The second half of the century resulted in more than one hundred bridges being built. The building of bridges is important to Pittsburgh as well. Pittsburgh is known for its bridge companies dating back to the early s. Several important industrialists and designers had their companies in the city. This company help builds all of the bridges around America. In the s George Ferris own a company in this city named The G. G Ferris Company. They inspected the bridges and made parts for bridges.
The American Bridge Company is currently fixing bridges across the country. These companies tell the rich history of Pittsburgh and how it relates to bridges. The first bridge I will look at is the Smithfield Street Bridge. The image of it:. Wikipedia This Bridge is designed in the style of a steel lenticular truss.
It has some wrought iron members. It crosses the Monongahela River and has a pedestrian walkway on both sides. The first bridge erected at this site in was a wooden covered bridge.
It was the first river crossing bridge in Pittsburgh. The wooden bridge was destroyed by fire in The designer for the replacement bridge was Gustav Lindenthal built in He worked for the Keystone Company. This bridge was restored three times. John Roebling was the engineer who was in charge of restoring the original design.
It was restored again in to the Lindenthal original design. It is the oldest river bridge in Allegheny County. This bridge is one of the oldest truss bridges in the United States and has the longest span for its type.
One of its many awards is the United States National Historical Civil Engineering Landmark and it has received many local and national rewards. The second bridge is a combination bridge. It is a steel trussed arch with a suspended deck.
The original covered wood bridge at this location was destroyed by fire in The current bridge was built in, ornamented with bronze structures. Architects Warren and Wetmore designed it. Pedestrian walkways with two way traffic lanes are included in the design of this bridge. The Pittsburgh Arts commission was heavily involved in the design process because they wanted more artistic involvement with the designing of the bridges.
The third bridge is the McKee's Rock Bridge. It crosses over the Ohio River. This bridge is a steel trussed arch. This bridge stretches one and half miles. It is multi structured and was built in the early s. Now the students will look at these bridges through the strategies in blooms taxonomy when giving the history of the bridges. Knowledge will be experienced through naming the three bridges as well as recalling the types of bridges.
The students will show comprehension through describing the bridges as they put it into their own words. We can also compare the differences of the bridges. The application part will take place as the students draw illustrations of the bridges. At the field trip to visit the bridges the students can relate to experiencing the bridge by walking under them and driving over them. As we walk under the McKee's Rocks Bridge, we will explore its structural design.
They will get the chance to see the truss design up close. Walking on this bridge will show the lattice design in the arch. The analysis will also take place during the field trip to the bridges. We will get a chance to distinguish between the three bridges. The synthesis will be through designing their own bridges and doing a skit using all of the jobs that were named to construct a bridge.
This is the skill of schematizing bridge design through role playing. The evaluation process will be through the choosing of a bridge that they like out of the three and do a painting of it.
The painting w ill be labeled by the students and put on a rubric. The triangle is a polygon, because all of its sides have straight lines. It has three corners and three sides the type of triangle I am talking about is equilateral.
The angles of a triangle add up to one hundred and eighty degrees. It is one of the geometric shapes. All triangles are two dimensional. It is studied in geometry.
Geometry is the study of property and relationships of points, lines, angles surfaces and solids. Some important facts about triangles, they have three sides. They have three points, corners or angles. All three sides connect and are straight. A triangle is a rigid strong shape because of its stability. The triangles make up the truss design. They are in an assembly of triangles made from a series of straight bars. The triangle is used because of its strength and stability.
The truss is also identified by the shapes of the triangle in its design. The extremely strong triangle is the only geometric form that can not be bent out of shape. From as far back as ancient times the triangle has been held in high esteem.
For the Egyptian, they were very sacred in the form of the pyramids. The pyramid has four triangles as sides and a square base. A modern extension of the triangle and the pyramid is the geodesic dome which combines triangles and pyramids.
