BY: WILLIAM JANG, JACK DANYLIK, KUSHAL SHAH, AND ANTHONY SRABIAN

DATE: 17 MARCH 2014

MAE 152 Final Project: Finite Element Analysis (FEA)

of Car Jack Stand

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Table of Contents 1. Introduction / Problem Statement: ............................................................................................................ 3

2. Purpose of the Project: ............................................................................................................................... 3

3. Description of Parts: ................................................................................................................................... 3

4. Description of Boundary Conditions: ......................................................................................................... 4

5. Description of Contact Sets: ....................................................................................................................... 5

6. Description of Loads: .................................................................................................................................. 5

7. Study Descriptions for Different Case Scenarios ........................................................................................ 6

8. Results from Original Part .......................................................................................................................... 8

9. Closed Form Solution / Verification of the FEA Results ............................................................................. 9

10. Design Iteration ..................................................................................................................................... 11

11. Results of Revised Part: ......................................................................................................................... 12

12. Comparisons of the Results: .................................................................................................................. 13

13. Fatigue ................................................................................................................................................... 14

14. Conclusion ............................................................................................................................................. 15

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List of Figures Figure 1: Jack Stand BOM ................................................................................................................................... 3

Figure 2: Pictures of the Original Jack Stand ...................................................................................................... 4

Figure 3: Boundary Conditions ........................................................................................................................... 4

Figure 4: Contact Set Definition ......................................................................................................................... 5

Figure 5: Loads for Studies ................................................................................................................................. 5

Figure 6: FBD for Closed Form Solution ........................................................................................................... 10

Figure 7. Design Iteration ................................................................................................................................. 11

Figure 8: S-N Curve for Aluminum .................................................................................................................... 14

List of Table Table 1: Descriptions of Jack Stand Parts ........................................................................................................... 3

Table 2: Study Descriptions ................................................................................................................................ 7

Table 3: Original Design Studies Results............................................................................................................. 8

Table 4: Original Design Modal Analysis ............................................................................................................ 9

Table 5: Closed Form Solution Calculations ..................................................................................................... 10

Table 6: Closed Form Comparisons .................................................................................................................. 10

Table 7: Improved Design Studies Results........................................................................................................ 12

Table 8: Improved Design Modal Analysis ....................................................................................................... 13

Table 9: Comparisons of Buckling Load Factor for Design Iteration ................................................................ 13

Table 10: Comparisons of Stress for Design Iteration ...................................................................................... 13

Table 11: Boundary Conditions Comparisons .................................................................................................. 14

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1. Introduction / Problem Statement:

For our group project, we decided to do an analysis on an automotive jack stand. We decided that this

study was of relevant importance because of the vital function jack stands serve. Jack stands are tools used

to support automotive vehicles from underneath the chassis and are entrusted to support the weight of the

vehicle rigidly. However, there have been several reported cases where jack stands have either slipped or

failed during operation resulting in great injury and or fatalities. Although it cannot be determined what

was responsible for the failure of the jack stands, whether it was user error or mechanical failure, our group

was curious to see what kind of loading a jack stand could withstand. We conducted several analyses to see

what the results would be from employing the jack stand in methods unconventional and also as intended.

2. Purpose of the Project:

The purpose of this project was to conduct a FEA analysis on an automotive jack stand in order to

understand the various stresses and displacements resultant from various loads on the jack stand. We

appropriated our loads in order to understand a case where the part is loaded to fail, the max load capable

of the part, and also a load that is well below the max capabilities of the part. The intent from analyzing a

failure case was to determine the method of how failure would occur and also to determine the location it

would most likely occur. As a result from this data, a design iteration was made to improve the safety factor

of the part and also to increase its performance. The results from the FEA analysis was also compared to a

closed form solution in order to determine the percent error between our calculated results from the

theoretical. A discussion of fatigue failure was also included in order to explore another feasible cause of

failure for the part.

