Activity 1



Reading Information

The Design Process

Step 1 – Define the Problem

In the most general sense, engineering design is simply a form of problem-solving. Before you can effectively solve any problem, you must fully define and understand it.

In the West Point Bridge Designer, the problem is to design a truss bridge to carry a two-lane highway across a river. To fully define the problem, you must:

1. select a design project, and

2. read and understand the design specifications.

The West Point Bridge Designer offers seven different design projects for you to work on. Each project consists of a unique combination of span length, support conditions, and height restrictions. Except for these unique characteristics, all seven projects are based on the same set of design specifications.

[pic]

What is a Truss?

A truss is an arrangement of structural members that are connected together to form a rigid framework. In most trusses, members are arranged in interconnected triangles, as shown in the example below:

[pic]

As a result of this configuration, truss members carry load primarily in axial tension and compression. Because they are very rigid and they carry load efficiently, trusses are able to span large distances with a minimum of material.

[pic]

[pic]

Truss Bridges

Trusses have been used extensively in bridges since the early 19th Century. Early truss bridges were made of wood. The classic American covered bridges are all trusses, though the wooden truss members are covered by walls and a roof, for protection from the elements. Later truss bridges were made of cast iron and wrought iron. Most modern trusses are made of structural steel. Truss bridges can be found in many different configurations, but virtually all have the same basic component parts.

There are many other types of bridges besides truss bridges. These include beam bridges, arches, suspension bridges, and cable-stayed bridges.

Dunlap’s Creek Bridge

Dunlap's Creek Bridge in Brownsville, Pennsylvania, was the first iron bridge built in the United States. It was constructed between 1836 and 1839, replacing a suspension bridge which collapsed under the weight of a heavy snowfall in 1820. The bridge was a vital link in the newly constructed National Road (also called the Cumberland Road), the first important road built with U. S. Government funds. Both the road and the bridge were designed and constructed by the U. S. Army Corps of Engineers.

Dunlap's Creek Bridge was a unique and highly innovative arch structure, consisting of five parallel cast iron tubes spanning 80 feet (approximately 24 meters). It was designed by Captain Richard Delafield of the Corps of Engineers, a graduate of the West Point Class of 1818. Captain Delafield also supervised the construction of the span. His creative vision and proficiency as an engineer are clearly evidenced by the fact that the bridge remains in service today, carrying the high-speed traffic of U. S. Route 40 over Dunlap's Creek.

Dunlap's Creek Bridge is one example of the many contributions made by West Point graduates to the infrastructure of our nation. Designated a National Historic Civil Engineering Landmark in 1978, it is an important part of the heritage of our nation and of the engineering profession.

Step 2 - Decide on a Truss Configuration.

Truss Configurations

Truss bridges are usually categorized in two different ways:

➢ according to the location of the deck, and

[pic]

➢ according to the orientation of the vertical and diagonal members.

Truss configurations, based on deck location:

➢ The deck truss has its deck located at the top chord.

[pic]

[pic]

➢ The through truss has its deck located at the bottom chord.

[pic]

[pic]

➢ The pony truss looks just like a through truss, except it is not as high and has no lateral bracing between the top chords.

[pic]

Truss configurations, based on orientation of members.

A number of standard truss configurations are commonly used in bridge structures. These configurations are defined primarily by the geometry of their members. Three of the most common standard configurations are pictured below. All of them are named for the 19th Century engineers who developed them.

[pic] [pic] [pic]

Regardless of their configuration, all trusses have the same basic component parts.

The major component parts of a typical truss bridge are:

chords (top and bottom)

verticals (also called vertical members)

diagonals (also called diagonal members)

floor beams

deck

pinned support (also called a fixed bearing)

roller support (also called an expansion bearing)

abutments (or piers)

These component parts are illustrated below:

[pic]

[pic]

Step 3 - Creating the structural model.

How to Draw a Joint:

1. Select the Joint tool from the Design Tools palette.

2. Position the mouse pointer at the location on the Drawing Board where you want to add a joint.

3. Click the left mouse button to create the new joint.

How to Draw a Member:

1. Select the Member tool from the Design Tools palette.

2. Position the mouse pointer over a joint.

3. Click the left mouse button, and hold it down.

4. Drag the mouse pointer to another joint, and release the button. A new member will be created from the first joint to the second.

