Mechanics of materials/Problem set 4

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Problem 4.1[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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

Solution[edit | edit source]


Step 1[edit | edit source]

FBD


Step 2[edit | edit source]

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




FBD


Step 3[edit | edit source]

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






(a)


FBD


Step 4[edit | edit source]

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






Step 5[edit | edit source]

Solve



Step 6[edit | edit source]

Solve for the diameter of shaft CDE





(b)

Step 7[edit | edit source]


FBD


Step 8[edit | edit source]

Solve



Step 9[edit | edit source]

Solve for the diameter of shaft FGH

Problem 4.2[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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

Solution[edit | edit source]

Step 1[edit | edit source]






First sum the moments around gears A and E





Solve for F



Step 2[edit | edit source]

Sum the Forces



Step 3[edit | edit source]

Solve for





The magnitude of = 3.125 kip*in

Step 4[edit | edit source]

Use the formula for to solve for the radius







Step 5[edit | edit source]

Input the Given values into the equation for the radius