Calculations

Calculations

• Copes from rectangular openings

  The length and depth of a cope read from a box-shaped opening.

  length = round(reach × 2) ÷ 2; depth = round(reach × 2) ÷ 2

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Bolts from fasteners

  The diameter, length, head point and direction of each bolt read from the file.

  d, length rounded to 0.1 mm; head rounded to 0.001 mm

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• A number in the file

  How each length and coordinate is written.

  text = toFixed(2); |v| < 0.005 → 0.00

  DSTV NC files nc1.js

  • DetailCraft
  64-bit

• Header sizes and weights

  The length, section sizes, weight and paint surface written in the header.

  plates: weight = t × steel density ÷ 1000 (kg/m²); others: paint surface = perimeter ÷ 1000

  DSTV NC files nc1.js

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  64-bit

• Skew cut angles of a mitre

  The web and flange cut angles written in the header for a mitred I-shape.

  web = −atan(kv) × 180 ÷ π; flange = atan(ku) × 180 ÷ π

  DSTV NC files nc1.js

  • DetailCraft
  64-bit

• Web contour with copes

  The outline of the web face, notched for copes or ending on the mitre cut.

  cope corners at (length, depth), (L − length, depth), (L − length, h − depth) …

  DSTV NC files nc1.js

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• Flange contour after copes

  Where a flange starts and ends once the copes on its side are cut.

  x0 = cope length when cope depth ≥ t, else 0

  DSTV NC files nc1.js

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  64-bit

• Contours at a mitre end

  The end points of the web and flange contours where a plane cut crosses them.

  x = x0 + ku·u + kv·v at the web's middle plane and at each flange's outside face

  DSTV NC files nc1.js

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  64-bit

• Hole positions on each face

  The x and y of each hole in the file's own face coordinates.

  web: y = offset + d ÷ 2; flange of an I: y = bf ÷ 2 − offset; plate: y = offset + b ÷ 2

  DSTV NC files nc1.js

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  64-bit

• Reading an NC file back

  The header values and block rows read from an NC file.

  DSTV NC files nc1.js

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  64-bit

• ASTM bar sizes in metric

  The diameter, mass per meter, area and bend diameter of bars #3 to #11.

  d_b = in × 25.4; mass = lb/ft × 1.48816394; area = in² × 645.16; bend D = 6·d_b (to #8) or 8·d_b

  Reinforcing bars and the bending schedule rebar.js

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• Metric bar area and mass

  The section area and mass per meter of bars H8 to H40.

  area = π·d² ÷ 4; mass = area × 7850 × 10⁻⁶

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Number of bars and their spacing

  How many bars go across a width at no more than a given spacing, and the spacing that results.

  n = max(2, ⌈w ÷ s − 1e-9⌉ + 1); spacing = w ÷ (n − 1)

  Reinforcing bars and the bending schedule rebar.js

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• Hook leg length

  The out-to-out length of a standard 90 degree hook leg.

  ASTM: D ÷ 2 + d_b + 12·d_b; BS: the tabulated end projection P

  Reinforcing bars and the bending schedule rebar.js

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• Cut length of a bent bar

  The length of bar to cut for a straight, L or U shape given its out-to-out sizes.

  ASTM L: A + B − 2k + (π ÷ 2)·r_c; U: A + B + C − 4k + π·r_c; k = D ÷ 2 + d_b, r_c = D ÷ 2 + d_b ÷ 2; BS L: A + B − 0.5r − d; U: A + B + C − r − 2d

  Reinforcing bars and the bending schedule rebar.js

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• Center line of a bar

  The center line of a bar in its own plane as straight pieces and quarter-circle arcs.

  arc radius r_c = D ÷ 2 + d_b ÷ 2; points c + r_c·(cos a, sin a)

  Reinforcing bars and the bending schedule rebar.js

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• Length of a center line

  The length along a bar's center line.

  Σ straight lengths + Σ r·π ÷ 2

  Reinforcing bars and the bending schedule rebar.js

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• Bottom mat bars

  The size, shape, count and position of the bottom bars each way.

  A = run − 2·cover; hook B = min(hook leg, room); offset_i = −width ÷ 2 + cover + d_b ÷ 2 + i·spacing

  Reinforcing bars and the bending schedule rebar.js

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• Starter bars

  The length and position of each starter bar.

  z0 = bottom + cover + d_bX + d_bY; A = top + projection − z0; position = ((i − (n − 1) ÷ 2)·s_x, (j − (n − 1) ÷ 2)·s_y)

  Reinforcing bars and the bending schedule rebar.js

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• Clear spacing check

  Warns when bars are closer than the minimum clear spacing.

  clear = spacing − d_b ≥ max(25.4, d_b) for ASTM bars, max(20, d_b) for BS bars

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Concrete volume

  The volume of a footing in cubic meters.

