Abstract
Bridges are the most complicated structures to design in the Engineering field. The following experiment conducted using spaghetti and any type of glue in building a bridge model. The experiment involved testing how much weight can the spaghetti hold in tensile using a tensile strength testing machine. The experiment aimed at making a practical representation of real bridges and the forces on them. Three main real bridges are discussed, truss bridge, srch bridge, and suspension bridge. The tests were conducted through hanging weights on the constructed spagheti bridge and determining the breaking loads. The experiment result analysis showed that truss pattern brigdes are the strongests. In addition, it was discovered that the heavier the bridge the less load it can withstand.
List of figure
Figure 1: A spaghetti-made bridge for experiment 6
Figure 2: Designs of the Osage County truss bridge 9
Figure 3: A representation of a truss bridge under the compression and tension forces. 10
Figure 4: Design of the Union arch Bridge 12
Figure 5: The Arch bridge 13
5 (a): Loads distribution in an arch bridge 13
5 (c: load distribution from the arches to the ground 14
Figure 6: Design of the Golden Gate Bridge 16
Figure 7 (a): Unsupported span test 20
Figure 7 (b): Simple truss test 20
Figure 7 (c): maximum load on bridge test 21
Figure 8: relationship between type of trusses and breaking weights 23
Figure 9(a): strengths of triangular truss bridges 24
Figure 9(b); Distribution of compression and tension forces in the spaghetti bridge 24
Figure 10: Sample tensile strength results 26
List of tables
Introduction
This was an experiment conducted using spaghetti and any type of glue in building a bridge model. The experiment involved testing how much weight can the spaghetti hold in tensile using a tensile strength testing machine. The main reason of constructing a spaghetti bridge was to make a practical repsresentation of a real bridge involving design, planning and construction. The aim of the experiment was to build a 50 cm long bridge spanning 40 cm that could carry as much weight as possible weighing as little weight as possible and yet meet all the requirements required of a real bridge. Moreover, the experiement analyzed the stree and structure of spaghetti bridge as a model representing a real suspension bridge. Figure one shows the representation of a spaghetti bridge used in the experiement.
Figure 1: A spaghetti-made bridge for experiment
Real Bridges designs
Introduction
A bridge is a complicated structure that required a detailed planning and execution of the plan in order to avoid failure of the design. Bridges perform a variety of activities and are used for different reasons. For instance, a bridge can connect two areas separated by a river or they can span the distance between two valleys. These terms should be first understood in the construction of bridges before discussing several types of bridges. These are:
- Tension
- Compression
- Buckling
Tension refers to opposing forces acting on a bridge structure that result into tension forces. Compression refers to forces that bring structures in a bridge together resulting into compression forces. A bridge should be able to withstand compression and tension forces for it last. All bridges have tension and compression forces and have the capability of destroying a real bridge because of the varying load weights and other external forces acting on the bridge. a bridge designer should put into consideration these two forces in order to avoid buckling or snapping of a bridge. Buckling is a situation that occurs when compression forces are more that the structure has no ability to endure compression forces (Robert and Morrissey 2000). There are three types of bridges, truss bridges, arch bridges and suspension bridges.
Truss Bridges
A truss could be described a framework of materials acting primarily in compression and tension. Being light in weight, a truss is a very stiff form of construction and that is the reason why it is used in bridge construction. Two common types of truss bridges are common, through truss constructed above the bridge and deck truss constructed beneath the bridge. A good example of a real truss bridge is bridge found on an Osage County road in United States of America constructed in 1948. The picture of the bridge is shown below.
- (B)
(C) (D)
Photo 1: The Osage County road truss bridges
Design of a truss bridge
The Osage County road bridges are 48 meter long with eight panels and 20 meters wide. The bridge weighs 450, 000 tons can withstand maximum live load of 1 ton per square m. the total weight of steel structures used is 890,000 tons. The bridge forms one of the most prolific types of truss bridges in the states that has served for a very long time. Figure 2 (A-D) shows the design of the 8-panel Parker and K-trusses. Their respective pictures are shown in A to D above. The truss is made up of horizontal, diagonal, and vertical members (also referred to Chords) that only act in tension or compression. Piles represent vertical members of a truss and help in support of vertical loads. Members are pinned at the nodes at the point where straight members meet allowing movement of members without buckling. Figure 3 gives a better representation of members used in designing a truss bridge. Simple supporting frameworks of triangles are used in the construction of this truss bridge. These triangles act as a support to the beam or the span and helps in adding rigidity. In addition, the horizontal nominal strut helps in reducing the size of the longest verticals (Klopp 1999).
