shaft AB and CD respectively
= Required
= 500 N·m
and
= Length of shafts AB an CD respectively
= 600 mm = 0.6 m
= 900 mm = 0.9 m
G = Shear modulus of the material = 77.2 GPa
Therefore;
=
2.76 × 10⁻² rad =
=
Therefore;
T = 79.54 N.m
Where T = + T
=
Therefore T = 500 - 79.54 = 420.46 N·m
τ =
=
=
= 15 MPa
=
=
= 45.9 MPa