1

(note – the original title page was not included with the file, hence the information here is

not necessarily complete or representative of a normal title page. Also, the letter of

transmittal is not included with this version, but is normally present. In addition, the

appendices are not included with this file)

University of Victoria

Faculty of Engineering

ENGR 446 Report

Semi Trailer Main Beam Design

Robert Lowdon

Mechanical Engineering

Spring 2007

2

Table of Contents

List of Tables and Figures................................................................................................... 3 Summary ............................................................................................................................. 4 Glossary of Terms............................................................................................................... 5 Introduction......................................................................................................................... 6 Discussion ........................................................................................................................... 8

Load and Dimension Restrictions................................................................................... 8 Overall Length ................................................................................................................ 8 King Pin Set Back........................................................................................................... 9 Axle Spread..................................................................................................................... 9 Trailer Wheel Base ......................................................................................................... 9 Landing Legs .................................................................................................................. 9 Load .............................................................................................................................. 10 Main Beams .................................................................................................................. 11

Loading Scenarios..................................................................................................... 11 Scenario 1: King Pin - Even Distribution ................................................................. 12 Scenario 2: King Pin - Point Load ............................................................................ 12 Scenario 3: Landing Legs - Even Distribution ......................................................... 12 Scenario 4: Landing Legs - Point Loads................................................................... 13

Reaction Loads.............................................................................................................. 13 Shear and Moment Diagrams........................................................................................ 14 Beam Design................................................................................................................. 15 Beam Data Analysis...................................................................................................... 18 Stress Analysis .............................................................................................................. 21 Finite Element Analysis................................................................................................ 24 FEA Results .................................................................................................................. 25

Conclusion ........................................................................................................................ 26 Recommendations............................................................................................................. 28 References......................................................................................................................... 29

Appendix A Loading Scenarios

Appendix B Reaction Load Calculations

Appendix C von Misses Sample Calculation

Appendix D FEA Figures

3

List of Tables and Figures

Table 1 Summary of Trailer Specifications ...................................................................... 11 Table 2 Beam Loads ......................................................................................................... 13 Table 3 Reaction Loads .................................................................................................... 14 Table 4 Extreme Fiber Bending Stresses for Different Web Depths................................ 17 Table 5 Shear Loads.......................................................................................................... 19 Table 6 Bending Moments................................................................................................ 19 Table 7 Web Depths.......................................................................................................... 20 Table 8 Maximum Stresses............................................................................................... 23 Table 9 FEA Results ......................................................................................................... 25

Figure 1 Commercial Transportation Act Dimension Restrictions .................................... 8 Figure 2 Shear Diagram.................................................................................................... 14 Figure 3 Moment Diagram................................................................................................ 15 Figure 4 Beam Cross Section............................................................................................ 16 Figure 5 Extreme Fiber Bending Stress ............................................................................ 16 Figure 6 Web Depth Requirements................................................................................... 18 Figure 7 Minimum Required Web Depth ......................................................................... 20 Figure 8 Extreme Fiber Bending Stress ............................................................................ 21 Figure 9 Shear and Bending Stress ................................................................................... 22 Figure 10 von Misses Stress ............................................................................................. 22

4

Summary

In this report, a beam design for a semi trailer is proposed. The design is based on rules

and regulations set forth by the Provincial Government in the Commercial Transportation

Act, and from the loads the trailer is expected to carry.

The proposed beam design is optimized to reduce the overall weight of the trailer. The

optimization is based purely on static loading using hand calculations and Finite Element

analysis. Dynamic loads were not considered due to the difficulty of determining the

dynamic loads. The final beam design consists of a 3/8" flange, a 3/16" web, a 5" flange

width, and a web depth that varies along the length of the beam. The material used is a

high tensile steel with a minimum yield of 900 MPa.

A prototype is required so testing can be done to both verify the theoretical hand

calculations, and to investigate the effects of dynamic loading.

5

Glossary of Terms

King Pin: A high strength pin that is welded to the front of the trailer, and slides into the

fifth wheel on the tractor to connect the trailer to the tractor.