Figure 2: Designs of the Osage County truss bridge
Truss bridges experiences both compression and tensional forces as materials like vehicles pass through them. The compression on the upper side of the truss deck causes the underside to undergo tension hence stretching. The diagonal and horizontal members of the truss transfer tension forces to pilings (Alampalli & Kunin 2001). Figure 3 below shows how tension and compression forces act on a truss bridge.
Figure 3: A representation of a truss bridge under the compression and tension forces.
Advantages
A truss bridge has the following advantages over the arch and suspension bridge:
- It has a good strength to weight performance,
- A truss bridge is compatible to almost every design,
- It is less costly because there no many repeated parts as in the case of a suspension bridge hence saving manufacturing costs.
However, a truss bridge has the following disadvantages:
- They are expensive to fabricate and maintain,
- Truss bridges are labor intensive,
- They are only suited for shorter distances (less than 500 meters) like foot bridges unlike suspension bridges that can bridge a gap of more than 500 meters.
Arch Bridge
Arch bridge design has continually featured in the Engineering for the design of bridges for more than 2,000 years. An arch bridge is a semicircular structure with two abutments whose design assists in transferring weight of the bridge and the loads acting on it to the abutments found on either side of the bridge. An arch bridge can be of a longer span than a truss bridge because it only requires a series of arches (Johmann, Rieth & Kline 1999). A real example of an arch bridge is the Union Arch Bridge (also called Cabin John Bridge) found in Maryland. It is a roadway bridge constructed from 1857 to 1864. The representation of this bridge is shown below.
Photo 2: The Union Arch Bridge
Design of the Union Arch Bridge
According to Cleary (2007), traditional arch bridges were built of stones or bricks but the modern arch bridges are made of reinforced concrete or steel. The bridge is 140 meters long and 6.1 meters wide. The bridge was constructed of Massachusetts granite and red sand stone that has made it stand to date. In addition, the bridge rises 31 m. the main arch has a span of 67 m long and raised 17.45 m. the interior of the bridge is made up of spandrel wall structure consisting of nine additional arches. Figure 4 represents the full design of the Union Arch Bridge.
Figure 4: Design of the Union arch Bridge
Forces acting on the bridge
The arch bridge experiences both tension and compression forces. The loads on the arch bridge do not push straight downwards or upwards but are carried outwards along the curve of the arch to abutments at each end. In addition, each weight acting on the bridge is transferred to each support/abutment. The abutments perform two tasks; they carry the loads and prevent ends of the arch from spreading out. As seen from figure 5(a), the load on each section representing an arch in the bridge presses on the next until the whole weight is applied to the end supports. Figure 5(b) shows the distribution of loads around the abutment. In addition, for every action there should be an equal and opposite reaction. The ground where the abutment rests creates a resistance that is passed from one arch to the other until it pushes the main arch supporting the load (Egbu 2004). This is shown on figure 5 (c).
Figure 5: The Arch bridge
(a): Loads distribution in an arch bridge
(b): Load distribution around the abutment
5 (c): load distribution from the arches to the ground
Advantages of arch bridges
- There is even distribution of pressure as opposed to truss bridges
- Arch bridges can carry a bigger load than suspension or truss bridges
- They can span over a longer distance than truss bridges
Disadvantages of arch bridges
- They require a lot of labor and materials to construct,
- They must be constructed on a very stable ground to prevent the weight of abutment from crashing the ground.
Suspension bridges
The modern suspension bridge is the most admirable type compared to all other bridges. A suspension bridge consists of framework of steel supported with vertical suspenders and suspension cables. It is one of the modern bridges constructed today especially for long spans. The suspension cables are anchored at the end of the bridge because every load acting on the bridge is transformed into tension in suspension cables. Suspension bridges can cross-distances of between 600 and 2100 meters (Cleary 2007). A good example of a real suspension bridge is the Golden Gate Bridge shown in the picture below.
Photo 3: The Golden Gate Bridge
Design of the Golden Gate Bridge
The Golden Gate Bridge has 2,737 m long with a span of 2,788 m and 27 m wide. The bridge weighs 887,000 tones. The Golden Gate Bridge is designed to withstand a total deflection of 8.4 m at the center span and can hold live load of 1.8 tons per m. the bridge has two main towers supporting two main cables. The height of the tower is 227 m and the height above the road way is 152 m. the weight on both towers is 44, 000 tons. The towers can withstand a transverse deflection of 0.32 m and longitudinal deflection of 0.46 m. The Golden Gate Bridge has two cables passing over two main towers and secured at either ends with huge anchors. The diameter of one main cable is 0.92 m with a length of 2,332 m (Office of historic Preservation 2012). Table 1 represents the concrete qualities while table 2 shows the steel qualities used in the construction of the bridge. Figure 6 shows the bridge design in details.
