The Tau Beta Pi Association MindSET Bridges Module Worksheet Created by Lockheed Martin and Florida Delta
Facilitate any questions or activities that the lecture presenter may have. If the students have questions, make sure that they are heard and seen. Help set up any activities prior to beginning the lecture.
The first bridges were designed by nature herself. Perhaps it was simply a log that fell across the river. Since then, man has used bridges to cross great distances across treacherous terrain. There are many things to be thought of when making a bridge.
How much does it have to hold? What is going to be used for? What materials should it be made of? How far does it have to span?
Answer any questions that the students may have about forces or bridges. To explain
compression, stand on a low surface and explain how you are pressing on the object, much like crushing a can. To explain tension, use a rubber band and show how the pulling force causes the band to disfigure and stretch, the same happens to metal and bridge materials.
There are many types of bridges that support many types of transportation. There are bridges that are held up by a pulling force, some that stand on their own, and a few that support weight simply by the strength of the material.
Suspension bridges have the deck held up by cables that are tied to tall support beams at strategic points along the length of the bridge. This pulling force is called tension.
Introduction
Bridge Technology
Arch bridges support a load by distributing the weight across the apex, highest point, of an arch. The weight on any single point along the deck gets spread out so that more of the arch can support it. The whole arch is
under compression. This is the Possum Kingdom Masonry Arch Bridge in Texas.
Beam bridges are decks suspended by columns, or beams. When a load, the item supported, is put on the deck, the end beams pull on it from both ends. This is tension. The weight of the deck and the load push down and compress the beams.
This is the Seven Mile Bridge that connects the Florida Keys to the mainland.
Truss bridges are made from sections that are usually straight and connected in such a way that as a load moves across the deck, it is possible for the section to be first in compression then in tension. A few different designs exist and most use the advantages of triangles to get their strength. In the bridges below, notice that the truss can be below, or above.
Engage the students in conversation. Make sure that they read this material that way they’re all on the same page. Make certain that they understand each vocabulary word as it is covered an provide examples of the different units if more clarification is needed.
Bridges have a variety of things that can be measured. The length of the members, the width of the deck, the weight of the load, the force on the different components of the bridge, these are all things that can be measured. It is important to know how to analyze the units associated with these measurements, that way it is easier to see how the different numbers match up.
Units: units are defined amounts of a certain thing. They are standard across the world and can be transferred from one unit to another. An example of this is the dollar. The dollar is the unit for the American currency system. It can be converted into Japanese Yen. There are two requirements to converting units.
You need to know the ratio between one unit and the other unit
They both have to be units of the same thing.
Dollars and Yen are both money.
Measurements of any quantity involve comparison with some precisely defined unit value of the quantity. For example to measure the distance between two points we need a standard unit of length. A unit of distance is the meter. If you say that a distance between two points is 25 meters it means that:
The distance is 25 times the length of a unit meter.
A meter stick will fit into that distance 25 times.
Remember that it is important to include the unit, in this case meters, along with the number 25. To say that the distance between two points is 25 is meaningless because there are other units of measuring distance such as feet, miles, or kilometers. Also, since these are all units of length, you can convert meters to feet and back.
Units
Three main types of units: Length, time, and mass. The two systems of units are the metric system and the U.S. customary system.
The metric system is the most common system of measuring units. The standard unit of length is the meter, the standard unit of time is the second, and the standard unit of mass is the kilogram.
The U.S. customary system is the official system used only in Burma (Southeast Asia), Liberia (west coast of Africa), and the Unites States. This is according to the CIA World Fact Book of 2006, which is a book about all the countries in the world. The standard unit of length is the foot, for time it uses the second, and the unit of mass is the slug. Note that in the U.S.
customary system it is uncommon to measure mass, instead the force of the earth’s gravity on an object’s mass is measured, this is called weight. The standard unit of weight is the pound.