Wheel Scrub: The rubbing of the tires that occurs when a trailer takes a tight turn, due to

the fact that there is no perfect pivot point. The further apart the axles are on the trailer,

the more wear or 'scrub' will occur when taking corners.

Tandem: A trailer with two axles at the rear of the trailer.

Tridem: A trailer with three axles at the rear of the trailer.

Landing Legs: The legs towards the front of the trailer that support the trailer when it is

not being supported by a tractor.

6

Introduction

This report looks at the design of the main beams for a typical semi trailer that operates

on B.C. highways. A typical semi trailer that operates in B.C. will haul loads such as

plywood and lumber products, construction equipment and supplies, machinery, and

crated goods.

The main beams of a semi trailer are two identical beams that run the length of the trailer

and are the primary longitudinal support. The other main supports are the cross members

and the side beams which are typically channel tubing. In this report only the beam

design is considered.

The first consideration for the beam design are the constraints from the Commercial

Transportation Act, which is Provincial legislation that governs dimensions and loads for

semi trailers. The dimensions and various specifications that are selected for the beams

are discussed in the report, such as trailer length and axle location.

After the basic beam is determined, the loading scenarios are considered. Four worst case

loading scenarios were identified. These loading scenarios are used to eventually

determine the structural requirements of the beams. From the loading scenarios, the

reaction loads were first calculated. The shear and bending diagrams were then created

for all four loading scenarios.

The dimensions and material of the beam are largely specified based on industry

standard, with the exception of the web depth of the beam. Typically web depths on

trailer beams are not constant, as different parts of the beam are subjected to different

loads. Because of this, the beams typically have a varying web depth. From the shear and

bending data, the web depths (along the length of the beam) required to support each

loading scenario were determined using a spreadsheet.

7

The data for the web depths for all four loading scenarios was then compiled, and a final

beam was determined that could support all four worst case scenarios. Following this, a

more in depth stress analysis was completed on the proposed beam to check the shear

stresses and the corresponding von Misses stresses. As a result of this analysis, a few

modifications were made to the beam.

Finally, a CAD model of the beam was created, and a Finite Element analysis (FEA) was

conducted. The FEA investigated the stresses in the beam, as well as the deflections.

A final beam is proposed, along with recommendations to build a prototype and test

certain areas. In particular, the effects of dynamic loading must be determined from

testing.

The beam will be manufactured by cutting the web and flanges out of steel plate using a

numerically controlled burn table based on a CAD model. The flanges and web will then

be welded with a full length fillet weld on both sides.

8

Discussion

Load and Dimension Restrictions

Allowable loads and dimensions for semi trailers are regulated by the Provincial

Government's Commercial Transportation Act, which are discussed below. One of the

figures in the Commercial Transportation Act is shown in Figure 1.

Figure 1 Commercial Transportation Act Dimension Restrictions

Overall Length

The overall trailer length is 16.2m, the longest allowable length. This was chosen to

maximize the trailer area.

9

King Pin Set Back

The king pin is the pin attached to the trailer, that connects to the fifth wheel on the

tractor. The set back is the distance from the front of the trailer to the centre of the king

pin. The set back is 2', or 0.61m. This was selected as it is a typical setback used in

industry.

Axle Spread

The axle spread for the trailer is 49". This is a typical value used in industry, and it is also

the smallest spread that can be used while maintaining an acceptable clearance between

the tires so they don't rub. Small axle spreads are desirable to minimize wheel scrub.

Larger wheel spreads allow for a shorter unsupported span, which allows the main beams

to be smaller and allows for a lighter trailer. However, tires on these trailers wear more

quickly.

Trailer Wheel Base

The trailer wheel base depends on the location of the fifth wheel on the tractor. The fifth

wheel on tractors can be adjusted by sliding it forward or backward. The driver must

adjust the fifth wheel location to ensure the wheel base is within the specified limits.