Step 4 - Run the Load Test

During this simulation forces will be applied to the bridge.

To load test your design:

1. Click the Load Test Mode button.

2. Sit back and watch. The West Point Bridge Designer will perform the load test, display the load test animation, and update the load test status display.

3. Once the load test is complete, click the Drawing Board Mode button to return to the Drawing Board.

[pic]

[pic]

[pic]

Step 5 - Strengthen failed members.

Structural Stability

A truss is stable if all of its members are arranged in a network of interconnected triangles. For example, the simple truss below is composed of 6 joints and 9 members, which together form four interconnected triangles (

ABF, BCF, CEF, and CDE).

[pic]

If member CF is removed, however, the truss becomes unstable.

[pic]

Without its diagonal member, the center panel of the truss now consists of a rectangle (BCEF) formed by four members, rather than two triangles (BCF and CEF). This configuration is unstable because there is nothing to prevent the rectangle BCEF from distorting into a parallelogram, as shown below:

[pic]

The triangular arrangement of members ensures the rigidity of a truss structure.

To fix an unstable truss, look for any "panel" of the structural model that is not a triangle, then add one or more members to transform that panel into a series of interconnected triangular shapes.

Strengthening Unsafe Members

Your design is successful only if all of the members in your structural model are determined to be safe in the most recent load test. Thus, after each load test, you must strengthen any members that are found to be unsafe.

To determine if any members in your structural model are unsafe, use either of the following two methods:

1. After the load test is complete, return to the Drawing Board and look at the picture of your structural model. Any member that is highlighted in red is unsafe in compression. Any member that is highlighted in blue is unsafe in tension. If no members are highlighted, there are no unsafe members in your structural model.

2. View the two Load Test Results columns on the right side of the Member List. Any member highlighted in red is unsafe in compression, and any member highlighted in blue is unsafe in tension.

To strengthen an unsafe member, use either of the following two methods:

1. Increase the member size. Choose the next larger member size, then run the load test again to see if the larger member is strong enough. Repeat the process until the member passes the load test.

2. Use a stronger material. If the unsafe member is carbon steel, try changing it to high-strength steel; if it is high-strength steel, try quenched and tempered steel. Then run the load test again to see if the increased strength of the new material is sufficient.

To use either method, you will need to change the properties of a member.

Notes and Tips

Of the two alternative methods, the better solution is the one that produces the required increase in strength with less increase in cost. Generally, increasing member size is the more effective method, because there are far more available member sizes than there are materials.

If a member is unsafe in compression, using a stronger material may produce little or no increase in strength. For relatively slender members, the compressive strength is not dependent on the yield stress of the material.

When you change the properties of an unsafe member (for example, by making it larger), the red or blue highlighting will disappear. This does not necessarily mean that the member is safe. To determine the true status of a member that has been modified, you must run the load test again.

Step 6 - To optimize the shape of your current structural model:

1. Try changing the depth of your truss.

2. For example, suppose you started with the standard Pratt Through Truss for your current design:

[pic]

You might try reducing its depth:

[pic]

And you might try increasing its depth:

[pic]

At first glance, reducing the depth of the truss might seem like the better alternative. Reducing the depth will make the verticals and diagonals shorter and, since these members will require less material, their cost will decrease. However, reducing the depth of a truss also causes the member force in the top and bottom chords to increase. Thus you will probably need to increase the size (and cost) of the top and bottom chord members to ensure that the design still passes the load test.

If you increase the depth of the truss, the opposite effects will occur. The verticals and diagonals will get longer and, thus, they will increase in cost. But the member forces in the top and bottom chords will decrease, allowing you to use smaller, less expensive members for the chords.

Clearly there is a trade-off between these two competing factors: (1) the member force in the top and bottom chords and (2) the length of the verticals and diagonals. Every truss has an optimum depth, which represents the best compromise between these two factors. The best way to find the optimum depth for your design is through trial and error.

3. Try changing the overall shape of your truss.

For example, suppose you started with the standard Pratt Through Truss for your current design:

[pic]

Try moving the top-chord joints to create a more rounded shape:

[pic]

Often this minor adjustment can reduce the cost of a design significantly. When a truss has this rounded shape, the member forces tend to be nearly equal in every member in the top chord. Thus, if you get the shape just right, you can use a single optimum member size for the entire top chord--resulting in a substantial reduction in product cost.

