Posts Tagged ‘simple’

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Simple Equation For Calculating Skyscraper Sway in an Earthquake

October 2, 2018

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.

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

October 2, 2018

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.

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Trick 2: The Math Teacher Knows

August 4, 2018

……………………………………………………………………………………

The Math Teacher Knows Everything

Requirements: 1 die, a fanfare would be nice.

You will find a fanfare here.

Ask a student to roll the die, double the number and add 5.  He can show the class the number, but not you.

Ask the student to multiply this number by 5.

Ask the student to roll the die again and add this number to the total.

Now you can tell them the numbers they rolled.

Example:

N1 = 3

Double: 2N1 = 6

Add 5: 2N1 + 5 = 11

x5:   5(2N1 + 5) = 55

Roll dice:

N2 = 4

Add 4:

55 + 4 = 59

The Math Teacher Knows:

Secretly subtracts 25 from this number:

59 – 25 = 34

Da! Da! There are the two numbers rolled.

Source: Magic/Menatalism Tips and Tricks

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Trick 3: Maths Swami Knows Your Age and Foot Size

July 9, 2018

Maths Swami 1: A Magic No.

Maths Swami 2: I Know Your Birthday

Requirements: Calculator and spooky demeanor

Imagine your birthday was 24 September 1973.

Written as an American date (not UK or Australia) this would be:

9-24-73.

Give the calculator to a student:

Take birthday month and add 18:

9 + 18 = 27

x 25

27 x 25 = 675

– 333

675 – 333 = 342

x 8

342 x 8 = 2736

– 554

2736 – 554 = 2182

Divide by 2

2182/2 = 1091

Add day of birthday date

1091 + 24 = 1115

x5

1115 x 5 = 5575

+ 692

5575 + 692 = 6267

x 20

6267 x 20 = 125340

Add the last two digits only of your birth year

125340 + 73 = 125413

– 32940

125413 – 32940 = 92473 = 9-24-73

Yes! Yes!

Hint: It probably would be easier to ask them for their birthday. Ha! But Maths Swami’s are mysterious beings.

You will find a video link on Youtube

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Trick 5: Cool Math Trick

June 4, 2018

Requirements: A Pack of Cards and a willing assistant.

Take 10 cards from pack including the 10 Diamonds.

Lay out card in 3 columns in a pattern of 4 down, 2 down, 4 down.

Put the 10 Diamonds at the top of the  left hand column.

Group students around. You turn your head away and ask a student to point to a card.

You carry on, think allowed and then ask your assistant to point to cards asking:

Is it this one?

No.

Is it this one?

No.…………………………………………………………………………………

When your assistant points to the 10 Diamonds he will show you the position using the diamonds. The cards are laid out on the table in the pattern of the diamonds on the 10 Diamonds.

Whenever your assistant asks is it this one? You will know.

See Mentalism Card Trick:

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Trick 8: Spooky Maths Magic

May 4, 2018

Spooky Maths Magic

Requirements; Smart board/data projector.

 This is mental maths, but not hard maths. You can play this video by Marco Frezza  directly to the class.

It may not work on everybody, but it would be very interesting to see how many students are fooled by this spooky magic man.

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1. Maths is BORING!

December 9, 2017

Middle School Maths that is AMAZING

psst! That means it’s not boooorrrrinng!

NEW POSTS!

1a. The WORLD POPULATION as ONE BIG CROWD … METRIC

1b. The WORLD POPULATION as ONE BIG CROWD … USA Units

2a. If all the cars in the world were parked together what area would they cover? Metric Units

2b. If all the cars in the world were parked together what area would they cover? USA UNITS

3. If you put the population of the world into AUSTRALIA what area in m2 would we get each?

Meanwhile this Mathspig blog is full of AMAZING middle school maths such as:

KARATE MATHS

HOW MUCH BLOOD CAN YOU LOSE AND SURVIVE?

WHAT VOL OF ALCOHOL IS LETHAL FOR TEENS?

THE TERRIFYING MATH OF RUNNING FROM A BEAR USA UNITS

THE TERRIFYING MATHS OF RUNNING FROM A BEAR METRIC UNITS

PARABOLAS AND THE ART OF SPIITING WATERMELON PIPS