3. Description of Parts:

Part # Part

Description Material

Elastic

Module

(Ksi)

Poisson's

Ratio

Yield

Strength

(Psi)

Density

(lbs/in3)

1 Jack Stand 6061-T6

Aluminum 10,000 0.3 30,000 0.0975

2 Jack body 6061- T6

Aluminum 10,000 0.3 30,000 0.0975

3 Jack Head 6061-T6

Aluminum 10,000 0.3 30,000 0.0975

4 Lock Pin

18-8

Stainless

Steel

29,000 0.29 32,000 0.29

Table 1: Descriptions of Jack Stand Parts

Figure 1: Jack Stand BOM

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The table above, table 1, shows the material properties and some important mechanical properties

of the jack stand used for these FES studies. The pictures below are the pictures of the original parts:

Figure 2: Pictures of the Original Jack Stand

4. Description of Boundary Conditions:

In order to compare the effects of different boundary conditions, we created two boundary condition

cases as shown below. They are both simply supported because the jack stand is not bonded to the ground

and has the freedom to translate and compress on its stand. B.C (a) is modeled for the jack stand flat on the

ground and B.C. (b) is modeled for the jack stand on rollers for two corners and fixed for the third corner.

Figure 3: Boundary Conditions

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5. Description of Contact Sets:

A. Contact between jack head and pin:

The freeze contact was developed between jack head and pin. This type of freeze contact enforces

zero relative displacements on the contact interface.

B. Contact between jack body and pin:

The freeze contact was developed between jack body and pin. This type of freeze contact

enforces zero relative displacements on the contact interface.

C. Contact between jack body and jack stand:

The freeze contact was developed between jack body and jack stand. This type of freeze contact

enforces zero relative displacements on the contact interface.

6. Description of Loads:

For different studies, the loads were applied in the center distributed or they were applied on one side

of the jack head. The load values were 2 ton, 1.5 ton, and 1 ton. These loads and how they were used in the

studies are tabulated in the next section.

Figure 5: Loads for Studies

Figure 4: Contact Set Definition

(A) (B) (C)

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7. Study Descriptions for Different Case Scenarios

This section describes different studies that were performed. In our analysis of the Jack Stand, we ran 6

FEA analyses (4 static analyses, 1 buckling analysis, and 1 modal Analysis) and one closed form solution for

comparison. These six studies were performed for original design and the improved design. Boundary

conditions were also varied for the study number 1 and 4, and the results of varying these parameters are

shown in the comparison section of the report.

Studies Description

Study Number

Type of Study Force (Ton)

Force Location

Case FBD

1 Static

Analysis 2 (F1)

Center of Jack Head

Overloading

2 Static

Analysis 1.5 (F2)

Center of Jack Head

Rated Maximum

3 Static

Analysis 1 (F3)

Center of Jack Head

Average Loading

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4 Static

Analysis 1.5

One Side of Jack Head

Rated Maximum

Misuse

5 Buckling 1.5 Center of Jack Head

Rated Maximum

6 Modal N/A N/A N/A

Table 2: Study Descriptions

In studies 1-3 we assume proper use of the device and place the load distributed across the entire

center of the jack head. We tested one case with a force over the suggested maximum loading given by the

part at 2 tons, one force at the rated maximum (1.5 ton) and one beneath the max loading. In study 4 we

tested a case in which the part is being misused and the entire 1.5 ton load is placed on one edge of the

jack head, which would be a very easy and common thing to do. Study 5 is the buckling analysis with the

rated maximum loading applied at the center of the jack head. Our final FEA study is the modal analysis in

order to determine any frequencies that may cause problems for the stand.

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8. Results from Original Part

For the first set of boundary conditions we developed a set of results that follows our intuition. Stress is

linearly related to the applied force in the elastic region of the material (below the yield stress), which is

almost exactly reflected in our results. When used properly, given that we obtained a factor of safety of

1.02 with a 2 ton load.

