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Bridges ERT
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Bridges ERT
yamum Sun Aug 24, 2008 3:39 pm
Bridges
Extended Response Task
YEAR 11
Physics
Mid Semester ll
2008
Jesse Pehrson
18/8/2008
Contents
1.0 Introduction 3
2.0 Theoretical Orientation 4
3.0.0 Method 11
3.1.0 Experiment 1 11
3.1.1 Materials 11
3.1.2 Safety hazards 11
3.1.3Method 11
4.0 Results 14
4.1 Experiment 1 14
5.0 Analysis of Results and Discussion 16
5.1 Experiment 1 16
6.0 Conclusion(s) 19
7.0 References 20
1.0 Introduction
From the beginning of time, the need to cross rivers and gaps was needed. This was solved by the creation of the bridge. The bridge was said to be first created by animals wanting to cross rivers and lakes. The animals would push logs across the creek to make a bridge for them to cross. It is thought that humans then cloned this idea and made bridges of their own. In the early days this was done by vines and plant matter. This then slowly transformed into triangular designs consisting of wood and iron called trusses. These designs then adopted other materials such steel and more advanced metal compounds.
This report will be analysing the bridge design, the Howe (wooden brace/iron rod). It will include the construction of a model bridge of this type and compare how it breaks in real life to how it breaks on the computer software WestPoint Bridge Designer. An experiment will be undertaken using a bridge hand constructed from pasta and then subjected to loads until it reaches failing point. The results will be recorded to come up with a suitable and knowledgeable outcome.
The Howe comes in three different styles as shown in the images below:
(Cridlebaugh, B ,June 2008)
Figure 1
The style of truss bridge this report will be analysing is the ‘Howe Truss (wooden brace/iron rod).’
2.0 Theoretical Orientation
There are multiple types of bridges; the basic few types include the Girder, Arch, Truss, Cable Stayed, Rigid Frame and Suspension as shown below:
Girder
Truss
Rigid Frame
Arch
Cable Stayed
Suspension
The Bridge type that this task will be assessing is the Truss Bridge. The truss is a simple skeletal structure. Triangles that are self bracing are used to create a stable design avoiding ‘shear’ that is more typical of square shapes. In design theory, the individual members of a simple truss are only subject to tension and compression forces and not bending forces.
As stated by Matsuo Bridge Co “All beams in a truss bridge are straight. Trusses are comprised of many small beams that together can support a large amount of weight and span great distances. In most cases the design, fabrication, and erection of trusses is relatively simple. However, once assembled trusses take up a greater amount of space and, in more complex structures, can serve as a distraction to drivers.”
Like the girder bridges, there are both simple and continuous trusses. The small size of individual parts of a truss makes it the ideal bridge for places where large parts or sections cannot be shipped or where large cranes and heavy equipment cannot be used during erection. Because the truss is a hollow skeletal structure, the roadway may pass over (illustration #2) or even through (illustration #1) the structure allowing for clearance below the bridge often not possible with other bridge types. (matsuo-bridge)
The typical span lengths of a truss are that of 40 to 500 meters. In fact the world’s largest bridge has a total span of 863 meters and a centre span of 549 meters. (matsuo-bridge)
As stated by Ohio-state education ‘Determinacy deals with whether or not the reactions and forces in a structure can be analysed based solely on static equilibrium or whether principles from strength of materials must be introduced. Put differently, it deals with whether the forces in a structure can be determined knowing only the geometry of the structure or whether the stiffness attributes of the individual components must be known. A statically determinate structure is analysable based only on its geometry. A statically indeterminate structure is analysable based on geometry and component stiffness.’
The following equations are used to check if the bridge is stable and either statically determinate or indeterminate.
2j=m+3 = statically determinate
2j>m+3 = unstable
2j
20=20
Therefore this bridge design is staticaly determinate
Truss bridges where created because the provided a stable support. Trusses are used in all different types of support to create a way to diverge the force evenly. Trusses are not just used in bridges, but also in buildings and various other models aimed to create a strong support.