Landing Legs

The position of landing legs is not regulated by the Commercial Transport Act. The

landing legs are not labeled in Figure 1, but are shown just aft of the tractor wheels

located on the main beam of the trailer.

10

The landing legs have been placed 6 m from the front of the trailer. This allows sufficient

room for the tractor wheels under the trailer. It also places them far enough forward so

that a large load on the front of the trailer would not tip the trailer forward when

supported by landing legs.

Load

The maximum load allowable for a tandem axle, either on a trailer or tractor, is 17000 kg.

A maximum load capacity of 17000 kg for a tandem axle set means that when both axles

are put onto a commercial highway scale, the total load cannot exceed 17000 kg. This

means that the actual total payload capacity is 34000 kg minus the weight of the trailer,

and minus the weight of the tractor on the drive axles.

For example, a tractor may weigh 5000 kg, with 2000 kg on the front steer axle, and 3000

kg on the rear tandem drive axle. The maximum allowable on the tandem drive axle is

17000 kg, so the driver can only add another 14000 kg. Suppose a 5000 kg trailer is then

hooked up to the tractor with no payload. Suppose the tractor supports 2000 kg, and the

trailer tandem axle set supports the remaining 3000 kg. The tractor tandem axle set now

supports 5000 kg, and therefore can only support 12000 kg of payload. The trailer tandem

axle supports 3000 kg, and therefore can only support 14000 kg of payload.

Using this example, the maximum allowable payload on the trailer would be 26000 kg,

distributed such that there are 2000 kg more on the trailer tandem axle set then the tractor

tandem axle set.

The actual payload capacity for this trailer has been selected to be 34000 kg. This takes

into account that a tridem axle tractor may be used. The maximum load for a tridem axle

set is 24000 kg. Thus, a tridem tractor with a tandem trailer could support 24000 kg +

17000 kg for a total of 41000 kg. Using the previous example, if a total of 8000 kg is

subtracted from this total due to the tractor and trailer weight, then the total payload

11

capacity is 33000 kg. 34000 kg (75,000 lb) was selected because it's closer to the 75000

lb capacity trailers that are common.

A load capacity beyond 34000 kg will likely be over weight at a weigh scale. Some

manufacturers still build trailers with higher ratings because they can market it as an

overbuilt trailer, and because some jurisdictions allow larger loads, or allow larger loads

with a special permit.

Table 1 Summary of Trailer Specifications

Design Specification Value

Trailer Length 16.2m

King Pin Set Back 2' / 0.6m

Axle Spread 49" / 1.25m

Rear Overhang 1.375 m

Load Capacity 34000 kg

Main Beams

Loading Scenarios

In order to begin designing the main beams, the different ways in which the trailer could

be loaded needed to be established. Appendix A shows four scenarios in which the trailer

can be loaded. These scenarios cover the most common way to load a trailer, and cover

the worst case scenario for loading in terms of stresses.

The four variables in the loading scenarios are whether the trailer is hooked up to the

tractor via the king pin or being supported by landing legs, and whether the load is

distributed or a point load. These scenarios are discussed below.

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Scenario 1: King Pin - Even Distribution

This scenario places an even distribution along the length of the trailer, while the trailer is

supported by the tractor through the king pin. This scenario is the most common way to

load a trailer for bulk loads, such as plywood, lumber, or crated loads.

Scenario 2: King Pin - Point Load

This scenario places a point load in the middle of the span while the trailer is supported

by the tractor through the king pin.

This scenario is used when the driver has to haul a heavy unit, such as a large heavy

casting, or a large piece of machinery. The load has to be put onto the middle of the

trailer so the load is evenly distributed between the tractor tandem axles and the trailer

tandem axles.

Scenario 3: Landing Legs - Even Distribution

This scenario places an even distribution along the length of the trailer with the trailer

supported by the landing legs.

This scenario occurs frequently when a trailer is loaded ahead of time, and then a tractor

comes to pick up the trailer. This also occurs when a tractor drops off a trailer at its

destination with the payload still on the trailer. Another situation is when a trailer breaks

down and has to be abandoned temporarily on the side of the road.