FEA Results for 2 ton load case study are shown below:

Original Design Studies Results

Study Case Stress (Psi) Displacement (in) Boundary Condition

Yield Stress (Psi)

Percent Difference (%)

F.S

A.1a 2.93E+04 4.51E-03 B(a) 30000 2.27% 1.02

A.1b 1.58E+05 1.92E-02 B(b) 30000 -426.67% 0.19

A.2 2.20E+04 3.38E-03 B(a) 30000 26.73% 1.36

A.3 1.47E+04 2.25E-03 B(b) 30000 51.13% 2.05

A.4a 2.98E+04 2.07E-02 B(a) 30000 0.60% 1.01

A.4b 1.14E+05 2.57E-02 B(b) 30000 -279.33% 0.26

A.5 N/A N/A B(a) 30000 N/A 40.00

Table 3: Original Design Studies Results

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The maximum stress that the original model experienced is 1.58E+5 Psi, however this was achieved

due to wrong boundary conditions but the true maximum stress for the studies was 29,300 Psi which is less

than the yield stress. In addition, true maximum displacement that we obtained was 0.0451 inches.

All of the max values in studies 1-3 correspond to a point near the lower edge of the stand hole and

the pin where they are in contact. The analysis shows that the jack stand can withstand approximately .5

tons, or 1000 lbf, more than the rated maximum before it begins to yield

When the part is loaded incorrectly, the jack experiences elevated stress results just under the head of

the stand equal to that of the properly placed 2 ton load. This type of loading is creating the bending

stresses in the model. This value is just under the yield stress, thus the part will yield if misused as long as

the load is kept under the rated maximum.

Studies A.1b and A.4b represent the B.C. (b) supported model which created highly exaggerated

stress results. The stand easily passed the buckling test with a factor of safety of 40 when the maximum

rated load is applied in the proper location. This means that the stand will yield far before it ever begins to

buckle.

The modal study reveals several natural frequencies of the jack stand. Fortunately none of these

values are anywhere near the idling rpm or any of a normal cars rpm capabilities. Typically a car idles

between 600-100 RPM which correlates to about 10-16 Hz. Even at the jacks lowest natural frequency the

car would need to rev at over 49,000 RPM, which is far beyond the capabilities of just about every car on

the market.

9. Closed Form Solution / Verification of the FEA Results

A simple closed form solution was difficult to apply to this kind of model. The twists, curves and pin

holes were not considered for a simple model for a closed form solution The moel was assumed to be simply

supported hollow cylinder and load of 2 applied on the top.. What we used was an edge load on the end of

the blade and assumed it was a simply supported cantilever beam. The calculations we used were:

Original Design Modal Analysis

Modes Frequency (Hz)

1 822

2 865

3 2294

4 2447

5 3621

Table 4: Original Design Modal Analysis

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𝝈𝑨𝐯𝐞𝐫𝐚𝐠𝐞 =𝑭

𝑨 ; 𝑨 = 𝝅(𝒓𝒐

𝟐 − 𝒓𝒊𝟐)

𝝈𝑩𝒖𝒄𝒌𝒍𝒊𝒏𝒈 =𝑭𝑩𝒖𝒄𝒌𝒍𝒊𝒏𝒈

𝑨=

𝝅𝟐∗𝑬∗𝑰

(𝟐∗𝑳)𝟐∗𝑨 ; I =

𝝅

𝟒(𝒓𝒐

𝟒 − 𝒓𝒊𝟒); BLF =

𝝈𝑨𝐯𝐞𝐫𝐚𝐠𝐞

𝝈𝑩𝒖𝒄𝒌𝒍𝒊𝒏𝒈

Where, 𝝈𝑨𝐯𝐞𝐫𝐚𝐠𝐞 = is average stress; 𝑭 = Applied Force (2 ton) ;

A = Area of cylinder, r_o = Outer Radius; r_i = Inner radius

𝝈𝑩𝒖𝒄𝒌𝒍𝒊𝒏𝒈 = is average buckling stress, E = Elastic Modules

I = Second Moment of Inertia, and L = Length of the cylinder

The Calculations are shown in the table below:

