Torsional Stress In A Section Of A Shaft
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Torsional Shear Stress In A Section Of A Shaft Determine the horse power (hp) transmitted at 1800 rpm by a shaft with diameter, d =1.306 if the torsional shear stress is limited to 8000 psi.

The strings: S7P3A32 (Force - Push).

The math:
Pj Problem of Interest is of type force (push). work and power problems are of type force. Torsional Shear Stress results from twisting.

Assumptions: sectional area of shaft is circular.
Neutral axis (line of zero stress) is located on the center line of the shaft.
Polar moment of inertia is a property of the shape of the section.

Equations of Interest:
Torsional shear stress, τ = (TD)/J ----------(1)
Where T = torque or twisting moment applied to section (lb in)
D = distance from neutral axis to outermost edges of section (inches)
J = Polar moment of inertia = (πd4)/32, for circular section (in4).

T = [63,000(hp)]/n ----------(2)
Where hp = horse power
n = revolution per min (rpm)

So, from equation (1);
Torsional shear stress, τ = (TD)/J
So, 8000 = [T(d/2)]/(πd4)/32
So, T = 3500 lb in.

So, From equation (2):
T = [63,000(hp)]/n
So, hp = (1800)(3500)/63000 = 100 hp.

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