Changing to a more rounded shape is also effective for the bottom chord of a deck truss:

[pic]

Notes and Tips

Whenever you change the shape of your truss, you will need to repeat the previous three steps in the design process: (1) run the load test, (2) identify and strengthen all unsafe members, and (3) optimize the member properties. Only then can you determine whether or not the change was effective in reducing the cost of your design.

Step 7 – Try a New Truss Configuration

To find the optimum truss configuration:

Try a different deck location. If your first design was a deck truss, try the corresponding through truss configuration, and vice versa.

Try a different standard truss configuration. For example, if your first design was a Pratt truss, try a Howe or Warren configuration.

Try reducing the length of the compression members in the truss. The compressive strength of a member is a function of its length. As a member gets longer, its compressive strength decreases substantially--it has much less resistance to buckling. For this reason, the cost of a truss design can sometimes be reduced by shortening compression members.

[pic]

For example, let's start with a standard Warren Through Truss: [pic]

Because the top chords of a simple-span truss bridge are always in compression, we might be able to reduce the cost of the Warren truss by subdividing its top chord members, like this: [pic]

Now consider a standard Pratt Through Truss: [pic]

In this configuration, the top chords and the verticals are normally in compression. Thus, we could subdivide both the top chords and the verticals, like this:

[pic]

Note that, in both examples, the length of each compression member is reduced by half. This reduction in length will usually allow the designer to use a substantially smaller member size to achieve the required compressive strength.

Note also that, when you subdivide a member, you will always need to add additional members to maintain the stability of the truss. To be stable, a truss must be made up of a series of interconnected triangles.

To subdivide a compression member in the West Point Bridge Designer, you must:

delete the compression member you want to subdivide,

add a new joint at or near the midpoint of the member you just deleted,

add two new members to replace the original member,

add additional members to ensure stability, and

optimize the member properties of all new members.

Reducing the length of compression members may or may not reduce the total cost of your design, depending on whether the cost savings from using smaller member sizes are enough to offset the increased cost of the additional joints and members.

4. Try reducing the number of joints. The cost of your design includes a fixed cost per joint. Thus you may be able to reduce the total cost by reducing the number of joints in your structural model.

For example, consider the standard Howe Deck Truss:

[pic]

This configuration can be improved by simply removing the joint at the midpoint of the bottom chord, like this:

[pic]

When you delete this joint, all three attached members will be deleted as well. You will need to add a single new member to replace the two bottom chord members you deleted.

This modification is often effective for tension members (like the bottom chord members in the example above), because tensile strength is not a function of length. However, removing a joint from the top chord of a truss, as shown below, is less likely to be effective.

By deleting a top chord joint and replacing two chord members with one, you would double the length of a compression member, making it much weaker. You would need to use a substantially larger member size to make this member strong enough to pass the load test. Thus any benefit from the reduced number of joints would probably be lost.

Try inventing your own truss configuration, or copy the configuration of an actual bridge. Here are some examples of actual bridge configurations you might consider:

[pic] [pic]

Recognize that each of these through trusses could also be designed as a deck truss.

West Point Bridge Designer

Activity 2

Objective

In this activity you will learn how to work with the West Point Bridge Designer program to design a Warren Deck truss bridge.

Warren Deck Truss Exercise

Notes: 1. You will need a copy of the Warren Deck Truss Worksheet, the Member Information Worksheet, Member List Worksheet, and Cost Summary Worksheet to complete during this activity.

2. Information contained within the examples (screen captures) may not be what you are supposed to utilize. These are only examples to direct you where to look or what to look for on the computer screen.

1. Open the West Point Bridge Designer Software by double clicking on the WPBD4.exe icon [pic] on the desktop.

2. The following window will appear:

[pic]

3. Click on the circle in front of Create a New Bridge Design.

[pic]

4. Click the OK Button. [pic]

5. You will now need to select a Design Project. Choose Single Span Truss (24meters).

[pic]

6. Click the Next button [pic]

7. You will now need to select a Standard Truss Template. Choose Warren Deck Truss.

[pic]

8. Click the Next button [pic]

9. Fill in the Information for the Title Block in the spaces provided.

Designed by: Type your first and last name and your partners first and last name (example: John Doe Jane Doe)

Project ID: Type in Warren Deck Truss

[pic]