The truss comes in multiple structure varieties. Examples of the three common travel surface configurations are shown in the Truss type drawings below. In a Deck configuration, traffic travels on top of the main structure; in a Pony configuration, traffic travels between parallel superstructures which are not cross-braced at the top; in a Through configuration, traffic travels through the superstructure (usually a truss) which is cross-braced above and below the traffic. ( PGH Bridges)
Figure 3 (Cridlebaugh, B ,June 2008)
For this task the bridge used will be through truss.
The Through Truss Bridge consists of two side trusses connected across the top and bottom. Trains drive through the box formed by the members.
Steel trusses were created from riveted iron plates and bars that create straight truss members. The stick-like members are connected together at the joints so that they form triangular and then rectangular shaped sections. This diagonal webbing effect gives the complete truss its strength to carry the heavy locomotives with a minimum amount of steel. (ghostdepot)
There are many different types of through trusses the Howe Truss is just one of these. The Howe Truss, with counter braces, is an add-on from the original Howe Truss Bridge. A Howe truss at first appears similar to a Pratt truss, but the Howe diagonal web members are inclined toward the centre of the span to form A-shapes. The vertical members are in tension while the diagonal members are in compression, exactly opposite the structure of a Pratt truss. Patented in 1840 by William Howe, this design was common on early railroads. The three drawings show various levels of detail. The thicker lines represent wood braces; the thinner lines are iron tension rods. The Howe truss was patented as an improvemethe Long truss. ( PGH Bridges)
Figure 4 (Daviel, A. March 2008)
As stated above, the Howe was originally made out of wood and iron, but this design then moved to a steel truss. It has an impressive strength over long distances and had a high popularity as a railroad bridge.
Figure 5 (Cridlebaugh, B ,June 2008)
Trusses are used to stiffen and support a bridge by distributing the loads and forces acting upon the bridge based on the positions of the vertical, horizontal and diagonal chords. They are based on triangular configurations. How those chords are arranged identifies the type of truss. Trusses are also used on cantilever bridges and to support the decks in suspension bridges. Trusses are "through trusses" when the truss is above the deck, and "deck trusses" when they are underneath, supporting the truss. Three early American bridgebuilders--Timothy Palmer (1751-1821), Lewis Wernwag (1770-1843) and Theodore Burr (1771-1822) built truss bridges and are known as the "Inspired Carpenters." Palmer is credited among the first to cover the truss, leading to construction of covered bridges in the United States. The truss bridge was described as long ago as the sixteenth century by Andrea Palladio in his Four Books on Architecture. (Steven M. Richman)
To complete a truss bridge there is a need for cross bracing. Cross bracing is used to stabilise the individual trusses, it is used as an essential in holding the bridge together. The cross bracing is the bracing on top and bottom of the design which is attached to the top and bottom chords and holds both sides of the trusses together.
These bridges hold different types of load. Dead load is ‘The permanent, static load on a building or structural element due to the mass of all permanent structural members, install plant, services installations and other fixed loads which imposed definite stresses and strains upon the structure (Glossary of Building Terms).’ This would be the mass of the bridge without any other forces acting upon it.
Live loads are ‘the load(s) assumed to arise from the intended use or occupancy of a building or structure; including distributed, concentrated, impact or inertial loads, but excluding wind, snow, or earthquake loads and the load of the structure. By comparison with dead loads which remain constant, live loads on a building maybe be removed or replaced (Glossary of Building Terms).’ This is the weights subjected to during its life. E.g. trucks and other traffic
The following are the results found through WestPoint bridge designer. The following is a model made the same way the test model was made. This program was used to create a virtual test of the bridge with a live load present. It will predict where the first members will break and what forces each member is carrying.
Figure 6 (West Point Bridge Design)
Figure 7 (West Point Bridge Design)
Figure 8 (West Point Bridge Design)
As can be shown from the information above both the diagonal and top horizontal supports are under compression and the vertical and base horizontal supports are under tension. (Blue = Tension, Red = Compression).