What can happen when units aren’t taken into account:
The Mars Climate Orbiter in 1998 was intended to enter orbit at an altitude of 140–150 km (460,000-500,000 ft.) above Mars. However, a navigation error caused the spacecraft to reach as low as 57 km (190,000 ft.). What happened? Two different teams of
engineers calculated the distances using two different systems of units and didn’t convert to each other’s systems. How much money did the mistake cost? $325 million.
As the students work through this section tell them how units have helped you solve problems, or of a time that using the wrong units caused you to miss something. Make sure that they understand that a number divided by itself is 1, and it is unit-less.
All physical quantities contain both a number and a unit. Suppose we want to convert 240 km to miles (mi). Using the fact that 1 mi = 1.61 km, we divide each side of this equality by 1.61 km to obtain:
1 mi = 1.61 km 1mi
1.61 km = 1.61 km
1.61 km 1.61 km1mi = 1
Because any quantity can be multiplied by 1 without changing its value, we can now change 240 km to miles by multiplying by the factor (1 mi) / (1.61 km):
240 km = 240 km X 1mi
1.61 km =149 mi
Unit Conversion
The factor (1 mi) / (1.61 km) is called a conversion factor. All conversion factors have a value of 1 and are used to convert a quantity expressed in one unit of measure into its equivalent in another unit of measure.
For this section, ensure that the students see the pattern of crossing out units diagonally, a unit over itself is unit-less and can be canceled out.
How many seconds are in a year assuming a year has 365 days?
1 yr X 365 days
1 yr X 24 h r 1 day X
60 min
1 h r X 60 s
1 min = 31,536,000 s
Notice that we’re converting years to seconds, both units of time. This is very important, for example, it wouldn’t make sense to convert time to weight.
Now you try it!
FROM US CUSTOMARY TO METRIC
SYMBOL WHEN YOU KNOW MULTIPLY
BY
TO FIND SYMBOL
LENGTH
in inches 25.4 millimeters mm
ft feet 0.305 meters m
yd yards 0.914 meters m
mi miles 1.61 kilometers km
AREA
in2 square inches 645.2 square
millimeters
mm2
ft2 square feet 0.093 square meters m2
yd2 square yard 0.836 square meters m2
ac acres 0.405 hectares ha
mi2 square miles 2.59 square
kilometers km2 VOLUME
fl oz fluid ounces 29.57 milliliters mL
gal gallons 3.785 liters L
ft3 cubic feet 0.028 cubic meters m3
yd3 cubic yards 0.765 cubic meters m3
oz ounces 28.35 grams g
lb pounds 0.454 kilograms kg
T short tons (2000 lb) 0.907 megagrams (or
"metric ton")
Mg (or
"t") TEMPERATURE
oF Fahrenheit (F-32) x 5 / 9
or (F-32) / 1.8
Celsius oC
ILLUMINATION
fc foot-candles 10.76 lux lx
fl foot-Lamberts 3.426 candela/m2 cd/m2
FORCE and PRESSURE or STRESS
lbf poundforce 4.45 newtons N
lbf/in2 poundforce per square
inch 6.89 kilopascals kPa
There are 5,280 feet in one mile. How many feet are in one kilometer?
5280 feet
1 mile x 1 mile
1.6 1 kilometers=3,279.5 feet per kilometer
A fortnight is two weeks long. How many minutes are in a fortnight?
1 fortnight x 2 weeks
1 fortnight x 7 days
1 weekx24 hours
1 day x60 minutes
1hour =20,160 minutes Be prepared to answer the following question:
How come in the previous problem 5280 feet was placed on the numerator side of the fraction, and in the fortnight problem, the fortnight was placed on the denominator?
The rule is this: the top unit is in the bottom unit. There are twelve donuts in a dozen, 5,280 feet in a mile, 2 weeks in a fortnight. Also this generally only applies to the first term and if that doesn’t work and they end up with upside down units, dividing 1 by that umber (i.e. the reciprocal) will give them the right units and answer.
A pound is 16 ounces. With 78,000 ounces of chocolate chips, how many tons would you have?