10. Click the Next button [pic]

11. The following dialog box will appear:

[pic]

12. Click the Finish button [pic]

13. The following screen will appear.

[pic]

Do not attempt to add members and joints at this time - you will be instructed to do so in the next steps. Notice that the name Herman Haupt Memorial Bride appears in the lower right corner along with your names and the project ID information.. The East and West abutments, Floor Beam, Concrete Deck, Asphalt Road Surface, and the High-Water Level are identified on the screen. A sample truss design appears as gray hidden lines with gray joints. This is only a template showing you how a Warren Deck Truss is designed. You will now proceed to the next steps where you will be instructed on adding joints and members to your bridge.

14. Now that the 7 joints that support the roadbed are in place, answer questions 1 and 2 on the Warren Deck Truss Worksheet.

Note: The cost of the bridge is located at the top of the screen. See notation below:

[pic]

15. In the next steps you will be using the template as a guide for where to place the joints and members in your Warren Deck Truss.

To the right, is an example of the Design Tools [pic]

16. Begin by selecting the Joint Tool, [pic] from the Drawing Tools.

17. Click down where you want the joints to be placed. If you put a joint in the wrong place you can choose the select arrow from the Drawing Tools [pic], click on the incorrect joint and drag it to the correct location or click on the Erase button [pic] then click the joint you wish to remove.

18. Place all of the joints that you need to use for your bridge according to the template.

19. Answer questions 3, 4 & 5 on the Warren Deck Truss Worksheet.

20. Choose Carbon Steel as the material for your members. You can change the type of material by clicking on the arrow beside the material type. Your choices include Carbon Steel, High-Strength Low-Alloy Steel and Quenched and Tempered Steel.

This is the Material List box: [pic]

21. Select Solid Bar as the member cross section to be used. You can choose between Solid Bar or Hollow Tube.

This is the Cross Section List box: [pic]

22. Set the size of the members to 100mm.

This is the Member Size List: [pic]

23. Select the Member Tool [pic] from the Drawing Tools Menu, the member tool looks like a bar with circles on each end. Use the member tool to connect the joints together. Click at one joint and drag to the next joint to draw a member.

Notice that the members are solid blue with a yellow number on them as you place them. To keep the numbers on the members click on the yellow # symbol [pic] to make them appear or disappear if you do not wish to see them.

24. Answer questions 6, 7, 8, 9, & 10 on the Warren Deck Truss Worksheet.

25. It is now time to test the bridge that you have designed.

26. Select the Load Test Button [pic] from the Tool Bar. This icon looks like a bridge with a truck crossing it.

27. Does your bridge pass the Load Test. All failed members will appear in red or blue after the Load Test.

28. Return to the Drawing Board of the Program by clicking on the Drawing Board Icon [pic]. This icon looks like a T square with additional drawing instruments.

29. Answer questions 11 & 12 on the Warren Deck Truss Worksheet.

30. Change the failed members to a size of 110mm. To do this 1st choose the Select Tool [pic] from the Design Tools then click on the member you want to change, any red or blue member, and change the size to 110mm [pic]. Do this for each of the members that failed during the first test.

Note: You can use the multi-select option if you hold down the Ctrl (Control) Key on the keyboard while selecting the members.

31. Once you have changed all of the previously failed members, choose Load Test [pic] again.

32. Answer questions 13 & 14 on the Warren Deck Truss Worksheet.

33. Locate your Member Information Worksheet.

34. Click on the Report Engineering Properties of the Current Member Button [pic]. It is located to the right of the size selection box. Complete the Member Worksheet for each material you used. Be sure to change the member size to get the information for each size member.

Note: You should have used 2 different size members in this activity. What size member did you begin with and what did you change the failed members to?

35. Locate your Cost Summary Worksheet.

36. Click on the Calculator [pic] next to the Total Cost of the bridge at the top of the screen.

37. Complete the Cost Summary Worksheet at this time.

38. Locate your Load Test Results Worksheet.

39. Click on the Report the Load Test Results button [pic] in the results box.

Note: If this result button will not display you need to Run the Load Test again.

40. Click the Save Icon [pic]. Save your bridge as your names followed by Warren (example: John Doe Jane Doe Warren).

41. Pull down the File menu and select EXIT.

Note: If you do not complete this activity you can reopen the current bridge by pulling down the File menu and selecting Open OR CLICK ON THE open icon [pic]. Then select the name of your bridge (example PBWarren).