  V = L × B × H × 10⁻⁹

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Bar marks and schedule weights

  Groups identical bars under one mark and totals their length and weight.

  total length = length × count; weight each = mass × length ÷ 1000; total weight = weight each × count

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• The schedule as a table

  The figures printed in the bending schedule and its export.

  sizes and cut length: whole mm; total length: m, 2 decimals; kg/m: 3 decimals; weights: 2 and 1 decimals

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• A dimension figure

  The number printed on a dimension line of the shop drawing.

  figure = round(value)

  Single-part shop drawing shop.js

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  64-bit

• Hole stations along the part

  The chain of dimensions from the start of the part through each hole to its end.

  step_i = x_i − x_{i−1}; overall = L

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Scales of the view

  The scale along the part and the scale across it.

  first n in the list with size ÷ n ≤ room; paper = X0 + x ÷ n

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Mitre cut angles

  The angle from square of each cut end, in the web's plane and across the flanges.

  angle = atan(|k|) × 180 ÷ π, 1 decimal

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Weight in the title block

  The weight of one part and of the whole quantity.

  total = weight × count

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Risers, run and pitch

  The number of risers, the riser height, the run and the pitch.

  n = max(2, ⌈rise ÷ max riser − 1e-9⌉); r = rise ÷ n; run = (n − 1)·going; pitch = atan2(r, going)

  Straight stair geometry stair.js

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  64-bit

• Stringer axis

  The line the stringers run on, and where it meets the lower and upper floor.

  k = r ÷ g; drop = (depth ÷ 2 − 50) ÷ cos(atan k); z(a) = k·(a + g) − drop; a0 = drop ÷ k − g, a1 = (rise + drop) ÷ k − g

  Straight stair geometry stair.js

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  64-bit

• Tread plates

  The size and position of each tread.

  depth = going + nosing; middle = (i − 1)·going − nosing + depth ÷ 2; top = i·r

  Straight stair geometry stair.js

  • DetailCraft
  64-bit

• Riser, going and comfort checks

  Warnings when the riser, the going or twice the riser plus the going is outside its range.

  102 ≤ r ≤ 178; going ≥ 279; 600 ≤ 2r + going ≤ 650

  Straight stair geometry stair.js

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  64-bit

• Rotation about a vertical line

  The matrix and offset that turn points about a point in plan.

  A = [[c, −s], [s, c]]; t = center − A·center; c = cos(deg·π ÷ 180), s = sin(deg·π ÷ 180)

  Move, rotate and mirror transform.js

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• Mirror in a vertical plane

  The matrix and offset that reflect points across a line in plan.

  A = 2·d·dᵀ − I; t = p₁ − A·p₁; d = (p₂ − p₁) ÷ |p₂ − p₁|

  Move, rotate and mirror transform.js

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• A point through the transform

  The new position of a point.

  p′ = A·p + t

  Move, rotate and mirror transform.js

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• Cleaning a stored coordinate

  The rounding applied to every coordinate and angle a transform stores.

  |n − round(n)| < 10⁻⁶ → round(n); else round(n × 10⁶) ÷ 10⁶

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A member's new rotation

  The rotation that puts a member's section axis where the transform sent it.

  rotation = atan2(−want·u₀, want·v₀) × 180 ÷ π, brought into 0 to 360

  Move, rotate and mirror transform.js

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  64-bit

• A member through the transform

  The new end points, rotation, position, holes and copes of a member.

  Move, rotate and mirror transform.js

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  64-bit

• Mirrored angle with a top or bottom position

  Shifts a mirrored angle's line so the steel lands where the mirror image is.

  d = A·v̂·voff − v̂′·voff; start, end += d

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A footing through the transform

  The new position and rotation of a footing.

  rotate: rot + deg; mirror: 2·φ − rot; both brought into 0 to 360

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Center of a selection

  The plan middle of the selection, used as the point to rotate about.

  ((x_min + x_max) ÷ 2, (y_min + y_max) ÷ 2, z_min)

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Offset of a drag

  The offset a dragged part is moved by: onto a grid node, or in steps.

  node − held point, or round(raw ÷ step) × step

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Point coordinates

  The x, y and z of one point record.

  x = X × scaleₓ + offsetₓ (and the same for y and z)

  LAS and LAZ point coordinates las.js

  • CadCraft
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  • CivilCraft
  64-bit

• Scale, offset and bounds from the header

  Reads the header's scale, offset, minimum and maximum and refuses a scale that cannot be used.

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• 64-bit counts and offsets

  Reads an unsigned 64-bit integer (LAS 1.4 point count, extended record positions and lengths).

  value = hi × 2³² + lo

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Points the file really holds

  The number of whole point records between the first point and the end of the point data.

  available = ⌊(end − offset to points) ÷ record length⌋, at most the header's count

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  Exact

• Parameter values in dependency order

  Evaluates every parameter after the ones it uses and reports cycles and missing values.

  Parameters and equations params.js

  • CadCraft
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  64-bit

• Equation results written to their targets

  Evaluates each equation and writes the result into the dimension or feature value it drives.

  written when |current − v| > 1e-12 × max(1, |v|)

  Parameters and equations params.js

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• Limits on a driven value

  Checks a value against its target's kind: whole number, minimum, maximum.

  Parameters and equations params.js

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• Backward solve for a driving parameter

  Finds the parameter value that makes an equation give the value a person typed.

  secant: c = b − f(b) × (b − a) ÷ (f(b) − f(a)); stop when |f| ≤ 1e-10 × max(1, |target|, |x₀|)

  Parameters and equations params.js

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