3.0.0 Method
3.1.0 Experiment 1
Building the bridge
3.1.1 Materials
Pasta – San Remo – Tubular Spaghetti
Wire Cutters
Hot Glue Gun
Hot Glue Gun Glue sticks
Cardboard
Pins
Ruler
Scissors
Weights- 20g, 50g, 100g, 500g, 1kg
Helper
3.1.2 Safety hazards
Heat- the heat given off of the hot glue gun could burn.
Sharp objects- scissors, pins- could cause an injury
Make sure that all hazards are taken into account and all safety procedures are followed.
3.1.3 Method
1) Collect pasta and collate tools appropriately
2) Create base template on cardboard
3) Glue 7 pieces of full length pasta (25cm) together into a circle to create base and top horizontal chords.
4) Mount 2 base horizontal supports into the template and create cross bracing as shown in the diagram below.
5) Repeat stage four for the top cross bracing
6) Cut all protruding parts with a pair of wire cutters
7) Place both top and bottom cross braces created into the template and support seperated using one strand of pasta and glue using help from your partner. (Making sure the ends stay square)
Glue the side truss members on in the form shown below
9) Turn the bridge over and repeat stage 8 to create the truss on the opposite side
10) Cut off any protruding pieces of pasta
11) Weigh the bridge and record its mass
12) Place the bridge onto the side pillars (As shown in figure 7 above and photo below)
13) Slowly load the bridge with weights until failure
14) Record the weight the bridge held (noting where failure occurred)
4.0 Results
4.1 Experiment 1
Dead Load (Bridge Mass): 70g
Successful Live Load (Mass held by bridge): 14.5kg
Failure weight: 15.5kg
Photo 1 – Bridge at 14.5kg
Photo 2 – Bridge at 15.5kg (failure imminent)
Photo 3 –Bridge failing
Photo 4 – Bridge in full collapse
5.0 Analysis of Results and Discussion
5.1 Experiment 1
The experiment was an overall success. Outcomes were achieved that allowed successful analysis that produced good results.
The ratio of weight carried compared to the mass of the bridge can be express by the following equation:
Strength to Weight ratio
Ratio: 14.5:0.07 = 207:1
Therefore the bridge held approximately 207 times its own weight. An outstanding result, seeing as the record for Camosun College, Civil Engineering Department is 40.6 load ratio for grade 11 and 12 students. Engineers use this sort of information for designing the strength to weight ratio of modern bridges to reach economies in the amount of steel used in these structures.
Throughout the experiment the bridge started to bend towards the middle placing the bottom chords in tension and the top chords in compression, as shown in the model produced by WestPoint Bridge designer. The result showed the bridge bending downwards in the centre the same way shown in the experiment.
Photo 5
After placing weight on top of the bridge the side trusses started to distort showing distinct curves in the members (as shown in photo below).
Photo 6
As the weights reached approximately 10kg one of the side vertical members broke towards the top. This did not seem to disable the bridge in anyway because it still held another 5 kilograms approximately after that. The reason for this member breaking is unknown but could have something to do with the tension it was under.
Photo 7
The place of breaking point was at the first node point in from the left hand side of the bridge (Sa shown in the photo below). The reason for this break was due to experimental error. While the weights were being loaded onto the bottom supports, one member broke due to a misplacement of the weights. It was at this stage that the bridge finally broke.
Photo 8
This position of the break was not where it was predicted to occur in the West Point Bridge computer modelling. It was predicted that the break would occur in either of the diagonal brace supports and centrally on the horizontal members under compression.
This should have been correct in the pasta bridge design. In working with the pasta during construction and research it was found that pasta works well under tension and not as well under compression (Camosun College, Civil Engineering Department). This therefore would imply that the bridge should have broken at the top chord which is under compression and not at the bottom chord where the break did occur.
Experimental error plays a large part in the results achieved in this experiment. The first error occurred through the placement of the weights. The weights were placed onto the bridge as well as hanging off the base supports. After hanging all of the available weights onto the bridge, bricks were then placed on top of the structure.
Also error could occur in the strength of the pasta. i.e. the pasta was not uniform in size and may have had deformities in its structure. This is because these products are a mass produced with no need for quality control as these are food products.