West Point Bridge Designer

Activity 3

Objective

Design A Two-Span Truss Bridge for less than $10,000.00.

Note: You will need a copy of the Bridge Summary Worksheet to complete this activity.

Objective: Using what you have already learned about the West Point Bridge Designer Program, you should design a working bridge that meets all of the defined criteria.

1. Open the West Point Bridge Designer.

2. Select the Design Project - Two-Span Truss (48 meters)

3. Criteria for completing a working bridge:

a. Design Project: Two-Span Truss (48 meters)

b. Standard Truss Template None

c. Designed By Both Partners Names

d. Project ID Activity 3

e. Material: Quenched & Tempered Steel

f. Cross Section: Hollow Tube and/or Solid Bars

a. Truss Type Through, Pony or Deck

g. Maximum Cost: $10,000.00

Note: If you use a template for designing your bridge you can only earn a maximum grade of an 80 on this project.

4. Design a bridge that passes the load test. Remember that the bridge must be less that $10,000.00

5. Complete a Bridge Summary Worksheet for this bridge.

6. Save your bridge as your initials followed by 10000 (example: John Doe Jane Doe 10000).

West Point Bridge Designer

Activity 4

Objective

Design an Arch Truss or Single Span Truss Bridge for less than $7,500.00.

Note: You will need a copy of the Bridge Summary Worksheet to complete this activity.

Objective: Using what you have already learned about the West Point Bridge Designer Program, you should design a working bridge that meets all of the defined criteria.

1. Open the West Point Bridge Designer.

2. Select the Design Project - Arch Truss (36 meters) or Single Span Truss (44 meters)

3. Criteria for completing a working bridge:

a. Design Project: Arch Truss (36 meters) or

Single Span Truss (44 meters)

b. Standard Truss Template None

c. Designed By Both Partners Names

d. Project ID Activity 4

e. Material: High Strength Low Alloy Steel

f. Cross Section: Hollow Tube and/or Solid Bars

g. Truss Type Through, Pony or Deck

h. Maximum Cost: $7,500.00

Note: If you use a template for designing your bridge you can only earn a maximum grade of an 80 on this project.

4. Design a bridge that passes the load test. Remember the cost must be less than $7,500.00

5. Complete a Bridge Summary Worksheet for this bridge.

6. Save your bridge as your initials followed by 7500 (example: John Doe Jane Doe 7500).

West Point Bridge Designer

Activity 5

Objective

Design A 24 meter Bridge for less than $3,000.00.

Note: You will need a copy of the Bridge Summary Worksheet to complete this activity.

Objective: Using what you have already learned about the West Point Bridge Designer Program, you should design a working bridge that meets all of the defined criteria.

1. Open the West Point Bridge Designer.

2. Select the Design Project - Arch Truss (24 meters) or Single Span Truss (24 meters)

3. Criteria for completing a working bridge:

a. Design Project: Arch Truss (24 meters) or

Single Span Truss (24 meters)

b. Standard Truss Template None

c. Designed By Both Partners Names

d. Project ID Activity 5

e. Material: Carbon Steel, High Strength Low Alloy Steel or

Quenched & Tempered Steel

f. Cross Section: Hollow Tube and/or Solid Bars

g. Truss Type Through, Pony or Deck

h. Maximum Cost: $3,000.00

Note: If you use a template for designing your bridge you can only earn a maximum grade of an 80 on this project.

4. Design a bridge that passes the load test. Remember the cost must be less than $3,000.00

5. Complete a Bridge Summary Worksheet for this bridge.

6. Save your bridge as your names followed by 3000 (example: John Doe Jane Doe 3000).

West Point Bridge Designer

Activity 6

Objective

Design A 24 meter Through Truss Bridge that will be the pattern for your balsa wood bridge.

Note: This will be the pattern for your balsa wood bridge.

Objective: Using what you have already learned about the West Point Bridge Designer Program, you should design a working bridge that meets all of the defined criteria.