13

Scenario 4: Landing Legs - Point Loads

This scenario places two point loads at either end of the trailer, while the trailer is

supported by the landing legs.

This scenario occurs when the payload is small but heavy, and the loads are placed over

the tractor drive axles and trailer axles to get maximum traction. This occurs when the

trailer is pre-loaded, dropped off, or the trailer breaks down, as mentioned in scenario 3.

Reaction Loads

The reaction loads were calculated to determine the vertical forces on the king pin, the

landing legs, and each of the axles.

The calculations for each scenario are shown in Appendix B. The loads used are shown in

Table 2, and the reaction loads are summarized in Table 3. Because the trailer will be

using an air suspension, the loads on the lead axle and rear axle will be the same. The air

suspension system equalizes the pressure between the two axles, which also equalizes the

loading.

The loading in Table 2 is based on the maximum payload capacity of 34000 kg divided

by two (17,000 kg or 166.6 kN), as there will be two main beams. The distributed loading

of 10.284 kN/m is based on 166.6 kN divided by the length of the trailer (16.2m).

Table 2 Beam Loads

Load Type Scenario 1 Scenario 2 Scenario 3 Scenario 4

P1 - 166.6 kN - 83.3 kN

P2 - - - 83.3 kN

w 10.284 kN/m - 10.284 kN/m -

14

Table 3 Reaction Loads

Fb (kN) Fc (kN) Fd (kN)

Scenario 1 79.18 43.71 43.71

Scenario 2 86.80 39.90 39.90

Scenario 3 126.96 19.82 19.82

Scenario 4 126.96 19.82 19.82

Shear and Moment Diagrams

The shear and moment diagrams were calculated and graphed in Appendix B. These

graphs have been superimposed and are summarized in Figure 2 and Figure 3.

Figure 2 Shear Diagram

15

Figure 3 Moment Diagram

Beam Design

A custom wide flange beam will be used for the main beams. This is the most efficient

shape to support the load, and is the most commonly used beam for semi trailers.

The variables on the beam are the flange width, flange thickness, web depth, and web

thickness. These variables are labeled on a beam cross section shown in Figure 4.

The industry standard for flange thickness is typically 5/8", and the flange width varies

from 5" and up. The web thicknesses typically used is 3/16". These dimensions will be

used for the initial beam design. The depth varies depending on the load, with some

beams reaching 24" of depth at the centre of the trailer. A 900 MPa steel will be used for

the beams. This is a common grade of steel used in beams.

16

Figure 4 Beam Cross Section

Using a spread sheet, the stresses were calculated for each loading scenario, with the web

depth varying from 1" up to the largest depth that did not yield. The stresses were

multiplied by a factor of 1.2 to act as a factor of safety.

Shown in Figure 5 is the bending stress at the extreme fiber of the beam, shown at 0.1m

intervals along the beam from 0m to 16.2m for scenario 1. Each series represents a beam

with a different web depth.

Figure 5 Extreme Fiber Bending Stress

A portion of the numerical values used to create Figure 5 are shown below in Table 4.

The values are shown in MPa. The values that are below the yield of 900 MPa are

17

highlighted in red. The actual data extends to 16.2m in the vertical rows, and extends to

10" in the horizontal columns.

