University of Florida/Egm3520/s13.team5.r4

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Problem 4.1 (Problem 3.23 in Beer, 2012)[edit]

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]

Under normal operating conditions a motor exerts a torque of magnitude at . Knowing that
and the maximum allowable shearing stress is 10.5 ksi.

Determine the required diameter of member FH.

Shafts CE and FH with gears

Given[edit]


(4.1-1)


(4.1-2)


(4.1-3)


(4.1-4)


Soultion[edit]

Step One: Draw Free Body Diagrams[edit]

FBD of shafts


FBD of gears


For part A, by assuming constant velocity for the point of gear contact:


Step Two: Part "A" Analysis[edit]

The sum of the forces from the diagram equals zero

(4.1-5)


Isolating the torque in CE based on the applied torque,

(4.1-6)

(4.1-7)


Manipulating the stress formula the diameter can be determined,

(4.1-8)

Substituting the values given above, the diameter can be calculated

 

Step Three: Part "B" Analysis[edit]

(4.1-9)

Solving for the radius,

(4.1-10)

To get the diameter, multiply the equation of the radius by 2

(4.1-11)

Solving the Equation 4.1-11 with the values given, the diameter can be calculated

 

Problem 4.2 (Problem 3.25 in Beer, 2012)[edit]

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]

In the image below, there are two steel shafts, ABC and DEF, for which the maximum allowable shear stress is 8500 psi. They are connected by gears at A and D of given radii 4 in. and 2.5 in., respectively. There is a known applied torque at C, TC of 5 kips•in. and an unknown torque, TF, applied at F.

shafts AC and DF



a) Determine the required diameter of shaft BC
b) Determine the required diameter of shaft EF

Given[edit]

The magnitude of the torque at C,
Allowable shearing stress in the shafts,
Radius of the gear A,
Radius of the gear D,

Solution[edit]

Step One: Draw Free Body Diagrams[edit]

Bars ABC and DEF
Gears A and D


Step Two: Analysis[edit]

From the relation between the torques and the radius of the gears,

(4.2-1)


Therefore,

(4.2-2)


Now inserting the given values,

(4.2-3)


(4.2-4)


Step Three: Application[edit]

Part A[edit]

Allowable shearing stress in the shaft BC,

(4.2-5)


Where J for a solid circular shaft is

(4.2-6)


Insert the values and solve for the radius C.

(4.2-7)


(4.2-8)


(4.2-9)


Diameter of the shaft BC,

(4.2-10)


(4.2-11)


 

(4.2-12)

Part B[edit]

Allowable shearing stress in the shaft EF,

(4.2-13)


Insert the values and solve for the radius C.

(4.2-14)


(4.2-15)


(4.2-16)


Diameter of the shaft EF,

(4.2-17)


(4.2-18)


 

(4.2-19)

Contributors[edit]

Team Designee: Daniel Siefman

Table of Assignments
Problem Number

Solved by

Reviewed by

4.1

María José Carrasquilla, Joshua Herrera, Gregory Grannell, and Phil D Mauro

All

4.2

Tim Shankwitz, Andrew Moffatt, Michael Lindsay, and Daniel Siefman

All