Variable Equation Value

Length (L): Product Design 8.7 in

Elastic Modulus (E) : Material Property 10,000 Ksi

Force (F): Rated Maximum 2 Ton lbf

Outer Diameter (r_o): Product Design 2.36 in

Inner Diameter (r_i): Product Design 1.97 in

Area (A): 𝜋(𝑟𝑜2 − 𝑟𝑖

2) 1.325 in^2

Second Moment of Inertia

(I):

𝜋

4(𝑟𝑜

4 − 𝑟𝑖4) 0.783 in^4

Average Stress: 𝜎𝐴verage =𝐹

𝐴 3018 Psi

Critical Buckling Stress: 𝜎𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔 =𝐹𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔

𝐴=

𝜋2∗𝐸∗𝐼

(2∗𝐿)2∗𝐴 192640 Psi

Buckling Load Factor: BLF = 𝜎𝐴verage

𝜎𝐵𝑢𝑐𝑘𝑙𝑖𝑛𝑔 63.83

Table 5: Closed Form Solution Calculations

Table 6: Closed Form Comparisons

From the table 4, it can be observed that the error associated with simple closed form solution and

FEA results is in the range of 5-50 % error. It can be taken as verification of the results because most of the

values fall under 5-10% error range and rest of it produced due to pin that holds this cylinder as shown in

the FEA results.

Closed Form Results Comparison Study Case A. Original Design B. Closed Form Error %

Closed Form Average Stress Range : 3200-6000 Psi Average Stress: 3018 Psi 5 % - 49.7 %

Figure 6: FBD for Closed Form Solution

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10. Design Iteration

Based off the results from the original part, we determined that the pin was the limiting factor for

the loading capabilities of the jack stand. This conclusion was derived from the fact that the majority of the

stresses were concentrated around the surfaces that were in contact with the pin. The pin appears to have

been manufactured by a casting method using a stainless steel material and the original diameter of this

pin is .50 inches.

In order to improve the performance of the jack stand in terms of loading capability and increasing

the factory of safety, our design iteration for the jack stand was to increase the pin diameter to .75 inches.

This increase in diameter of the pin should allow for the load that is applied to the jack stand to be

distributed over a greater area and thus increase the loading capability of the overall jack stand.

Although increasing the diameter of the pin would cause a slight increase in the mass of the jack

stand, this additional weight would be slightly offset by the additional material that would have to be

removed from the body of the jack stand in order to accept the larger pin. The marginal increase in mass

for the jack stand is irrelevant because it is not substantial enough to cause any inconvenience to the user.

Figure 7. Design Iteration

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11. Results of Revised Part:

Table 7 represents our analysis of our improved design with a pin diameter of .75 in. Again, we see a

linear correlation for the first three studies as the load is ramped up. The max stress values are located at

the pin/hole contact and just under the jack head for the misuse study. The resultant stress values are far

below the yield stress of the part. With this thicker pin the jack stand would theoretically be able to

withstand loads on the order of about 4 tons, given that the part has a factor of safety of 2 with the 2 ton

loading.

The part clearly passes the buckling test and has a factor of safety of 160 with the rated maximum load

applied. Again, the part will yield long before it buckles.

FEA Results for 2 Ton Improved Design

Improved Design Studies Results

Study Case Stress (Psi) Displacement (in) Boundary Condition

Yield Stress (Psi)

Percent Difference (%)

F.S

B.1 1.46E+04 4.62E-03 B(a) 30000 51.27 2.05

B.2 1.10E+04 3.47E-03 B(a) 30000 63.43 2.73

B.3 7.31E+03 2.31E-03 B(a) 30000 75.62 4.10

B.4 2.98E+04 2.75E-02 B(a) 30000 0.60 1.01

B.5 N/A N/A B(a) 30000 N/A 160

Table 7: Improved Design Studies Results

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The frequency analysis of our improved design, table 8, also shows that the part’s natural

frequencies, although lower than the original design, are still at much higher values than the stand would

ever experience.

