# ME480/580: Quiz 3 W2013

### Prof. W. H. Warnes Office: Dearborn Hall 303E Phone and Voice Mail: (541) 737-7016 FAX: (541) 737-2600

email: warnesw@engr.orst.edu

NOTE: Yep...there were two versions of this quiz again. Solutions for both are listed here.

VERSION ONE

1) (40 points TOTAL) You are asked to design a new type of disposable fork for a fast food restaurant. The tines of the fork can be modeled as a cantilever beam under an end load. We are told that the size and shape of the forks are fixed, but that the thickness, t, of the tines can vary.
The design statement is as follows:

• The length, L, and width, w, are fixed;
• We want to minimize the cost of the forks;
• The tines must not fail under a buckling end load, Fbuckle;
• The tines must not fail with a bending end load, Fbreak.
 Given the equations below, answer the following questions.

1a) (15 points) Derive the materials selection index, M1, for the breaking constraint.

1b) (15 points) The measure of performance using the buckling constraint gives:

Derive the coupling equation between M1 and M2 for the design.

1c) (10 points) What are the axes of the plot you will make for the coupling chart?

VERSION TWO

1) (40 points TOTAL) You are tasked with selecting a material for a foundry tool used for moving hot metal around during the casting process. It is basically a long pole of a fixed length and unknown circular cross section that is used in two ways.

First, it is used as a prod, during which there may be a large end load (see figure A) that could lead to buckling failure.

Second, it is used as a pry-bar, during which it is loaded in bending (see figure B) that could lead to a yielding failure.

The foundry needs to reduce costs, and so would like the tool to be as inexpensive as possible. Use this information and the equations below to answer the following questions.

1a) (15 points) Derive the materials selection index, M1, for the bending constraint.

1b) (15 points) The measure of performance using the buckling constraint gives:

Derive the coupling equation between M1 and M2 for the design.

1c) (10 points) What are the axes of the plot you will make for the coupling chart?

 VERSION ONE 2) (20 points) A given design problem has one objective function, two free parameters and five constraints. How many M-values are possible in this design? Explain your reasoning. VERSION TWO 2) (20 points) A given design problem has one objective function, four free parameters and five constraints. How many M-values are possible in this design? Explain your reasoning.

 VERSION ONE 3) (40 points TOTAL) I made the coupling selection chart below using CES for a completely different design problem. For this problem, the coupling equation is: Given that L = 10.0 [m], Tf = 10 [N m] and B = 13,200 [USD], VERSION TWO 3) (40 points TOTAL) I made the coupling selection chart below using CES for a completely different design problem. For this problem, the coupling equation is: Given that L = 100.0 [m], Tf = 10 [N m] and B = 1.32 [USD],

3a) (20 points) calculate the value of the coupling constant; and

3b) (20 points) PLOT the position of the coupling line on the coupling chart below.  Clearly indicate the best materials for the job.

SOLUTIONS

 VERSION ONE: FORK 1a) (15 points) Derive the materials selection index, M1, for the breaking constraint. 1b) (15 points) ...derive the coupling equation between M1 and M2 for the design. Set the two equations for PMAX equal to each other: 1c) (10 points) What are the axes of the plot you will make for the coupling chart? The axes will be M1 and M2, or VERSION TWO: FOUNDRY TOOL 1a) (15 points) Derive the materials selection index, M1, for the bending constraint. 1b) (15 points) ...derive the coupling equation between M1 and M2 for the design. Set the two equations for PMAX equal to each other: 1c) (10 points) What are the axes of the plot you will make for the coupling chart? The axes will be M1 and M2, or

 VERSION ONE 2) (20 points) ...how many M-values are possible in this design? Explain ... This is a 1P: 2F5C design. To get an M-value, we have to put sets of two constraints together to solve for the two free parameters. There are five choices for the first constraint, and four left for the second choice. Thus, there are 5 x 4 = 20 combinations of constraints in sets of two. This number overcounts by a factor of 2! = 2 x 1 = 2, so the final answer is: VERSION TWO 2) (20 points) ...how many M-values are possible in this design? Explain ... This is a 1P: 4F5C design. To get an M-value, we have to put sets of four constraints together to solve for the four free parameters. There are five choices for the first constraint, four left for the second choice, three left for the third choice, and two left for the last constraint. Thus, there are 5 x 4 x 3 x 2 = 120 combinations of constraints in sets of four. This number overcounts by a factor of 4! = 4 x 3 x 2 x 1 = 24, so the final answer is:

VERSION ONE

3a) (20 points) ...calculate the value of the coupling constant...

Plug and Chug:

3b) (20 points) PLOT the position of the coupling line on the coupling chart below.  Clearly indicate the best materials for the job.

VERSION TWO

3a) (20 points) ...calculate the value of the coupling constant...

Plug and Chug:

3b) (20 points) PLOT the position of the coupling line on the coupling chart below.  Clearly indicate the best materials for the job.

End of File.