78,000 ounces x 1 lb
16 ouncesx 1 ton
2,000 lbs=2.4375 tons
Make sure the students read and understand the example before they attempt the “Now you try it!” section. When they get to the examples, help them, but do not do the problems for them. Explain how this skill has been relevant to you in your job or schoolwork.
Sometimes we don’t need to convert from one unit system to another, but knowing the different conversion factors helps. Sometimes we are given one quantity in terms of another quantity.
Example: There are four wheels per car. At TBP Dealership, we have 35 cars, and need to replace the tires on all of them. How many wheels do we need?
4 wheels
1 car x 35 cars=140 wheels
That is a simple example, problems can get much more complicated.
Example: John, from Britain, tells Macy, in Florida, that he pitched a ball at 45 meters per second. Macy thinks that’s slow, but doesn’t really know anything about meters per second.
She’s used to miles per hour. How many miles per hour did John pitch his baseball?
45 meters
1 second x60 seconds
1minute x60 minutes
1 hour x 0.305 feet
1 meter x 1mile
5,280 feet=100.7 mph
The fastest ball ever pitched and recorded officially in the Guinness World Book of Records clocks in at 100.9 mph by Nolan Ryan of the California Angels in 1974. Faster balls have been
observed, but this is still the fastest, officially.
Now you try it!
Michael gets a report of pipes breaking in his oil refinery. Since he is the lead mechanical engineer it’s his responsibility to figure out why they’re breaking. He knows that the 6 inch PVC pipes are supposed to be holding 106 psi (pounds per square inch) of pressure, but will only burst at 560 psi. He sends Norman to check the pressure in the pipes, and Norman comes back and tells Michael that he measured 3,815,000 Pascals in the pipes. Michael doesn’t panic, and calculates if that’s enough force to break his pipes. What did he find?
3,815,000 pascals x 1 kilopascal
1,000 pascals=3,815 kilopascals 1 psi
Using Units to Solve Complex Problems
Although the measurement isn’t large enough to burst the pipes, it’s more than 5 times the size it ought to be, so the pipes could be breaking because of this. Michael orders the pressure reduced in the pipes.
Measure how long it takes you to walk 20 ft using a timer. How fast were you going in miles per hour?
¿¿ 20 ft
X X seconds x 1 mile
5,280 feet x60 seconds
1 minute x60 minutes
1hour =¿miles ¿
hour∨mph
Scales are useful tools to represent something that is very large in a small way. The same can be said of something very small, made to look large. Maps usually have a scale. For one inch of length on a map, it could mean 100 miles in reality. A model car can be a fraction of the size of a real car. A drawing of an atom is usually millions of times bigger than the atom it is representing.
The distance from the Earth to the Sun is 149,600,000 kilometers at its closest. You know this because the scale on your map reads “2 cm = 18,700,000 km.” How long is the line you traced on your map?
149,600,000 km 18,700,000 km =4
It is four units long, each unit is 2 cm 2 cm x 4=8 cm
Now you try it!
A model replica of the Statue of Liberty is 10 inches tall. You know that the real statue is 151 feet tall. What is the scale of the model?
151 feet x12inches
1 foot =1,812 inches 1,812 inches
10 inches =18.12inches per inch This is approximately one foot and a half per inch.
During lunch, a few volunteers should return to the room to help set up for the activity.
Afterwards, join a team and have fun!
You have been hired to design and build a bridge by the town mayor. He has these requirements in mind:
Scale
Activity – Build A Bridge
Gap to span: 200 feet
Min width: 1 lane
One lane is 8 feet 4 inches wide
You will see the use in this later, in determining the bridge “capacity”
Bridge can only be built using local materials
The mayor wants a report on how you designed your bridge
You decide you’re going to build the mayor a model bridge. The 200 foot span will be 12” long.
What is your scale?
How wide is your scale lane?
At the end of his busy day the Mayor will decide which bridge to commission. Read the rules and competitions included in the report worksheet carefully.
Rev 07/21/2009
