University of New Haven

Department of Mechanical Engineering

ME 307 Solid Mechanics

Fall semester 2001

Design Project

Done by:

Paul Gibson

Fahad Khan

Instructor: Dr. Stanley

Table of Contents

I. Abstract 3

II. Introduction 4

III. Design approach 5

IV. Design Prototype 6

V. Design Prototype Specifications 10

VI. Failed Design Prototype 11

VII. Conclusion 13

VIII. Appendix of ANSYS Plots

i. Line Plot (with dimensions) 14ii. Area Plot 15iii. Elements Plot 16iv. Von Mises Stress 17

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Abstract

The purpose of this project was to design a bracket that could withstand a

2000 psi linearly applied pressure located in a circular cutaway. Only two dimensions

were to remain constant, the radius of the cutaway and the distance the center of

that cutaway was from the left side of the bracket. The final dimensions of the

bracket are provided on the line plot in the appendix. The final area of the bracket

was 14.636 with a maximum Von Mises stress of 22112 psi. The file for the project

itself is located on the M drive under the name project2. Further results and details

are provided later in this report.

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Introduction

In this project a bracket has to be designed using the program ANSYS. The

bracket has the following criteria:

Made of steel with modules of elasticity of E=30x106 psi.

Poisson’s ratio, , of 0.3.

Yield stress of 40,000 psi

Has to be designed to carry a pressure that carries linearly from 0 to 2000

psi on a 180° circular cut out.

Max Von Misses stress ≤ 60% yield stress. That number is found to be

24000 psi.

The bracket dimensions are given to be:

Height H ≤ 8”

Width W1 = 8 “

Radius R = 1.0”

The minimum width for any section is ≥ 0.25”. Also, cross sectional area

should be as small as possible. Figure 1 depicts the preliminary design

requirements. The physical shape of the bracket is in no means restricted to this

exact shape. A design is valid so long as dimension requirements are met and the

≤ 24000 psi.

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Figure 1

Design Approach

As a start, the shape of the bracket shown on the handout was manipulated in

nearly every conceivable manner to achieve the smallest possible surface area. It

was soon discovered that the model shape was not the best one to use if surface

area is to be kept at a minimum. Many failed modifications to the existing shape

resulted in a search for a better shape to start with. Plant hangers are surprisingly

sturdy despite their physical appearance, and perhaps, with a few design alterations,

a similar shape could be used for this design. The design criterion calls for the

bracket to be built into a solid surface from the left side, and for a linearly dependent

pressure to be applied to the cutaway on the right side. Although surface area was

to be at a minimum, manufacturing time must also be considered. If the design has

multiple holes or cuttings that need to be made, this can make the design

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impractical. This need only be a concern if the bracket is being manufactured by

hand. If the bracket is being made form a pre-made die , then complicated hole cut

outs are not a problem. However, since it not specifically stated in the handout how

this bracket is being manufactured, one must take that into account as a variable. To

summarize the basic design approach:

Basic design and shape was determined.

Alterations were made on the design to minimize area.

A check was made to verify that design did not exceed the maximum

of 24000 psi.

Design Prototype

Figure 2 shows a line plot of the final design of the bracket. Figure 3 shows

the area plot of the bracket. These screens were captured directly from ANSYS.

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Figure 2

It was quickly discovered that stress tends to be high in areas where a sharp

or defined corner was. Nearly every corner in this design was filleted to reduce that

tendency for stress accumulation in those areas.

Figure 4 is an element plot. A mesh size of .05 was used for all final meshes.

It was also found that as mesh size got smaller, the stress got more accurate. Some

designs passed the Von Mises test with a mesh size of .25, but failed when a smaller

mesh was used. Figure 5 is a nodal plot.

Of course, this design would amount to nothing if it failed the Von Mises stress

test. Figure 6 is a Von Mises plot of the deformed shape after loading. It is shown

with raster graphics and 144 contours. Note that the maximum value reached by the

is 22112 psi. This is 8.54% lower than the maximum allowed value of 24000 psi.

With the SMX value of 22112 and the SMXB value of 24108, an error of 9.03% is

obtained. Figure 7 is an element solution of the deformed shape. Slightly different

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values of stress are obtained. Approximate dimensions of the bracket are provided

on the line plot located in the appendix of this report.

Figure 3

Figure 4

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Figure 5

Figure 6

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Figure 7

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Design Prototype Specifications

What follows below in this section are the geometric properties of the

prototype. The final area was found to be 14.636 sq. inches. The original unaltered

design had an area of 28.429. The final design for the bracket cut area down by

48.52%, nearly half the original.

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PRINT GEOMETRY ITEMS ASSOCIATED WITH THE CURRENTLY SELECTED AREAS

*** NOTE *** CP= 256.379 TIME= 18:04:40 Density not associated with all selected areas. Geometry items are based on a unit density.

TOTAL NUMBER OF AREAS SELECTED = 1 (OUT OF 1 DEFINED)

TOTAL SURFACE AREA OF ALL SELECTED AREAS = 14.636

TOTAL VOLUME OF ALL SELECTED AREAS = 14.636

CENTROID: XC= 4.4570 YC= 5.4648 ZC= 0.0000

*** MOMENTS OF INERTIA *** (BASED ON A UNIT DENSITY AND A UNIT THICKNESS)

ABOUT ORIGIN ABOUT CENTROID PRINCIPAL IXX = 514.87 77.790 49.805 IYY = 375.67 84.933 112.92 IZZ = 890.53 162.72 162.72 IXY = -387.83 -31.354 IYZ = 0.0000 0.0000 IZX = 0.0000 0.0000

PRINCIPAL ORIENTATION VECTORS (X,Y,Z): 0.746 0.666 0.000 -0.666 0.746 0.000 0.000 0.000 1.000 (THXY= 41.751 THYZ= 0.000 THZX= 0.000)

Failed Design Prototype

The final design bracket was not the first design that was considered. A

similarly shaped rectangular bracket resembling a magnet was also considered.

However, the design was not efficient. It had a large area and also always had high

levels of stress. It was soon learned that having a bracket made of two parallel

sections was poor at minimizing stress. This is why the final design has one section

at an angle to the other. Even though this design failed the Von Mises stress test, it

was also rejected for its large area an general crudeness. Its inclusion in this report

is strictly for comparison purposes. Figure 8 shows the element plot of this design

while Figure 9 is an ordinary line plot. . Figures 10 and 11 are raster and vector

plots, respectively, of the Von Mises stress.

Figure 8

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Figure 9

Figure 10

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Figure 11

Conclusion

The final design prototype in this report in by no means the absolute best

design possible, nor is it the only one. There are an infinite number of other

possibilities. Perhaps making both sections at angles to each other (rather than have

one at an angle and the other straight) would have lowered the maximum stress

slightly, thus allowing for more area to be subtracted. Whatever the case, it was

definitely essential to round all essential corners. The only areas that had very high

stress levels were usually located at sharp, non-rounded corners. By rounding

corners, stress concentrations are less likely to occur. Also, drilled holes were kept to

a minimum in case this bracket is to be manufactured by hand. In conclusion, this

design passed all design requirements established for the project.

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