Work Plan• History of Bridge Development• How Bridges Work• Basic Concepts• Types of Bridges• Concepts Associated with Bridge Engineering• Truss Analysis• Tips for Building Bridges• Bridge Construction
History of Bridge Development Natural Bridges 700 A.D. Asia Great Stone Bridge in China Clapper BridgeTree trunk Low BridgeStone Shallow Arch Strength of Materials Mathematical Theories Roman Arch Bridge Development of The Arch Metal Natural Cement 100 B.C. Romans 1300 A.D. Renaissance
History of Bridge Development 1800 A.D. 1900 A.D. 2000 A.D. Truss Bridges PrestressedFirst Cast-Iron Bridge Mechanics of Concrete DesignCoalbrookdale, England Steel Britannia Tubular Bridge Suspension Bridges Wrought Iron Use of Steel for the suspending cables 1850 A.D. 1920 A.D.
How Bridges Work?Every passing vehicle shakes the bridge upand down, making waves that can travel athundreds of kilometers per hour. Luckily thebridge is designed to damp them out, just as itis designed to ignore the efforts of the wind toturn it into a giant harp. A bridge is not a deadmass of metal and concrete: it has a life of itsown, and understanding its movements is asimportant as understanding the static forces.
Basic ConceptsSpan - the distance between two bridgesupports, whether they are columns, towersor the wall of a canyon.Force - any action that tends to maintain or alter the position ofa structureCompression - a force which acts tocompress or shorten the thing it is actingon.Tension - a force which acts to expand orlengthen the thing it is acting on. Compression Tension
Basic ConceptsBeam - a rigid, usually horizontal, structural element Beam PierPier - a vertical supporting structure, such as a pillarCantilever - a projecting structure supported only at one end,like a shelf bracket or a diving boardLoad - weight distribution throughout a structure
Basic ConceptsTruss - a rigid frame composed of short, straight pieces joinedto form a series of triangles or other stable shapesStable - (adj.) ability to resist collapse and deformation;stability (n.) characteristic of a structure that is able to carry arealistic load without collapsing or deforming significantlyDeform - to change shape
Basic ConceptsBuckling is what happens when the force ofcompression overcomes an objects ability tohandle compression. A mode of failurecharacterized generally by an unstablelateral deflection due to compressive actionon the structural element involved.Snapping is what happens when tension overcomes anobjects ability to handle tension.To dissipate forces is to spread them out over a greater area,so that no one spot has to bear the brunt of the concentratedforce.To transfer forces is to move the forces from an area ofweakness to an area of strength, an area designed to handlethe forces.
Types of Bridges Basic Types: •Beam Bridge •Arch Bridge •Suspension BridgeThe type of bridge used depends on various features of theobstacle. The main feature that controls the bridge type is thesize of the obstacle. How far is it from one side to the other?This is a major factor in determining what type of bridge to use.The biggest difference between the three is the distances theycan each cross in a single span.
Types of BridgesBeam BridgeConsists of a horizontal beam supported at each end by piers.The weight of the beam pushes straight down on the piers. Thefarther apart its piers, the weaker the beam becomes. This iswhy beam bridges rarely span more than 250 feet.
Types of BridgesBeam BridgeForcesWhen something pushes down on the beam, the beambends. Its top edge is pushed together, and its bottomedge is pulled apart.
Types of BridgesTruss BridgeForcesEvery bar in this cantilever bridge experiences either apushing or pulling force. The bars rarely bend. This is whycantilever bridges can span farther than beam bridges
Types of BridgesArch BridgesThe arch has great natural strength. Thousands of years ago,Romans built arches out of stone. Today, most arch bridgesare made of steel or concrete, and they can span up to 800feet.
Types of BridgesArch BridgesForcesThe arch is squeezed together, and this squeezing force iscarried outward along the curve to the supports at each end.The supports, called abutments, push back on the arch andprevent the ends of the arch from spreading apart.
Types of BridgesSuspension BridgesThis kind of bridges can span 2,000 to 7,000 feet -- way fartherthan any other type of bridge! Most suspension bridges have atruss system beneath the roadway to resist bending andtwisting.
Types of BridgesSuspension BridgesForcesIn all suspension bridges, the roadway hangs from massivesteel cables, which are draped over two towers and securedinto solid concrete blocks, called anchorages, on both ends ofthe bridge. The cars push down on the roadway, but becausethe roadway is suspended, the cables transfer the load intocompression in the two towers. The two towers support most ofthe bridges weight.
Types of BridgesCable-Stayed BridgeThe cable-stayed bridge, like the suspension bridge, supportsthe roadway with massive steel cables, but in a different way.The cables run directly from the roadway up to a tower, forminga unique "A" shape.Cable-stayed bridges are becoming the most popular bridgesfor medium-length spans (between 500 and 3,000 feet).
Interactive PageHow do the following affect your structure?ForcesLoadsMaterialsShapesLet’s try it:http://www.pbs.org/wgbh/buildingbig/lab/forces.htmlThe bridge challenge at Croggy Rock:http://www.pbs.org/wgbh/buildingbig/bridge/index.htmlbridge/index.html
Bridge EngineeringBasic math and science conceptsPythagorean Theorem β c a γ α b c2=b2+a2 α+β+γ=180°
Bridge EngineeringBasic math and science conceptsFundamentals of Statics F y x R1 R2 ΣFx = 0 ΣFy = R1+R2-P = 0
Bridge EngineeringBasic math and science conceptsFundamentals of Mechanics of Materials Modulus of Elasticity (E): Stress F/A F σ E= = ∆L/L Strain oLo Where: E F = Longitudinal Force ε A = Cross-sectional Area F ∆L = Elongation Lo = Original Length
Bridge EngineeringBasic math and science conceptsTo design a bridge like you need to take into account themany forces acting on it : •The pull of the earth on every part •The ground pushing up the supports •The resistance of the ground to the pull of the cables •The weight of every vehicleThen there is the drag and lift produced by the wind •The turbulence as the air rushes past the towers
Bridge EngineeringBasic math and science conceptsBalsa Wood Information Density 163 ± 10 kg/m³ Compressive Strength¤ low density 4.7 MPa medium density 12.1 MPa high density 19.5 MPa Tensile Strength¤ low density 7.6 MPa medium density 19.9 MPa high density 32.2 MPa Elastic Modulus - Compression 460 ± 71 MPa Elastic Modulus - Tension 1280 ± 450 MPa
Bridge EngineeringTruss AnalysisStructural Stability Formula Where: K = The unknown to be solved K = 2J - R J = Number of Joints M = Number of Members R = 3 (number of sides of a triangle) K Results Analysis: If M = K Stable Design If M < K Unstable Design If M > K Indeterminate Design
Bridge EngineeringTruss AnalysisStructural Stability Formula (Example) Joints J=9 Members M=15 K = 2 (9) – 3 = 15 15 = M = K then The design is stable
Bridge EngineeringTruss Analysis http://www.jhu.edu/virtlab/bridge/truss.htm West Point Bridge Software: http://bridgecontest.usma.edu/
Tips for building a bridge1. Commitment - Dedication and attention to details. Be sure you understand the event rules before designing your prototype.1) Draw your preliminary design2) ALL joints should have absolutely flush surfaces before applying glue. Glue is not a "gap filler", it dooms the structure!1) Structures are symmetric.2) Most competitions require these structures to be weighed. Up to 20% of the structures mass may be from over gluing.
The Importance of ConnectionsStresses flow like water.Where members come together there are stressconcentrations that can destroy your structure.Here is a connection detail of one of the spaghettibridges.