Why Math Teachers should, um, speak proper!

Students can misunderstand teachers.

If math teachers mumble this is the result:

So I’m helping a Year 7 student. Smart kid. This is her test paper. 

NOTE: Students must hear terms clearly pronounced to learn them.

Simple Equation For Calculating Skyscraper Sway in an Earthquake

Skyscrapers swaying during earthquake in Japan from woahdude

A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.

This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

The Earthquake Engineering website offers a simple explanation.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

Earthquake Engineering

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.

Details Base Isolation Specialists

2. Shock absorbers or dampers are added to the structure to dissipate the seismic shock.

Details Damper Supplier

 

3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly vomit inducing (barfomatic?).

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Earthquake Engineering Maths

Take 1:

Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

But I’m going to use a student friendly equation from Wind Engineering for Large Structures.

Calculus Equation here.

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.

How far does the tallest buidling in the world SWAY in an earthquake?

Earthquake Engineering Maths

Take 2:

Structural Engineer Ron Klemencic explained on the Discover News that a simple rule of thumb for calculating skyscraper sway was to simply divide the buildings height in by 500 because the building codes demand the building fit a 1:500 sway ratio.

The tallest building in the world at 2,716 feet (828m), the Burj Khalifa, Dubai, would sway back and forth about 5.5 feet or 1.7 m.

Ahhhhhhhhh!  But you would have to drag Mathspig onto the 168th floor screaming.

But mathspigs you can work out the sway on the top ten tall buildings in the world.

Stunning Art based on Maths

Adam R McCausland is a Belfast-based graphic designer whose stunning works incorporate maths themes.

Here is his work (below) titled Fibonacci / Poinsettia

This work (below) is titled: At theHeart of it all. I’ve never seen mirrored Fibonacci curve before. Fascinating. 

What fibonacci art can your class make today?

You can find more of Adam’s inspiring maths art works here.

Trick 1: The Great MATHoudini

The Great MATHoudini

Requirements: 1 phone book, Great showmanship

Start by handing one member of the class a sealed envelope. It contains a name that you have seen in your mathematical mind.

All will be revealed at the end of the performance.

Ask one student to write a 3-digit number on the board.

Ask a second student to turn this number around and subtract the smallest number from the largest number.

Ask a third student to turn that number around and add the last two numbers.

Example: N1 = 371.

N2 = 173

N1 – N2 = N3 = 371 – 173 = 198

N4 = 891

N4 – N3 = 891 + 198 = 1089

Give a fourth student a phone book. Ask them to go to page 108 and count down 9 places on the first column and read out the name.

Now open the envelope.

Da! Da!

 

How does it work? The numbers ALWAYS add up to 1089 so you had plenty of time to check out the name in the phone book.

Source: Magic/Menatalism Tips and Tricks

Death by Caffeine: The Maths Part 1 METRIC

Death by Caffeine: The Math  Part 1 USA UNITS here.

The lethal dose for caffeine is about 150 milligrams per kg of body weight. While the average person’s caffeine consumption is around 200 milligrams a day, the Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 48 kg. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal. 

See Death by Caffeine: The Maths Part 2 METRIC

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.

 

Death by Caffeine: The Math Part 1 USA UNITS

Death by Caffeine: The Maths  Part 1 METRIC here

The lethal dose for caffeine is about 68 milligrams per lb of body weight. Average consumption of caffeine is about 200 milligrams a day. The Mayo Clinic advises against exceeding 500 to 600 milligrams per day.

 This work titled Timing is Everything is by street artist ABOVE in London.

You may want this much energy but be warned, energy drinks can kill.

It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 110 lb. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal. 

See Death by Caffeine: The Math Part 2 USA UNITS

Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.