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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**:
S_{7}P_{3}A_{32} (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 = (πd^{4})/32, for circular section (in^{4}).

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)]/(πd^{4})/32

So, T = 3500 lb in.

So, From equation (2):

T = [63,000(hp)]/n

So, hp = (1800)(3500)/63000 = 100 hp.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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