Posts Tagged ‘calculate’

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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 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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That Crazy Little Thing Called ZERO

July 4, 2018

Siri, what’s zero divided by zero?

Problems with Dividing by Zero

– Numberphile

Matthew Parker is an Australian stand-up comedian, author, YouTube personality and maths communicator.

Edible Zero. Really!

 

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Trick 6: Freaky Math Medium

May 27, 2018

Write the word carrot inside your math text book. Do not show students.

When Mathspig was a mathspiglet we used to play this trick. It doesn’t work on everyone, but it works  often enough.

Ask a student to say 15 times 15 fifteen times.

Then ask them to name a vegetable. Students say carrot 90% (I’m guessing) of the time.

To make this trick more dramatic send 10 students out of the class before you begin and tell the other half what you are about to do. Students return one at a time. How often do they say ‘carrot’? What % of students say carrot? 

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Maths News: Volcano Survivor 1

May 8, 2018

Kilauea erupts in Hawaii MAY 2018.

The amazing maths of volcano eruptions.

Can you out run a lava flow?

dantes_peak_ver2In every volcano disaster movie from Volcano (1997) with Tommy Lee Jones to Dante’s Peak (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow.

Is this possible? (See movie cliché busted by maths here.)

Now a lava flow from Hawaii’s Kilauea volcano is threatening tiny town of Pahoa, Hawaii again. (below).

1 Kilauea Volcano USGS

You will find excellent information about the Kilauea and other volcanoes at the

US Geological Survey here.

How to stop lava?

As the temperature of lava exceeds 10000 C there are very few ways to stop lava. According to the Taylor Kate Brown SMH (10 SEPT 2014) options include:

Bombing

Blasting (it with cold water)

Barricading it

Or adding concrete.

What if you are on your own.

Can you out run lava?

Lets do the maths.

Lava from Kilauea travels 17 yards per hour so the lava velocity is:

VL =   17 yds/hour = 15.5 metres /hour

(See Vox.com)

Mathspig simultaneous eqn 1

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

December 8, 2017