Extended Response Task
YEAR 11
Physics
Mid Semester ll
2008
Jesse Pehrson
18/8/2008
Contents
1.0 Introduction 3
2.0 Theoretical Orientation 4
3.0.0 Method 11
3.1.0 Experiment 1 11
3.1.1 Materials 11
3.1.2 Safety hazards 11
3.1.3Method 11
4.0 Results 14
4.1 Experiment 1 14
5.0 Analysis of Results and Discussion 16
5.1 Experiment 1 16
6.0 Conclusion(s) 19
7.0 References 20
1.0 Introduction
From the beginning of time, the need to cross rivers and gaps was needed. This was solved by the creation of the bridge. The bridge was said to be first created by animals wanting to cross rivers and lakes. The animals would push logs across the creek to make a bridge for them to cross. It is thought that humans then cloned this idea and made bridges of their own. In the early days this was done by vines and plant matter. This then slowly transformed into triangular designs consisting of wood and iron called trusses. These designs then adopted other materials such steel and more advanced metal compounds.
This report will be analysing the bridge design, the Howe (wooden brace/iron rod). It will include the construction of a model bridge of this type and compare how it breaks in real life to how it breaks on the computer software WestPoint Bridge Designer. An experiment will be undertaken using a bridge hand constructed from pasta and then subjected to loads until it reaches failing point. The results will be recorded to come up with a suitable and knowledgeable outcome.
The Howe comes in three different styles as shown in the images below:
(Cridlebaugh, B ,June 2008)
Figure 1
The style of truss bridge this report will be analysing is the ‘Howe Truss (wooden brace/iron rod).’
2.0 Theoretical Orientation
There are multiple types of bridges; the basic few types include the Girder, Arch, Truss, Cable Stayed, Rigid Frame and Suspension as shown below:
Girder
Truss
Rigid Frame
Arch
Cable Stayed
Suspension
The Bridge type that this task will be assessing is the Truss Bridge. The truss is a simple skeletal structure. Triangles that are self bracing are used to create a stable design avoiding ‘shear’ that is more typical of square shapes. In design theory, the individual members of a simple truss are only subject to tension and compression forces and not bending forces.
As stated by Matsuo Bridge Co “All beams in a truss bridge are straight. Trusses are comprised of many small beams that together can support a large amount of weight and span great distances. In most cases the design, fabrication, and erection of trusses is relatively simple. However, once assembled trusses take up a greater amount of space and, in more complex structures, can serve as a distraction to drivers.”
Like the girder bridges, there are both simple and continuous trusses. The small size of individual parts of a truss makes it the ideal bridge for places where large parts or sections cannot be shipped or where large cranes and heavy equipment cannot be used during erection. Because the truss is a hollow skeletal structure, the roadway may pass over (illustration #2) or even through (illustration #1) the structure allowing for clearance below the bridge often not possible with other bridge types. (matsuo-bridge)
The typical span lengths of a truss are that of 40 to 500 meters. In fact the world’s largest bridge has a total span of 863 meters and a centre span of 549 meters. (matsuo-bridge)
As stated by Ohio-state education ‘Determinacy deals with whether or not the reactions and forces in a structure can be analysed based solely on static equilibrium or whether principles from strength of materials must be introduced. Put differently, it deals with whether the forces in a structure can be determined knowing only the geometry of the structure or whether the stiffness attributes of the individual components must be known. A statically determinate structure is analysable based only on its geometry. A statically indeterminate structure is analysable based on geometry and component stiffness.’
The following equations are used to check if the bridge is stable and either statically determinate or indeterminate.
2j=m+3 = statically determinate
2j>m+3 = unstable
2j
20=20
Therefore this bridge design is staticaly determinate
Truss bridges where created because the provided a stable support. Trusses are used in all different types of support to create a way to diverge the force evenly. Trusses are not just used in bridges, but also in buildings and various other models aimed to create a strong support.
