Statics in BridgesStatics in Bridges

What is a force?What is a force?

A force is a push or pull on an object (compression and A force is a push or pull on an object (compression and tension).tension).

Stationary objects are static.Stationary objects are static.

No net forcesNo net forces No net moments No net moments

(torques)(torques)

Are there forces on you Are there forces on you now?now?

Gravity is pulling you down.Gravity is pulling you down. The stool is pushing you up.The stool is pushing you up.

Force is compression. Force is compression. Each leg supports ¼ of the weightEach leg supports ¼ of the weight

Total forces are zero (statics).Total forces are zero (statics).

What forces are on this girl?What forces are on this girl? Net force is zero. Net force is zero.

Gravity pulls the girl Gravity pulls the girl down (weight).down (weight).

Force in the line is Force in the line is tension.tension.

Sample calculation-Sample calculation-

Bending is Bad

•Bending- Beams have very little bending strength.

•Never design a structure that relies on bending strength to support a load.

Design and construction ideas:

1) Triangles are a construction engineer’s best friend, i.e.there are no bending moments in triangular elements.

Good design

Bad design (truss strength depends on bendingstrengths of members)

Truss Bridges Truss Bridges

Your bridge will be essentially a truss. Your bridge will be essentially a truss.

In a truss bridge forces are at an In a truss bridge forces are at an angle.angle.

Since the bridge is stationary the Net force must be zero.

Beams and loads--compression:

Beam in compression

Failure occurs two ways:

1) When L/d < 10, failure is by crushing2) When L/d > 10, failure is by buckling

We are almost always concerned with failure by buckling.

L

d

Compression- Buckling Strength: F = (k)d4/L2

If a beam of length L and diameter d can support a

compressive load of F,

L

dF

then a beam of length L/2 and diameter d cansupport a compressive load of 4F.

L/2

d4F

L

2d16F

and a beam of length L and diameter 2d cansupport a compressive load of 16F.

L

dF

Compression- Buckling Strength: F = (k)d4/L2

Compression- Buckling Strength: F = (k)d4/L2

•In compression short and fat members are good.

•Bigger beams can be fabricated out of smaller beams, as in a truss.

The fabricated beam will have the same buckling strength as a solid beam, provided the buckling/tension strengths of the component beams are not exceeded.

Tension: F=kR2

Beam under tension

•Failure occurs when tensile strength is exceeded.

•Maximum load is tensile strength times cross-sectional area.

•Load capacity does not depend on length.

Use Bridge Designer to calculate loads:

http://www.jhu.edu/~virtlab/bridge/bridge.htm

Tension members are in RED

Compression members are in BLUE

Design and construction ideas:

•Taller is better: note loads on these two structures.

Which is the better design and why (cont.)?

a) b)

a) b)

Calculate Tension & Calculate Tension & Compression Values for the Compression Values for the

Balsa BridgeBalsa Bridge Tension:Tension: F=kR F=kR22

Balsa wood k=19.9 MPaBalsa wood k=19.9 MPa

Compression: Compression: F= F= EEππ33RR44

64L64L22

Balsa wood E=1130 MPaBalsa wood E=1130 MPa E= young’s modulus (a measure of the E= young’s modulus (a measure of the

rigidity of a material, the large E is the less rigidity of a material, the large E is the less the material will deform when under stress)the material will deform when under stress)

Some properties of balsa wood (dry)

For comparison, cast aluminum (wet or dry):

1. Ultimate tensile strength ~10,000psi

2. Stiffness E~10,000,000psi

DensityDensity 150 kg/m150 kg/m33 .0054 lb/in.0054 lb/in22

Compressive Compressive StrengthStrength

12.1 MPa12.1 MPa 1750 lb/in1750 lb/in22

Tensile StrengthTensile Strength 19.9 MPa19.9 MPa 2890 lbs/in2890 lbs/in22

Elastic Modulus- Elastic Modulus- CompressionCompression

460 MPa460 MPa 66,700 lb/in66,700 lb/in22

Elastic Modulus- Elastic Modulus- TensionTension

1280 MPa1280 MPa 185,300 lb/in185,300 lb/in22

Design and construction ideas:

1. Don’t forget about the 3rd dimension. A good design in the x-y plane, may be a terrible one in the z-direction.

2. Plan the total bridge design. Estimate the weight of each of the components, so that you will not exceed the weight limit (95 grams).

3. Make a full-size pattern of your bridge. Build the bridge on this pattern. This will ensure that all components will assemble properly (use wax paper).

4. Rough cut members then sand to the desired length.

5. Common disqualifications:a. angles must be over 30 degrees. b. Gluing cannot go beyond 3mm from a joint.c. Mass of bridge <95 grams

Types of TrussesTypes of Trusses

Warren/ Neville Truss K Truss

Howe TrussPratt Truss

Use Bridge BuilderUse Bridge Builder

Go to Go to http://www.jhu.edu/~virtlab/virtual-http://www.jhu.edu/~virtlab/virtual-laboratory/laboratory/

StaticsStatics

Cantilevered truss--Firth of Forth rail bridge

Suspension--Golden Gate

New River gorge--largest single arched span (1978)