Mechanics of materials/Problem set 4

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Problem 4.1

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P3.23, Beer 2012
On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement

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Under normal operating conditions a motor exerts a torque of magnitude   =1200 lb*in. at F.   =8in.,   =3in., and the allowable shearing stress is 10.5 ksi in each shaft.
 

Objective

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Determine the required diameter of (a) shaft CDE, (b) shaft FGH.

Solution

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Step 1

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FBD

 

Step 2

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We can write an equilibrium equation: The moment about the center point D.

 

 


FBD
 

Step 3

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We can write an equilibrium equation: The moment about the center point G.


 

 

(a)


FBD
 

Step 4

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Now we set the two Forces (F) equal to each other and solve.


 



Step 5

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Solve  
 


Step 6

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Solve for the diameter of shaft CDE

 



(b)

Step 7

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FBD
 

Step 8

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Solve  

 

Step 9

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Solve for the diameter of shaft FGH

 

Problem 4.2

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P3.25, Beer 2012
On our honor, we did this problem on our own, without looking at the solutions in previous semesters or other online solutions.

Problem Statement

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The two solid shafts are connected by gears as shown and are made of steel for which the allowable shearing stress is 8500 psi. A torque of magnitude   =5 kip*in. is applied at C and the assembly is in equilibrium.
 

Objective

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Determine the required diameter of (a) shaft BC, (b) shaft EF.

Solution

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Step 1

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First sum the moments around gears A and E

 

 

Solve for F

 

Step 2

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Sum the Forces

 

Step 3

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Solve for  


 


The magnitude of   = 3.125 kip*in

Step 4

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Use the formula for   to solve for the radius


 

 

 

Step 5

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Input the Given values into the equation for the radius