The truss comes in multiple structure varieties. Examples of the three common travel surface configurations are shown in the Truss type drawings below. In a Deck configuration, traffic travels on top of the main structure; in a Pony configuration, traffic travels between parallel superstructures which are not cross-braced at the top; in a Through configuration, traffic travels through the superstructure (usually a truss) which is cross-braced above and below the traffic. ( PGH Bridges)
Figure 3 (Cridlebaugh, B ,June 2008)
For this task the bridge used will be through truss.
The Through Truss Bridge consists of two side trusses connected across the top and bottom. Trains drive through the box formed by the members.
Steel trusses were created from riveted iron plates and bars that create straight truss members. The stick-like members are connected together at the joints so that they form triangular and then rectangular shaped sections. This diagonal webbing effect gives the complete truss its strength to carry the heavy locomotives with a minimum amount of steel. (ghostdepot)
There are many different types of through trusses the Howe Truss is just one of these. The Howe Truss, with counter braces, is an add-on from the original Howe Truss Bridge. A Howe truss at first appears similar to a Pratt truss, but the Howe diagonal web members are inclined toward the centre of the span to form A-shapes. The vertical members are in tension while the diagonal members are in compression, exactly opposite the structure of a Pratt truss. Patented in 1840 by William Howe, this design was common on early railroads. The three drawings show various levels of detail. The thicker lines represent wood braces; the thinner lines are iron tension rods. The Howe truss was patented as an improvemethe Long truss. ( PGH Bridges)
Figure 4 (Daviel, A. March 2008)
As stated above, the Howe was originally made out of wood and iron, but this design then moved to a steel truss. It has an impressive strength over long distances and had a high popularity as a railroad bridge.
Figure 5 (Cridlebaugh, B ,June 2008)
Trusses are used to stiffen and support a bridge by distributing the loads and forces acting upon the bridge based on the positions of the vertical, horizontal and diagonal chords. They are based on triangular configurations. How those chords are arranged identifies the type of truss. Trusses are also used on cantilever bridges and to support the decks in suspension bridges. Trusses are "through trusses" when the truss is above the deck, and "deck trusses" when they are underneath, supporting the truss. Three early American bridgebuilders--Timothy Palmer (1751-1821), Lewis Wernwag (1770-1843) and Theodore Burr (1771-1822) built truss bridges and are known as the "Inspired Carpenters." Palmer is credited among the first to cover the truss, leading to construction of covered bridges in the United States. The truss bridge was described as long ago as the sixteenth century by Andrea Palladio in his Four Books on Architecture. (Steven M. Richman)
To complete a truss bridge there is a need for cross bracing. Cross bracing is used to stabilise the individual trusses, it is used as an essential in holding the bridge together. The cross bracing is the bracing on top and bottom of the design which is attached to the top and bottom chords and holds both sides of the trusses together.
These bridges hold different types of load. Dead load is ‘The permanent, static load on a building or structural element due to the mass of all permanent structural members, install plant, services installations and other fixed loads which imposed definite stresses and strains upon the structure (Glossary of Building Terms).’ This would be the mass of the bridge without any other forces acting upon it.
Live loads are ‘the load(s) assumed to arise from the intended use or occupancy of a building or structure; including distributed, concentrated, impact or inertial loads, but excluding wind, snow, or earthquake loads and the load of the structure. By comparison with dead loads which remain constant, live loads on a building maybe be removed or replaced (Glossary of Building Terms).’ This is the weights subjected to during its life. E.g. trucks and other traffic
The following are the results found through WestPoint bridge designer. The following is a model made the same way the test model was made. This program was used to create a virtual test of the bridge with a live load present. It will predict where the first members will break and what forces each member is carrying.
Figure 6 (West Point Bridge Design)
Figure 7 (West Point Bridge Design)
Figure 8 (West Point Bridge Design)
As can be shown from the information above both the diagonal and top horizontal supports are under compression and the vertical and base horizontal supports are under tension. (Blue = Tension, Red = Compression).
