Why did the bridge fall into the Mississippi River?  bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=1 bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=1  bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=5 bridge+collapse&total=206&start=0&num=10&so=0&type=search&plindex=5

Google “NY Times bridge disasters” Google “NY Times bridge disasters” _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.  How much force does the chair exert?

What forces are on this person?  Sometimes the forces are not just up and down.  How much tension is in the ropes?

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 40 o, what are the forces? 60N F2 F1 40 o Half of the upward force comes from each member. A Look at point F1 for horizontal member. A B A

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

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 tension compression load

Now examine truss members. compression tension compressiontension compression

Use symmetry to examine members.  Which members are under  tension (like a string)?  compression (like a rod)? compression tension compression tension compression Load

Now examine truss members.  Now make load 100 N.  Calculate the member forces.  50 N = T 1 sin 60 o  T 1 = C 1  T 2 = 57.7 N cos 60 o  C 2 = T 1 cos 60 o + C 1 cos 60 o compression tension compressiontension compression T1T1 T2T2 C1C1 C2C2

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

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.

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.