Improved Design Modal Analysis Modes Frequency (Hz)

1 640.00

2 673.00

3 2302.00

4 2777.00

5 3270.00 Table 8: Improved Design Modal Analysis

12. Comparisons of the Results:

Comparisons of Buckling Load Factor For Design Iteration

Study Case A. Original Design B. Improved Design Boundary Effects in Stesss %

5 40 160 300.00%

Table 9: Comparisons of Buckling Load Factor for Design Iteration

The improved design increases the buckling factor of safety from 40 to 160. In either case, buckling

is not our primary concern, since yielding will occur first.

Comparisons of Stress For Design Iteration

Study Case A. Original Design B. Improved Design Design Effects in Stress %

1 2.93E+04 1.46E+04 -50.14%

2 2.20E+04 1.10E+04 -50.09%

3 1.47E+04 7.31E+03 -50.12%

4 2.98E+04 2.98E+04 0.00%

Table 10: Comparisons of Stress for Design Iteration

This simple improvement doubles the part’s factor of safety for every load case except for the

buckling study in which the part improves by 400%. Stresses are located in the same places as the previous

case, but at significantly lower values due to the thicker diameter. With this improvement the jack stand

can withstand much higher loads than with the .5” diameter pin.

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Boundary Conditions Comparisons

Study Case B(a) Stress B(b) Stress Boundary Effects in Stress %

1 2.93E+04 1.58E+05 438.88%

2 2.98E+04 1.14E+05 281.62%

Table 11: Boundary Conditions Comparisons

This is a comparison of the two boundary conditions that we ran. It can clearly be seen that the

second condition results in much higher stress results than when the model is run using boundary condition

(a). Stresses resulting from B.C. (b) are over 4 times the amount we get with B.C.(a) and are located at the

points where the condition is applied. This is incorrect and the results from B.C.(b) are disregarded as these

do not simulate what would happen in real life.

13. Fatigue

If we assume an average loading of about 1 ton we get stress results of about 14.7 ksi for one cycle. The

aluminum part would need to undergo over 6*108 cycles before it failed. Considering the average person

would not use a jack stand more than several times a year, it is certain that the stand would fail due to

fatigue at this loading. Even at the 2 ton loading, it is highly doubtful that the part will endure more than

only a couple hundred loadings.

Figure 8: S-N Curve for Aluminum

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14. Conclusion

For the analysis on the automotive jack stand, we used a linear static model with several variables. The

initial variable we had to tune were the boundary conditions for our model. Initially we fixed one edge of

the base of the model restricting movement in all degrees of freedom, and then applied roller fixtures to

the rest of the bottom face. The results from loading the model under these conditions were very similar to

the closed form solution. After adjusting the boundary conditions to be fixed only at one node on the

bottom face with two rollers attached to nodes on adjacent edges, we applied a similar loading case as the

original configuration. From this adjustment we found that the results from this boundary condition were

inconsistent with the closed form solution by a magnitude of 10. Subsequently from these results, we

determined that our original boundary conditions would produce a more accurate model that then the

alternative boundary conditions. Upon applying the max loading case to the jack stand of 2 tons, we found

that the jack stand experienced a max stress of 29,320 psi, which is slightly lower than the yield stress of

30,000 psi of the material. Due to the close proximity of the max stress to the yield stress, it would be

unwise to assume that the part would not fail based off this model. Due to the max loading capacity

advertised by the jack stand company to be 1.5 ton, it would be wiser to assume that our model has a small

percentage of error since the part should have failed under the 2 ton loading case. Post the design

iteration, the max stress the jack stand experienced was reduced by 50%, and therefore it can be safely

assumed that the part would not fail after the upgrade has been implemented. Besides a linear static study,

a modal study and a fatigue study was conducted on the part as well. The modal study informed us that the

lowest natural frequency of the part would occur at 800 Hz for the original part and 640 Hz for the part

post the design iteration. These frequencies are very high and it is unlikely that our part would experience

such high frequencies, therefore it can be safe to assume that failure due to vibration is unlikely. The

fatigue analysis showed that the part could withstand 6*108 cycles before it failed. This is a peculiarly high

number of cycles, therefore it can be safely assumed that fatigue is also a mode of failure that does not

have to be considered for the jack stand.