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Formulae useful in Construction

Formulae useful in Construction. Pythagoras' Theorem can be written in one short equation: a 2 + b 2 = c 2. c is the longest side of the triangle a and b are the other two sides. Definition. The longest side of the triangle is called the hypotenuse , so the formal definition is:

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Formulae useful in Construction

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  1. Formulae useful in Construction

  2. Pythagoras' Theorem can be written in one short equation:a2 + b2 = c2 c is the longest side of the triangle a and b are the other two sides

  3. Definition The longest side of the triangle is called the hypotenuse, so the formal definition is: In a right angled trianglethe square of the hypotenuse is equal tothe sum of the squares of the other two sides. • http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/pythagorastheoremact.shtml

  4. Building a staircase C A B

  5. How to work out the length of STAIR STRING 36cm2 C = ? A = 6cm 64cm2 B = 8cm

  6. How to work out the Pitch + 36 cm2 64 cm2 = 100 cm2

  7. How to work out the Pitch You now need to find the square route of 100 cm. What number can you multiply by itself to get 100? 10 x 10 = 100 The square route of 100 is 10 This is the symbol we use to show square route = √ The answer to C is 10 cm C = 10 cm

  8. Stair calculations Measure the height of the staircase.

  9. Calculating the length of a stair string using pythagorAs Assuming a total rise of 728 mm from Finished Floor Level to Finished Floor Level and the Total going is 760 mm. Total Rise 728 mm Total Going 760 mm

  10. CALCULATING STEPS Once we have determined the stair string, we now need to estimate how many steps are needed by calculating the rise and going.

  11. Calculating the rise • Estimate how many steps you will need. • Suppose 4 steps were needed. • First divide 728 mm (the total rise) by 4 to determine the height of each individual riser. • 728 mm ÷ 4 = 182 mm.

  12. Calculating the step going The total going is 760 mm. Divide the total going by 3, which is one less than the number of risers; the landing forms the top step. This gives the width of each individual tread. 760 mm ÷ 3 = 253.3 mm (which is rounded to 253 mm).

  13. The sum of the going Total Rise of 728mm and a Total Going of 760. The sum of the going is: 2 x Rise + Going must fall in between 550 - 700mm. 4 risers @ 182mm and 3 goings (treads) @ 253mm.Therefore the sum of the going is:182 + 182 + 253 = 617.In a private staircase if the rises and goings fall in between: 155 - 220 rise with a 245 - 260 going or 165 - 200 rise with a 220 - 350 going The angle formed will be in between the acceptable limits for a max pitch of 38 – 42 degrees. 1052.4 cm 728 cm 38⁰ - 42⁰ 760 cm

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