Calculations

Calculations

• Mat settlement and contact pressure

  The largest and smallest settlement of the mat and the largest spring pressure.

  q = k_s × w ÷ 1000; reaction = Σ k_node × w ÷ 1000

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
  64-bit

• Mat bending moments and shear

  The largest sagging and hogging moments per meter each way and the largest transverse shear.

  M = max and min of the node moments ÷ 1000; V = max √(q_x² + q_y²) away from the columns

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
  64-bit

• Hogging capacity of plain concrete

  The hogging moment a mat with no top bars can take.

  capacity = 0.60 × 0.42·λ·√f′c × (H² ÷ 6) × 1000 ÷ 10⁶

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
  64-bit

• Spring pressure at a point

  The soil pressure at any point of the mat from the settlements of the nodes round it.

  q = k_s ÷ 1000 × bilinear blend of the four corner settlements

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
  64-bit

• Pile group reactions

  The load each pile takes under a vertical load and two moments.

  R_i = P ÷ n + M_x·y_i ÷ Σy² + M_y·x_i ÷ Σx²

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
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• Cantilever retaining wall

  Overturning, sliding and bearing of a cantilever wall with level backfill.

  K_a = tan²(45° − φ ÷ 2); P_a = ½·K_a·γ·H_t²; e = B ÷ 2 − (M_r − M_o) ÷ W

  Settlement, flexible mats, pile groups and retaining walls foundation.js

  • DetailCraft
  64-bit

• A real number in the file

  How every length, coordinate, direction component and weight is written.

  text = toFixed(6), trailing zeros dropped; |v| < 1e-9 → 0

  IFC export ifc.js

  • DetailCraft
  64-bit

• Storey of an element

  Which storey an element is put in: the highest level at or below its lowest point.

  level z ≤ lowest point + 0.5 mm

  IFC export ifc.js

  • DetailCraft
  64-bit

• Placement of a part

  The origin and the two axes each part is placed with, relative to its storey.

  location = (p_x, p_y, p_z − level z); Axis = part x; RefDirection = part u

  IFC export ifc.js

  • DetailCraft
  64-bit

• Profile dimensions

  The section dimensions written for each profile type.

  IFC export ifc.js

  • DetailCraft
  64-bit

• Mitre cut plane

  The plane that clips a part's extrusion at a mitre end.

  normal = unit(−sg·ku, −sg·kv, sg); point = (0, voff, x0)

  IFC export ifc.js

  • DetailCraft
  64-bit

• Hole openings

  The position, direction, depth and radius of each hole's opening.

  depth = thickness + 2; start = center − axis·depth ÷ 2; radius = d ÷ 2

  IFC export ifc.js

  • DetailCraft
  64-bit

• Cope openings

  The box that cuts each cope out of a part.

  center v = voff ± (depth ÷ 2 − cope depth ÷ 2 + 0.5); box = (width + 2) × (cope depth + 1) × (cope length + 1)

  IFC export ifc.js

  • DetailCraft
  64-bit

• Bolts and anchor rods

  The placement, diameter and length written for each bolt and rod.

  IFC export ifc.js

  • DetailCraft
  64-bit

• Reinforcing bar center lines

  The center line of each placed bar as lines and true arcs, with the bar's radius.

  point = origin + s·ŝ + t·t̂; arc through start, middle and end; radius = d_b ÷ 2

  IFC export ifc.js

  • DetailCraft
  64-bit

• Length and weight properties

  The cut length and weight written in each part's property set.

  IFC export ifc.js

  • DetailCraft
  64-bit

• Length unit to millimeters

  The factor that turns the file's lengths into millimeters.

  toMm = prefix × 1000; converted units: toMm = factor × prefix × 1000

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• A placement's axes

  The three axes and origin of an IFC axis placement.

  Z = unit(Axis); X = unit(Ref − Z·(Ref·Z)); Y = Z × X

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• Placements combined

  One placement expressed inside another.

  X′ = A·X, Y′ = A·Y, Z′ = A·Z, O′ = A·O + O_A

  IFC import ifc-import.js

  • DetailCraft
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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

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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

  • 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

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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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  64-bit

• 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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  64-bit

• 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
  64-bit