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.
Step 3[edit | edit source]
We can write an equilibrium equation: The moment about the center point G.
(a)
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]
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