Calculations

Calculations

• A rectangle from a closed outline

  Recognizes a four-point outline as a rectangle and reads its center, axes and size.

  square when |ê_i·ê_{i+1}| ≤ 1e-4; center = mean of the four points

  IFC import ifc-import.js

  • DetailCraft
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• Matching a profile to the catalog

  Decides whether a profile from the file is one of the catalog shapes.

  match when every |catalog − file| ≤ 0.5 mm

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Reusing a custom profile

  Decides whether two profiles from the file are the same custom profile.

  same when all dimensions agree after rounding to 0.01 mm

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Level heights

  The height of each storey, from its placement or its Elevation.

  z = round(z × toMm × 1000) ÷ 1000

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Grid lines

  Which grid axes become numbered or lettered grid lines, and where.

  x line when |d_y| > 0.9999; y line when |d_x| > 0.9999; position rounded to 0.001 mm

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Member line from the extrusion

  The start and end of a member from its extruded solid.

  start = O × toMm; end = start + ext·depth

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Plate from a rectangular solid

  The thickness, width and length of a plate from the three sizes of its box.

  thickness = smallest size; length = largest; plate when thickness < 0.25 × middle size

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Member rotation and stored coordinates

  The rotation that puts the section the way the file has it, and the values stored for the member.

  rot = atan2(U·v₀, U·u₀) × 180 ÷ π; stored: ends to 0.001 mm, rotation to 0.001°

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Holes from round openings

  The face, position and diameter of each hole read from an opening.

  d = round(2·r × 10) ÷ 10; x, y rounded to 0.001 mm

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• 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

• Numbers in the model file

  How the model's numbers are written to the file.

  The model file and what it stores model.js

  • DetailCraft
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• A point of a member

  Checks and stores a member's start or end point.

  The model file and what it stores model.js

  • DetailCraft
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• Member rotation and minimum length

  Brings a member's rotation into 0 to 360 degrees and refuses a member shorter than 1 mm.

  rotation = ((r mod 360) + 360) mod 360; length = √(Δx² + Δy² + Δz²) ≥ 1 mm

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• Grid lines from spacings

  The position of each grid line from the list of spacings typed.

  at_i = at_{i−1} + spacing_{i−1}

  The model file and what it stores model.js

  • DetailCraft
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• Spacings shown for existing grid lines

  The spacings text filled into the grid dialog from the stored grid positions.

  spacing = (at_i − at_{i−1}) to 3 decimals

  The model file and what it stores model.js

  • DetailCraft
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• A loose bolt as stored

  The diameter, length, head point and direction kept for a bolt that is not part of a connection.

  d, length, head: round(v × 1000) ÷ 1000; axis_i = round(a_i ÷ |a| × 10⁶) ÷ 10⁶

  The model file and what it stores model.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

  • DetailCraft
  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

  • DetailCraft
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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

  • DetailCraft
  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

  • DetailCraft
  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

  • DetailCraft
  64-bit

• Reading an NC file back

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

  DSTV NC files nc1.js

  • DetailCraft
  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

  • DetailCraft
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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

  • DetailCraft
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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

  • DetailCraft
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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

  • DetailCraft
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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

  • DetailCraft
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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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
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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

  • DetailCraft
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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
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• 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

  • DetailCraft
  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

  • DetailCraft
  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

  • DetailCraft
  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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• 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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  64-bit