To get ready for this lesson I will read The Shape of Things. The first strategy is knowledge. The students will recognize a triangle and distinguish it from other shapes. This will be through identifying it among other shapes. While drawing some of the pictures, they will be able to use the triangle.
The comprehension will take place when comparing them to other shapes while doing a puzzle and completing a truss making exercise. The truss bridge will help with comprehending what this shape looks like.
Application will be when the Popsicle triangles will be made. The students will be using triangles to make this type of bridge. The analysis will come when the distinguishing of the shape will be done. This will also be evident through when they do the actual making of the triangles. The triangle has equal sides and that has to be understood.
One of the characteristics that make it so unique is the equal sides. They will create designs using triangles. They will label their shape. How the student will be using evaluation of the knowledge of a triangle is through choosing the correct form to make triangles.
To further explore the strength of a triangle you must remember that two dimensional shapes are flat. I would hope to build a tetrahedron. A regular tetrahedron is a three dimensional form created by four equilateral triangles with all edges connected. It is just a four sided triangle. Each will build one and take it home. Also a learning center will be set up to let the students' build three dimensional objects from flat shapes. The tangram is a puzzle that dates back to the early s.
This game in China was considered to be a game for women and children. It comes from the Song Dynasty. According to Chinese history it was part of their furniture. Originally it had six triangular tables and later added rectangular one.
After the Ming Dynasty the objects used became wooden blocks. The legend is said that a servant of the emperor was carrying a very expensive tile and tripped and shattered the tile. The servant panicked and tried to put it back together in a square. Instead he created thousands of pictures and patterns as he tried. Tangram is an English word meaning puzzle or trinket. The word was first used by Thomas Hill a former president of Harvard in his book "Geometrical Puzzle for the Youth" in Tangrams were popular in the 19th century.
Some tangrams were made with ivory or jade. The puzzle is composed of five right angle triangles, a square, and a parallelogram. The parallelogram is unique because any way you turn the puzzles image can not be done through rotation but only through flipping over. The seven shapes are called tans. They fit together to form a new shape. The shapes make interesting designs.
The geometrical design provides mathematical relationships and forms. The tangram is important to this unit for three major reasons with the emphasis on the use of triangles. The tangram designing emphasis of objects and the way in which they will be used in throughout the unit will bring the technological use into focus. The tangram and technology is a combination of both the third and fourth T. The game that I will be using in this unit is called Sagwa. This game designs objects and is self correcting.
It is based on the story about the Chinese Cat. The game is from CineGroupe Sagwa Inc. The objects of the game are a cat or a storyteller and others. When the puzzle is completed there is praise. A hint button can be pushed to help with completing the puzzle. There are two levels for different levels of student's abilities. How I plan to apply the strategies in blooms taxonomy is knowledge. The students before going onto the game will cut out their individual pieces and make there own tangram puzzle.
They will do this activity and have enough time to manipulate and become familiar with making images with the puzzle. They will recognize the shapes and use them for designing. A student's comprehension will be tested when the Grandfather Tang's story is read. The students will answer questions concerning the story and how the tangram was used to tell the story. Application will be through manipulating the tangram into some of the things that are in the story.
Analysis will take place when they choose puzzle pieces to create designs. They will contrast and fit different triangle shapes together. The synthesis will be through discussion of the history of tangrams the story and how the puzzles are used.
Their designing of the objects will show their level of understanding how to use tangrams. Evaluation will be through the successful use of the software. Technology in the classroom helps keep the students up with the current sciences that are happening around the world.
In this unit the technology will be used as a tool to support the task of designing and making decisions. In part, the unit the teacher's role turns to being a facilitator and providing guidance as needed. The whole game offers a process of learning through experimentation.
The first book on bridge design was written in by Hubert Gautier. This is an account of how bridges evolved and arrived. The first bridge was made by a single log or by a wooden plank. The early bridges could not carry heavy weight. In China, one of the first low arch bridges in the world is the Zhoa Xian built in Some arch bridges date back to the second century.