Table 4 Extreme Fiber Bending Stresses for Different Web Depths

X (m) 1" Web 2" Web 3" Web 4" Web 5" Web

0.1 1.80 0.95 0.63 0.47 0.37

0.2 7.19 3.80 2.53 1.88 1.49

0.3 16.19 8.54 5.70 4.24 3.35

0.4 28.77 15.18 10.14 7.54 5.96

0.5 44.96 23.72 15.84 11.77 9.31

0.6 64.74 34.16 22.81 16.95 13.40

0.61 (KP) 66.92 35.30 23.57 17.52 13.85

0.7 -162.37 -85.66 -57.20 -42.52 -33.61

0.8 -413.73 -218.27 -145.74 -108.35 -85.64

0.9 -661.48 -348.97 -233.02 -173.23 -136.92

1 -905.64 -477.78 -319.02 -237.17 -187.45

1.1 -1146.21 -604.69 -403.76 -300.17 -237.25

1.2 -1383.17 -729.71 -487.24 -362.23 -286.30

1.3 -1616.54 -852.82 -569.44 -423.34 -334.60

1.4 -1846.32 -974.04 -650.38 -483.51 -382.16

1.5 -2072.49 -1093.36 -730.06 -542.74 -428.97

1.6 -2295.07 -1210.79 -808.46 -601.03 -475.04

1.7 -2514.05 -1326.31 -885.60 -658.38 -520.37

1.8 -2729.44 -1439.94 -961.47 -714.79 -564.95

1.9 -2941.23 -1551.67 -1036.08 -770.25 -608.79

2 -3149.42 -1661.50 -1109.42 -824.77 -651.88

2.1 -3354.01 -1769.44 -1181.49 -878.35 -694.23

2.2 -3555.01 -1875.48 -1252.29 -930.99 -735.83

2.3 -3752.41 -1979.62 -1321.83 -982.68 -776.69

2.4 -3946.22 -2081.86 -1390.10 -1033.44 -816.81

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It can be seen in Table 4 that the 1" beam is sufficient up to 0.9 m. At 1m, the stress is

905.64 MPa, which is just over the yield. Therefore at 1m, a 2" web depth is required.

The 2" web depth beam is sufficient to 1.3 m, and after that a 3" web depth is required.

The web depths required for scenario 1 are shown in Figure 6.

Figure 6 Web Depth Requirements

Web Depth Requirement

0

2

4

6

8

10

12

0 5 10 15 20

meters

inch

es Web DepthRequirement

From Figure 6, it can be seen the largest web depth required is 10", from 5.7m to 9.8m.

The same process was repeated for scenario 2, 3, and 4, with the web depths being

calculated for each scenario.

Beam Data Analysis

From the previous section, the web depth was calculated for each scenario for each 0.1m

interval. In this section the data from all four scenarios is compiled and compared to

determine what web depth will satisfy all four scenarios.

A sample table for the maximum shear and bending loads are shown in Table 5 and Table

6. The corresponding web depths are shown in Table 7.

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Table 5 Shear Loads

KP-Even

Dist. KP-Point

LL-Even

Dist.

LL-

Point

Max

Shear

X V V V V V

m N N N N N

0.1 1028 0 1028 83300 83300

0.2 2057 0 2057 83300 83300

0.3 3085 0 3085 83300 83300

0.4 4114 0 4114 83300 83300

0.5 5142 0 5142 83300 83300

0.6 6170 0 6170 83300 83300

0.61 6273 -86800 6273 83300 86800

0.7 -71981 -86800 7199 83300 86800

0.8 -70953 -86800 8227 83300 86800

Table 6 Bending Moments

KP-Even

Dist.

KP-

Point

LL-Even

Dist.

LL-

Point

Max

Bending

X M M M M M

m Nm Nm Nm Nm Nm

0.1 51 0 51 8330 8330

0.2 206 0 206 16660 16660

0.3 463 0 463 24990 24990

0.4 823 0 823 33320 33320

0.5 1286 0 1286 41650 41650

0.6 1851 0 1851 49980 49980

0.61 (KP) 1913 0 1913 50813 50813

0.7 -4643 -7812 2520 58310 58310

0.8 -11829 -16492 3291 66640 66640

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Table 7 Web Depths

KP-Even

Dist. KP-Point

LL-Even

Dist. LL-Point

Max

Depth

Web

inches

Web

inches

Web

inches

Web

inches

Web

inches

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 2 2

1 1 1 2 2

1 1 1 3 3

1 1 1 3 3

1 1 1 3 3

1 1 1 3 3

Table 7 shows the minimum required web depth that will not yield based on the bending

stress in the extreme fiber of the beam. The full table is graphed and shown in Figure 7.

