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Unit 16 Mathematics Bend allowance

Unit 16 Mathematics Bend allowance. Aim To understand the calculation of bend allowance and to identify how it is used in a practical environment. Objectives The learner will be able to identify the different parts of the bend allowance calculation.

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Unit 16 Mathematics Bend allowance

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  1. Unit 16 Mathematics Bend allowance Aim To understand the calculation of bend allowance and to identify how it is used in a practical environment. Objectives The learner will be able to identify the different parts of the bend allowance calculation. The learner will be able to correctly complete four bend allowance calculations The learner will be able to describe the link between the neutral line and the coefficient / k-factor.

  2. What is Bend Allowance? • Bend allowance is a calculation used to find the measurement required to accommodate bending material. • The bending of the material varies with the thickness of material and the type of material being bent. • The variable in bend allowance is know as the ‘coefficient/K-factor’. It is a variable between different materials.

  3. What is bend allowance identifying ? • When the plate is bend the outer radius of the material is under tension and expands. • The inner radius of the bend is under compression and shrinks. • There is a part of the bend between the tensioned outer radius and the compressed inner radius that is unaffected this is know as the “Neutral Axis” and this is what is used to determine the length of material need to create the correct sized piece of work.

  4. What is the Bend allowance calculation? 2pq[(T x k-factor)+R] 360 Angle of Bend The percentage of the thickness to find the neutral axis depth Internal bend radius Thickness of material Pi Degrees in a circle

  5. R 2p 2pq[(T x k-factor)+R] 360 The green section is the calculation 2pR which will gives the circumference of the internal radius.

  6. q = one sixth 360 60 ÷ 2pq[(T x k-factor)+R] 360 In the red section the ‘theta’ is the bend of the angle and the 360 is the complete degrees in the circle. It is used to give the proportion of the circumference the bend angle is acutely covering to get the correct distance of the material on the bend. A simple analogy of this is that if the bend was to be 60◦ it would be one sixth of the circumference.

  7. (T x k-factor)+R 2pq[(T x k-factor)+R] 360 5 + 6 = 11 (10 x 0.5)+6 The yellow section calculates the adjustment to be added to the internal radius so the bend is calculated to the ‘Neutral axis’. So if the internal radius is 6mm, the thickness of the material is 10mm and the k-factor is 0.5 (10 x 0.5) + 6 = 11. The neutral radius is 11.

  8. Working example You have been asked to work out the length of material required to make the angled bracket show. • What are the values we know? • What values do we need to find?

  9. Known Values • The bracket is bent to 60◦ • The base leg length is 122 to the apex of the angle. • The upper leg length is 130 to the apex of the angle. • The material thickness is 6 • The internal radius is 7 1 3 5 4 2

  10. Unknown Values • Where the internal radius begins to curve on the upper and base legs • The correct length of the base leg • The correct length of the upper leg • What angle is the plate actually bent through? 3 1 2

  11. What angle is the plate actually bent to? The piece of material is bent from a flat position so if the final internal angle is 60◦. The material has actually been bent through 120◦ to create the 60◦. So in the bend allowance calculation the angle of the bend is the external angle.

  12. Finding unknown values 1, 2 & 3 Using three of the values we know we can find the missing values 1, 2 & 3. • From the centre of the internal radius make two lines square to the base and upper leg as shown. • Once this has been done draw a line from the apex of the angle through the centre of the internal radius. This will half the inner angle. • There are now two right triangles bisecting the bend of the plate. We can now work out the length of the straight legs of the bracket 1 2 1

  13. Formula required :- Tangent = O A Tan 30◦ = O A Thickness 6 + Internal radius 7 = A = O Tan 30◦ H O A = 13 0.5773 13 30◦ A = Unknown distance to the beginning of the bend A = 22.52

  14. Minus 22.52 from both leg length ‘A’ & ‘B’, we now have the true length of each straight and the beginning and end of the curved section. A C B

  15. 2p120[(6 x 0.4)+7] 360 2pq[(T x k-factor)+R] 360 True length of C is 19.69 2p120[2.4+7] 360 2p1209.4 360 7087.433 360

  16. Material length = 226.65 The amount of material needed is 226.65mm A = 107.48 B = 99.48 C = 19.69 A 107.48 + 99.48 + 19.69 C B

  17. Bend allowance on bends over 90° When doing bend allowance for angles under 90° the calculations for finding the true lengths change. This is due to the change in position of the two intersecting triangles used to find the true lengths of the flats The material is 6mm thick

  18. Firstly the triangle we need must be identified. Formula required :- Tangent = O A 60° The angle of this section will be the what is left over from 180° 30° Tan 30◦ = O A 14mm O = A x Tan 30◦ O = 14 x 0.5773 O O = 8.08

  19. Now complete the calculation for the full length of the material 2pq[(T x k-factor)+R] 360

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