1. Open the West Point Bridge Designer.

2. Select the Design Project - Single Span Truss (24 meters)

3. Criteria for completing a working bridge:

a. Design Project: Single Span Truss (24 meters)

b. Standard Truss Template None

c. Designed By Both Partners Names

d. Project ID Activity 6

e. Material: Carbon Steel, High Strength Low Alloy Steel or

Quenched & Tempered Steel

f. Cross Section: Hollow Tube

g. Truss Type Through Truss

h. Maximum Cost: Does not matter.

Note: If you use a template for designing your bridge you can only earn a maximum grade of an 40 on this project.

4. Design a bridge that passes the load test.

5. Complete a Bridge Summary Worksheet for this bridge.

6. Save your bridge as your names followed by build (example John Doe Jane Doe build).

7. Have your instructor approve you design.

8. Print 1 copy of your design.

West Point Bridge Designer

Bonus Activity

Objective

Design A Single span truss bridge with anchorages for less than $10,000.00.

Note: You will need a copy of the Bridge Summary Worksheet to complete this activity.

Objective: Using what you have already learned about the West Point Bridge Designer Program, you should design a working bridge that meets all of the defined criteria.

1. Open the West Point Bridge Designer.

2. Select the Design Project - Single Span Truss with Anchorages (48 meters)

3. Criteria for completing a working bridge:

a. Design Project: Single Span Truss with Anchorages

b. Standard Truss Template None

c. Designed By Both Partners Names

d. Project ID Bonus

e. Material: Carbon Steel, High Strength Low Alloy Steel or

Quenched & Tempered Steel

f. Cross Section: Hollow Tube and/or Solid Bars

g. Maximum Cost: $10,000.00

Note: If you use a template for designing your bridge you can only earn a maximum grade of an 80 on this project.

4. Design a bridge that passes the load test. Remember the cost must be less than $10,000.00

5. Complete a Bridge Summary Worksheet for this bridge.

6. Save your bridge as your names followed by bonus (example: John Doe Jane Doe Bonus).

West Point Bridge Designer

Pre-Test

1. The distance that a bridge covers is called the?

a. load

b. span

c. truss

d. roadbed

2. This type of bridge has a superstructure that is built above the roadbed?

a. deck truss

b. roadbed

c. through truss

d. truss

3. Where is Dunlap’s Creek Bridge located?

a. Brownsville, Pennsylvania

b. Harrisburg, Pennsylvania

c. Newnan, Georgia

d. West Point, New York

4. This force tends to pull a bridge or a member apart?

a. Torsion

b. Tension

c. Compression

d. Sheer

5. What part of the bridge does the vehicle travel upon?

a. piers

b. truss

c. surface

d. roadbed

6. This force attempts to squeeze and object.

a. tension

b. torsion

c. compression

d. sheer

7. When applied to a bridge ice, snow, wind, people and vehicle are all types of ________.

a. forces

b. loads

c. stresses

d. weights

8. A truss bridge has a rigid framework made up of __________.

a. circles

b. lines

c. squares

d. triangles

9. Any bridge that is built below the roadbed is referred to as a _____________.

a. arch truss

b. through truss

c. deck truss

d. truss

10. When a member bends laterally it is said to be ____________.

a. bending

b. buckling

c. yielding

d. leaning

West Point Bridge Designer

Post-Test

1. This force attempts to squeeze and object.

a. tension

b. torsion

c. compression

d. sheer

2. When applied to a bridge ice, snow, wind, people and vehicle are all types of ________.

a. forces

b. loads

c. stresses

d. weights

3. A truss bridge has a rigid framework made up of __________.

a. circles

b. lines

e. squares

f. triangles

4. Any bridge that is built below the roadbed is referred to as a _____________.

a. arch truss

b. through truss

c. deck truss

d. truss

5. When a member bends laterally it is said to be ____________.

a. bending

b. buckling

c. yielding

d. leaning

6. The distance that a bridge covers is called the?

a. load

b. span

c. truss

d. roadbed

7. This type of bridge has a superstructure that is built above the roadbed?

a. deck truss

b. roadbed

c. through truss

d. truss

8. Where is Dunlap’s Creek Bridge located?

a. Brownsville, Pennsylvania

b. Harrisburg, Pennsylvania

c. Newnan, Georgia

d. West Point, New York

9. This force tends to pull a bridge or a member apart?

a. Torsion

b. Tension

c. Compression

d. Sheer

10. What part of the bridge does the vehicle travel upon?

a. piers

b. truss

c. surface

d. roadbed

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download