Figure 7 Minimum Required Web Depth

21

Stress Analysis

At this point, a preliminary beam design has been proposed. The flange thickness, width,

and web thickness were specified. The optimal web depth was then calculated. However,

this calculation was based only on the stress at the extreme fiber. Figure 8 shows the

bending stress in the extreme fiber of the beam based on the web depths of Figure 7.

Figure 8 Extreme Fiber Bending Stress

All stresses at the extreme fiber are under the yield stress of 900 MPa. This section

investigates the shear stress and the von Misses equivalent stress.

The shear stresses were calculated for the proposed beam with a spreadsheet, using the

web depths shown in Figure 7, and using the maximum shear and bending stresses shown

in Table 6 and Table 7. The shear was investigated in two areas, under the flange, and at

the neutral axis. The von Misses equivalent stress was then calculated.

22

The shear stresses at the neutral axis, and the shear and bending stress under the flange

were graphed and are shown in Figure 9. A stress multiplier of 1.2 was used.

Figure 9 Shear and Bending Stress

The equivalent von Misses stress was then calculated and is shown in Figure 10.

Figure 10 von Misses Stress

23

A sample calculation of the von Misses stresses is shown in Appendix C.

The Figure shows that the von Misses stresses are highest at the ends of the beam, and

exceeds the yield value of 900 MPa. This was expected because there was very little

bending load at the ends, and therefore gave a small web depth. The shear load however

was quite high, in particular due to scenario four where there were two points loads at

either end of the beam.

The lengths of the beam that exceeded the yield stress were 0.1, 0.2, and 0.3 m and the

front of beam, and 16.0, 16.1, and 16.2 m. For each of these six lengths, the von Misses

stress was 1044 MPa at the neutral axis, and 1021 MPa under the flange. The stresses

were the same at the front and back due to the symmetrical loading of scenario four.

By increasing the web depth from 1" to 2" for the above mentioned lengths, the von

Misses stress dropped from 1044 MPa to 633 MPa at the neutral axis, and from 1021

MPa to 595 MPa under the flange.

With the web depths updated, and the stresses recalculated, the maximum stresses were

determined and are shown in Table 8.

Table 8 Maximum Stresses

Stress Type Location Stress Value

Max Bending at Extreme Fiber 10.7 m 897 MPa

Max vM at Neutral Axis extreme ends 633 MPa

Max vM Under Flange 6.1 m 860 MPa

24

Finite Element Analysis

FEA (Finite Element Analysis) was used to further investigate the stresses in the beam

and validate the previous calculations, and to calculate the deflections.

A model was initially created in Solid Works. Cosmos Works was used to attempt a FE

analysis, however the program could not mesh the beam. The beam turned out to be too

large for the program to handle. More specifically, Cosmos gave errors stating that the

surface area to volume ratio was too large for meshing. Even with the mesh on its

coarsest setting, the problem could not be resolved.

The same beam model was then created in Pro Engineer, and Pro Mechanica was used in

an attempt to run a FE analysis. Again, the program had a hard time creating a mesh.

However, Pro Mechanica eventually managed to create a mesh. This process was very

time intensive, with each mesh requiring the program to run over night.

After this model was created, it was seen that it was impractical to have a continuously

varying web depth. The front of the trailer requires a flat section for the connection of the

trailer to the fifth wheel, and the rear requires a flat section for the suspension to sit flush

on the trailer. In light of this, the first 85" of the front of the beam were changed to a

constant 7" web depth, and the last 100" of the trailer were changed to a constant 7" web

depth.

The depths were changed at the front of the beam to 7" because this was the depth at the

cut-off of 85". The 7" web depth was also chosen at the rear of the beam because this

gave sufficient clearance for the suspension (100" from the rear of the beam).

25

FEA Results

The FE analysis was performed on the model for the four different loading scenarios.

Table 9 summarizes the results. A snapshot of the FEA for each loading scenario is

shown in Appendix D.