Following the lesson, students can conduct the fun and hands-on associated activity Truss Destruction in which they will construct trusses using Popsicle sticks and hot glue, and then test them to failure as they evaluate the relative strength of different truss configurations and construction styles.
Next, show students the Strength of Shapes Presentation using the suggested script provided in the Lesson Background section. Make sure students have paper and pencil handy to sketch their ideas as they follow along with the presentation. Slide 1 Today we will explore a fundamental structural engineering concept: the strength of shapes. Slide 2 When we look carefully at bridges, we can see how structural engineers use different shapes to make the overall design.
We can see triangles and squares. We can even see parabolas. Slide 3 Structural engineers use the same types of shapes in buildings. Many building frames are simply repeating squares, as shown in the top left.
The bottom left image shows how a square is reinforced by adding a diagonal cross brace in this scaffolding, which breaks the square into two triangles.
The image on the right shows an Antarctic geodesic under construction. The structure of geodesic domes is similar to the structure of soccer balls and can be viewed as a group of pentagons and hexagons. But, if we break each of those shapes down, we can see that they are fundamentally composed of triangles.
Slide 4 Even when we get outside the realm of civil or architectural engineering, we can see how engineers rely on the known strength of shapes. A motorcycle frame uses many triangles to support the wheels and seats. Mechanical engineers design cranes, which use triangles and squares in their frames.
Even satellites use these familiar and basic regular geometries. Slide 5 On your paper, sketch each of these regular polygons: square, diamond and triangle. If we push straight down on a shape, putting the whole shape into compression, what happens to the shape? Draw, using a different pen or pencil or dashed line, how the shape would look if you pushed on it. Assume that the sides of the shape are rigid and won't change length or bend. Slide 6 Take a look at this! If you push down on top of the square, it will no longer be a square, but instead takes the shape of a rhombus, which is a type of parallelogram.
This is called "racking. But what about the triangle? The triangle maintains its shape! Slide 7 The reason that the square and diamond collapse is because the angle between the structural members can change without having the length of the members change or bend.
Remember back to geometry when we talked about how polygons are defined? These can be used alone for short spans. Queenpost trusses further divide the triangle by placing a rectangle in the middle, thus creating three smaller triangles surrounding it. Howe trusses connect a series of overlapping equilateral triangles, each with a vertical tension rod. The triangles are connected by a chord at the top and base. They can be used to span large distances and hold much more weight than the Kingpost and Queenpost.
Simple trusses have been seen in building design in Europe since the s. In the U. As wood was plentiful, truss building designs eventually found their way into other aspects of structural engineering. In the mids, trusses began being manufactured for homebuilding designs, and they're still the primary method of erecting most buildings. Jason Law has been writing professionally since , when he first began writing research papers as an independent contractor.
This inherent rigidity of triangles is a geometric property. The triangle is the only polygon whose internal angles—and, therefore, shape—are uniquely defined by the lengths of its sides.
Applying the equations of statics, we can show that if a body is loaded at two points only, the resultant forces at those points are equal in magnitude; are opposite in direction; and act along the line between the two points.
For our truss members, this means that forces on the members are axial that is, they act along the axis of the member , putting them in either pure tension or pure compression.
The forces in the members can be calculated in several ways. In an axially-loaded member, the force is carried equally by every part of the member—no part is wasted. Contrast this to a beam. When you load a beam at the center, the stresses are much higher there than anywhere else. The material away from the center just isn't doing as much work, lowering the efficiency of the structure.
You have, by the way, an instinctive understanding of this. If someone hands you a pencil and asks you to break it, you put your thumbs against the center and bend it.
By sizing the members of a truss just right, you can tune it to carry huge loads while using very little material. This is how people win balsa wood bridge competitions. Types of truss bridges are also identified by the terms deck, pony and through which describe the placement of the travel surface in relation to the superstructure [3] :.
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