3.0.0 Method
3.1.0 Experiment 1
Building the bridge
3.1.1 Materials
Pasta – San Remo – Tubular Spaghetti
Wire Cutters
Hot Glue Gun
Hot Glue Gun Glue sticks
Cardboard
Pins
Ruler
Scissors
Weights- 20g, 50g, 100g, 500g, 1kg
Helper
3.1.2 Safety hazards
Heat- the heat given off of the hot glue gun could burn.
Sharp objects- scissors, pins- could cause an injury
Make sure that all hazards are taken into account and all safety procedures are followed.
3.1.3 Method
1) Collect pasta and collate tools appropriately
2) Create base template on cardboard
3) Glue 7 pieces of full length pasta (25cm) together into a circle to create base and top horizontal chords.
4) Mount 2 base horizontal supports into the template and create cross bracing as shown in the diagram below.
5) Repeat stage four for the top cross bracing
6) Cut all protruding parts with a pair of wire cutters
7) Place both top and bottom cross braces created into the template and support seperated using one strand of pasta and glue using help from your partner. (Making sure the ends stay square)
Glue the side truss members on in the form shown below9) Turn the bridge over and repeat stage 8 to create the truss on the opposite side
10) Cut off any protruding pieces of pasta
11) Weigh the bridge and record its mass
12) Place the bridge onto the side pillars (As shown in figure 7 above and photo below)
13) Slowly load the bridge with weights until failure
14) Record the weight the bridge held (noting where failure occurred)
4.0 Results
4.1 Experiment 1
Dead Load (Bridge Mass): 70g
Successful Live Load (Mass held by bridge): 14.5kg
Failure weight: 15.5kg
Photo 1 – Bridge at 14.5kg
Photo 2 – Bridge at 15.5kg (failure imminent)
Photo 3 –Bridge failing
Photo 4 – Bridge in full collapse
5.0 Analysis of Results and Discussion
5.1 Experiment 1
The experiment was an overall success. Outcomes were achieved that allowed successful analysis that produced good results.
The ratio of weight carried compared to the mass of the bridge can be express by the following equation:
Strength to Weight ratio
Ratio: 14.5:0.07 = 207:1
Therefore the bridge held approximately 207 times its own weight. An outstanding result, seeing as the record for Camosun College, Civil Engineering Department is 40.6 load ratio for grade 11 and 12 students. Engineers use this sort of information for designing the strength to weight ratio of modern bridges to reach economies in the amount of steel used in these structures.
Throughout the experiment the bridge started to bend towards the middle placing the bottom chords in tension and the top chords in compression, as shown in the model produced by WestPoint Bridge designer. The result showed the bridge bending downwards in the centre the same way shown in the experiment.
Photo 5
After placing weight on top of the bridge the side trusses started to distort showing distinct curves in the members (as shown in photo below).
Photo 6
As the weights reached approximately 10kg one of the side vertical members broke towards the top. This did not seem to disable the bridge in anyway because it still held another 5 kilograms approximately after that. The reason for this member breaking is unknown but could have something to do with the tension it was under.
Photo 7
The place of breaking point was at the first node point in from the left hand side of the bridge (Sa shown in the photo below). The reason for this break was due to experimental error. While the weights were being loaded onto the bottom supports, one member broke due to a misplacement of the weights. It was at this stage that the bridge finally broke.
Photo 8
This position of the break was not where it was predicted to occur in the West Point Bridge computer modelling. It was predicted that the break would occur in either of the diagonal brace supports and centrally on the horizontal members under compression.
This should have been correct in the pasta bridge design. In working with the pasta during construction and research it was found that pasta works well under tension and not as well under compression (Camosun College, Civil Engineering Department). This therefore would imply that the bridge should have broken at the top chord which is under compression and not at the bottom chord where the break did occur.
Experimental error plays a large part in the results achieved in this experiment. The first error occurred through the placement of the weights. The weights were placed onto the bridge as well as hanging off the base supports. After hanging all of the available weights onto the bridge, bricks were then placed on top of the structure.
Also error could occur in the strength of the pasta. i.e. the pasta was not uniform in size and may have had deformities in its structure. This is because these products are a mass produced with no need for quality control as these are food products.
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