Why did the bridge fall into the Mississippi River?

http://video.google.com/videoplay?docid=3263883846239520364&q=mississippi+bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=1

http://video.google.com/videoplay?docid=4039086257157184244&q=mississippi+bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=5

Google “NY Times bridge disasters”http://www.nytimes.com/ref/us/20070803_BRIDGE_GRAPHIC.html#step1

Go to Multimedia (down page middle column)

Construction is about static equilibrium (statics)

Statics = no motion (almost). All forces equal zero. All torques equal zero.

What is a force? A force is a push or pull on an object.

Are there forces on you now?

Gravity is pulling you down. The chair is pushing you up. Total forces are zero.

kg

N

lb

kglbF

maF

8.92.2

150

How much force does the chair exert?

NF 668

What forces are on this person?

Sometimes the forces are not just up and down.

How much tension is in the ropes?

NNF 1502300

Forces are often at an angle.

In equilibrium, net forces must be zero both

Right & left

Up & down

Vectors have magnitude and direction.

Find horizontal and vertical parts.

Simple triangle shows horizontal and vertical parts.

Google “Walter Fendt applet”.

Do equilibrium of three forces.

Calculate the vertical and horizontal forces.

If the angle at the top is 40o, what are the forces?

NNBN

B

8.1034.09.319.31

20sin

60N

F2F1

40o

Half of the upward force comes from each member.

A

NN

A

A

N

9.3194.0

30

3020cos

Look at point F1 for horizontal member.

A

B

A

Use Bridge Designer Google “jhu bridge designer” Calculate the forces on a triangle.

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

Statics in bridges.

Examine triangle members.

Look at any point on bridge. Forces = 0 and torques = 0. Determine which members are under

tension (like a string)? compression (like a rod)?

compression

tensioncompression compression

load

load

Now examine truss members.

compression

tensioncompression tension

compression

Use symmetry to examine members.

Which members are under tension (like a string)? compression (like a rod)?

compression

tensioncompression

tension

compression

Load

Now examine truss members.

Now make load 100 N. Calculate the member forces.

50 N = T1 sin 60o T1 = C1 T2 = 57.7 N cos 60o C2 = T1cos 60o + C1 cos 60o

compression

tensioncompression tension

compression

T1

T2

C1

C2

Use Bridge Designer Google “jhu bridge designer” Calculate the forces on a triangle.

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

Support a book with one sheet of paper and four 2" pieces of tape.

Judged based on weight (1 pt per 100 g) height (1 pt per cm)

Does your design change depending on how the scoring is calculated?

• add or multiply two factors

Problem 1

The traction device is applied to a broken leg as shown. What weight is needed if the traction force pulling the leg straight out (right) is 165 N? (The tension in the rope equals the weight.)

Problem 2

Students want to hang a 1200 N cannon from ropes on the football goalpost as shown. If the goalposts are 5 meters apart and the ropes are 3 meters long, would a rope which breaks at 1000 N be good enough?

Problem 3

A stop light is held by two cables as shown. If the stop light weighs 120 N, what are the tensions in the two cables?

Value of symmetry

There are only 3 unique members. a, c, e

Use Bridge Designer Google “jhu bridge designer” Calculate the forces on a triangle.

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

Which truss members are compression / tension?

Does strength depend only on the material properties?

Is paper very strong? How can you make paper stronger.

Make a cylinder Fold it into pleats

Make a beam from a popsicle stick.

Place the popsicle stick flat (horizontal) on two weights. Push down in center with your finger. How much bending do you observe? Now flip stick to vertical orientation. Push again. Any difference?

Failure from bending under perpendicular force

The perpendicular force (load) deforms the material.

The top half is compressed. The bottom half is pulled apart. Finally the tension breaks bonds

failure.

I beams are strong and light weight. Depends on top and bottom

and distance between. Larger separation makes I

beams stronger.

I beam’s strength is in its shape.

The top is under compression. The bottom is under tension. The center-line is neutral.

Truss works because the middle of the beam does little.

Top is under compression. Bottom is under tension.

A truss is like the bridge

You can drill out the center of a beam without losing much integrity.

Trusses are cheaper than beams.

Why are trusses made of triangles not rectangles?

Second condition for equilibrium. All torques at a point must be zero.

Make a popsicle rectangle.

How stable is it?

Gates have cross piece.