Table 9 FEA Results

Scenario Max Stress Max Stress Location Max Deflection Max Deflection Location

1 475 MPa Centre of Beam 1.6e-4 in Centre of Beam

2 809 MPa Centre of Beam 3.0e-4 in Centre of Beam

3 440 MPa In front of Landing Legs 3.5e-4 in Front of Beam

4 610 MPa In front of Landing Legs 5.8e-4 Front of Beam

To reach these results, a multi-pass method with a 10% convergence limit was used in

Pro-Mechanica. This multi-pass method is an iterative process where the order of the FE

equation polynomial increases by one for each iteration. The first iteration uses a

polynomial with an order of one, which invariable gives poor results. The second

iteration uses a polynomial of order two, which gives better results. Each time the order

increases, the equations produce more accurate results. The process ended when the

results converged to within 10%.

The stresses determined in the FEA are very similar to the previous stresses calculated,

which verify the hand calculations. The deflections were calculated using FEA as this

would have been very labor intensive by hand. The maximum deflection, 0.0058", occurs

during scenario four on the front of the beam, where two points loads are applied to the

front and back of the beam. If this result is accurate, then the deflections are well within

an acceptable range. This deflection seems low for the loads applied, and will have to be

verified by testing.

26

Conclusion

In order to design the main beams for a semi trailer, the loading and dimension

restrictions of the Commercial Transportation Act were first considered. After an initial

beam design had been proposed, four different worst case loading scenarios were

identified. From these scenarios, the reaction loads were then calculated.

The dimensions of the beam were specified based on industry standards, however the

depth of the web was calculated to optimize the strength and weight of the beam. To

calculate the depth of the web along the length of the beam, the shear and moment

diagrams for all four loading scenarios were calculated. The depth of the beam required

to support these loads was calculated, creating four different beam designs. The data for

all four scenarios was then compiled and compared, and one final beam design was

created that could support all four loading scenarios.

The von Misses stresses were then calculated along the entire length of the beam. This

analysis found that the shear load at the ends of the beam were too high and causing the

beam to yield. As such, the web depths at these points were increased by an inch which

reduced the stresses below the yield point.

The next stage in the design of the beams would be to build a prototype and perform

some tests to verify the theoretical calculations. This stage is very important because the

hand calculations only considered static loads. In reality the beams will be subjected to

dynamic loading from bumps on the road. The dynamic effect was taken into account in

the hand calculations by applying a factor of safety, however this was only a rough

estimate of the dynamic loads. Strain gauge testing and analysis will be required to

determine how the dynamic loads effect the main beams.

Strain gauges will also be required on the outside edge of both flanges mid span on the

beams to determine the stresses induced from turning when under full load. If the stresses

are too high, the width of the beams may need to be increased.

27

The trailer will also have to be tested for harmonic responses to road vibration. If the

effective spring constant of the beam is such that the frequency of oscillation matches the

suspension frequency, large deflections and stresses may occur. Large deflection due to

harmonic oscillation can be monitored by the strain gauges, and may also be visually

noticeable.

28

Recommendations

1. The beam shall have a 3/8" flange, 3/16" web, 5" flange width, and a web depth

that varies as calculated.

2. The material shall be a high tensile steel with a yield not less then 900 MPa.

3. The web and flange will have a full length fillet weld along the length of the

entire beam.

4. A prototype is to be built and tested with strain gauges located mid span, in front

of the landing legs on the upper and lower flange, and on the outside edge of the

flange mid span. The trailer is to be tested with all four loading scenarios

identified. Harmonic oscillations will also have to be monitored for.

29

References

Beer F.P., Johnston E.R., DeWolf J.T., "Mechanics of Materials", McGraw Hill, Third

Edition, 2002

Norton R.L., "Machine Design, An Integrated Approach", Prentice Hall, Second Edition,

2000

British Columbia Ministry of Transportation, "Commercial Transportation Act,

Commercial Transport Regulations", Filed January 30, 1978, Available at:

http://www.qp.gov.bc.ca/statreg/reg/C/CommerTrans/30_78/30_78.htm