Figure 6: Design of the Golden Gate Bridge
Forces acting on the bridge
Compression forces push down the deck of the bridge, but the cables transfer the compression to the towers. Transverse deflection occurs because of the sustained transverse wind load. The maximum downward deflection occurs due to the effect of live loads at the center of the span. Moreover, the maximum upward deflection occurs due to the tension forces of suspension cables (Office of historic Preservation 2012).
Advantages of a suspension bridge
- It can span over longer distances than the truss bridge or the arch bridge.
- A suspension bridge is less labor intensive
Disadvantages
- It requires a lot of design work because it is used in risky areas
- It can swing in high velocity winds
- It requires many materials to construct and is costly compared to truss and arch bridges.
The experiment
This forms an educational experiment demonstrating how bridges work. I was in group O/M and dealt with the truss bridge. The bridge was made of spaghetti stuck together with glue. The main aim of the experiment was to determine the amount of load the structure would hold before falling.
Materials
- Raw Spaghetti bundles
- Two table anchors
- Tape supporters
- Rubber bands
- Weights
Properties of spaghetti
- Ultimate tensile strength ~2000 psi
- Stiffness (Young’s modulus) E ~10,000,000 psi
(E=stress/strain)
Procedure
- The supports for the bridge were made by putting several pieces of spaghetti together to make a tube-shape. Glue was applied to each strand and held together with a rubber band
- The deck for the bridge (the part of the bridge where load will be placed) was constructed. This was made of a round bundle of unglued spaghetti. .
- The trusses of the bridge were designed made. Trusses were made of different types, square, triangle etc to determine the breaking force of each design. My group used a square truss.
- All the bridge components were glued together and the bridge was placed on the two supports.
The destruction tests
- Firstly, the breaking weight of each truss in an unsupported span was determined. The truss was placed on the supports and weights added until it break. The results are shown in table 3 (a). See figure 7 (a) below
Figure 7 (a): Unsupported span test
- The second test was of a simple truss. My group used larger holder plus the smaller holder and 12 blocks (figure 7(b). The results of my group were compared with those of other groups to determine the strongest truss.
Figure 7 (b): Simple truss test
- Using a 50 cm long bridge with a 40 cm span, the bridge was placed between the two supports and the breaking weight determined (figure 7(c). Various bridge weights were used and their breaking weight and load weight recorded in table 3 (b).
Figure 7 (c): maximum load on bridge test
Results
Unsupported span
Simple truss
Results Discussion
Figure 8: relationship between type of trusses and breaking weights
Results from table 3 (a) shows that the triangular trusses resists the most load hence are the best for constructing bridges. According to Patnaik & Hopkins (2004), triangular trusses can withstand more weight because they have members’ places in diagonal, horizontal and vertical positions that assist in equal distributions of weight. The second stand (Group (M/A) did not manage a lot of weight because its members could not withstand the tensile forces introduced by the hanging weights. This is graphically represented in figure 8. On the other hand, the direction of a truss bridge determines the amount of load it can carry. Inverted triangular bridges are more stable than bridges with peak at the top as shown on figure 9 (a).
Figure 9(a): strengths of triangular truss bridges
While designing a spaghetti bridge, compression and tension forces are the most important aspects tom put into consideration. Even with no weight on the bridge, these two forces must be considered carefully because the spaghetti also has some weight. Figure (b) shows how tension and compression forces were distributed on the bridge.
Figure 9(b); Distribution of compression and tension forces in the spaghetti bridge
FB = Psin Ø . 1
The following results show that the shape of the bridge is an important factor to consider when designing a bridge. Different shapes forming a bridge pattern give different results hence; the pattern of a bridge might increase or decrease its strength.
Figure 10: Sample tensile strength results
Using figure 10 above, for our bridge, the offset yield stress is equivalent to:
8.2 grams = 8.2*9.81/1000 = 0.080 N
Fracture stress = 53g = 53*9.81/1000 = 0.52N
The bridge used for my group test (M/O) weighed 155 g, had a breaking weight of 8.2 g and load weight of 53 g. The heavier the bridge the less weight it could carry. Various factors determine the weight of the bridge. Firstly, the materials used in the construction affects the weight of the bridge. Bridges constructed of steel and concrete are heavier than bridges constructed of wood and ropes. Constructors should put into considerations while designing bridges in order to avoid making overweight bridges (Washington, DC: U.S. Dept. of Transportation, 2006).
Conclusion
This experiment shows that a lot of calculations and research should be done before constructing any type of bridge. From the spaghetti bridge model, it was realized that truss bridges are the most efficient type of bridges because they can carry more weight. In addition, the pattern of the trusses matters. Triangular pattern is the most recommended because it ensures distribution of tensile and compression forces on the points if attachment of members. This experiment shows engineers how a real bridge would look like and is essential for the learning experience in construction of real bridges.
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