Calculations

Calculations

• Joist and rafter span from the table

  The allowed span of a joist or rafter size at its spacing.

  column = first listed spacing ≥ spacing ÷ 25.4 − 0.05; span = least span of the listed species

  Regulation limits read from the pack's tables addons/regs/lib/check.js

  • BimCraft
  64-bit

• Horizontal span of a rafter

  The span of the longest rafter or ceiling joist measured on the horizontal, compared with the table.

  span = sloped length × cos(pitch × π ÷ 180)

  Regulation limits read from the pack's tables addons/regs/lib/check.js

  • BimCraft
  64-bit

• Insulation R-value of a wall type

  The nominal R-value of a wall type's cavity and continuous insulation layers, in imperial units.

  R = thickness (mm) ÷ 1000 ÷ λ × 5.678263

  Regulation limits read from the pack's tables addons/regs/lib/check.js

  • BimCraft
  64-bit

• Wall insulation against the table's options

  Whether a wall type's insulation meets any of the cavity and continuous options of its climate zone.

  met if cavity + 0.05 ≥ option cavity and continuous + 0.05 ≥ option continuous, for any option

  Regulation limits read from the pack's tables addons/regs/lib/check.js

  • BimCraft
  64-bit

• K-factor in SI units

  Converts a head's K-factor from L/min per √bar to m³/s per √Pa.

  k = K ÷ 1000 ÷ 60 ÷ √100000

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Pipe friction

  The friction loss in pascals per meter of pipe for a flow, an inside diameter and a roughness coefficient C.

  Δp per m = 10.67 × Q^1.852 ÷ (C^1.852 × D^4.871) × 998.2 × 9.80665

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Pipe sizes

  Chooses for each pipe the smallest steel schedule 40 size that keeps the velocity within the limit.

  Q = heads below × flow per head ÷ 1000 × 1.15; v = Q ÷ (π d² ÷ 4) ≤ vmax

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Design areas to test

  The groups of heads tried as the design area: blocks of rows at the far and near ends of the branch lines.

  heads = ceil(area ÷ coverage); per row m = ceil(1.2 × √area ÷ spacing); rows = ceil(heads ÷ m)

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Minimum flow and pressure at a head

  The least flow and pressure every operating head must have.

  q = density ÷ 1000 ÷ 60 × coverage; P = max((q ÷ k)², minimum head pressure)

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Pressures and flows for a source pressure

  The pressure at every node and the flow in every pipe when the source is at a given pressure and each operating head discharges K √P.

  P(b) = P(a) − friction × (length + equivalent length) − ρ g Δz

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Lowest source pressure

  The lowest source pressure at which every operating head has its minimum.

  upper bound doubled from 200000 Pa until it works, then halved 40 times

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Head and pipe results

  Each head's flow, pressure and density, each pipe's flow, velocity and pressure drop, and the total flow.

  density = q × 1000 × 60 ÷ coverage; v = Q ÷ (π D² ÷ 4); total = Σ head flows

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Supply pressure at a flow

  The pressure the water supply gives at a flow, from the static and residual pressures of a flow test.

  P = Ps − (Ps − Pr) × (Q ÷ Qr)^1.85

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Required against available pressure

  Takes the design area needing the most pressure, adds the hose allowance and margin, and compares with the supply.

  Q total = Q heads × 60 + hose; required = P source ÷ 100000 + margin; ok if available ≥ required − 10⁻⁹

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/hydraulics.js

  • BimCraft
  64-bit

• Head spacing

  The number of heads each way and their spacing, the largest the hazard's maximum spacing and coverage allow.

  nx = ceil(W ÷ maxS − 10⁻⁹); ny likewise; raised until (W ÷ nx)(D ÷ ny) ≤ max coverage; sx = W ÷ nx

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Point inside the room

  Whether a point lies inside the room outline.

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Head in a partly filled cell

  Moves the head of a grid cell the room only partly fills to the middle of the part inside.

  position = mean of the cell's 6 × 6 sample points that lie inside

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Uncovered share of the room

  The share of the room farther than 0.75 × the allowed spacing from every head.

  uncovered = samples with no head within 0.75 × maxS ÷ samples inside the room

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Pipe length and rise

  The length in meters and the rise of each pipe of the network from its two end points.

  length = √(Δx² + Δy² + Δz²) ÷ 1000; dz = Δz ÷ 1000

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/layout.js

  • BimCraft
  64-bit

• Sprinkler properties in the model

  The K-factor, coverage, design density and hazard class written on each placed head.

  CoverageM2 = round(coverage × 100) ÷ 100

  Sprinkler layout and hydraulic calculation addons/sprinkler/lib/place.js

  • BimCraft
  64-bit

• Segments of an arc

  How many chords replace an arc of a given sweep.

  n = max(2, ceil(|sweep| ÷ 2π × 36))

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  Exact

• Arc through three points

  The circular arc of an indexed poly-curve from its start, middle and end points.

  center = a + ((|ab|² (ac × n)) + (|ac|² (n × ab))) ÷ (2 |n|²), n = ab × ac

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Circle and ellipse points

  Points on a circle or ellipse between two parameters.

  p = M · (r₁ cos θ, r₂ sin θ, 0), θ = a₀ + sweep × i ÷ n

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Trimmed curve

  The part of a line, circle, ellipse or other curve between two trims given as parameters or points.

  conic: angle = parameter × angle unit, or atan2 of the trim point in the conic's frame

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• B-spline curve points

  Points on a B-spline curve, rational or not, at 12 evenly spaced parameters per knot span.

  de Boor: d_j = (1 − a) d_{j−1} + a d_j, a = (u − k_i) ÷ (k_{i+p+1−r} − k_i); point = (x, y, z) ÷ w

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Offset of a polyline

  A 2D polyline moved to its left by a distance, with mitered corners.

  p' = p + n × d ÷ max(0.2, n · n₁), n = normalized sum of the two edge normals

  IFC curves and profiles as point lists ifc/geo-curve.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Circle and ellipse profiles

  The outline of a circular, hollow circular or elliptical profile.

  (r₁ cos a, r₂ sin a), a = 2π i ÷ 36

  IFC curves and profiles as point lists ifc/geo-profile.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Fillets and edge radii

  Replaces corners of a profile outline with arcs of given radii tangent to both edges.

  d = r ÷ tan(half); center = corner + bisector × r ÷ sin(half), half = half the corner angle

  IFC curves and profiles as point lists ifc/geo-profile.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• I-shape outline

  The outline of a symmetric or asymmetric I-section with flange slopes, fillets and edge radii.

  inner flange face = thickness + tan(slope) × distance from the quarter point of the outstand

  IFC curves and profiles as point lists ifc/geo-profile.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Closing an outline

  Drops repeated points of a profile curve and its closing point.

  IFC curves and profiles as point lists ifc/geo-profile.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Straight extrusion

  The solid of a profile swept along a direction by a depth, with end caps and sides.

  top = bottom + direction × depth

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Side face of a sweep

  Adds a four-sided face as one flat face or as two triangles.

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Revolved solid

  The solid of a profile turned about an axis by an angle.

  p_k = o + R(axis, angle × k ÷ steps) · (p − o), steps = 36 per full turn

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Frames along a path

  The tangent, normal and binormal at each point of a 3D polyline, and the miter stretch at each bend.

  tangent = normalize(t_in + t_out); miter = 1 ÷ max(0.25, t_in · tangent)

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Normal carried round a bend

  Turns the section's normal by the rotation that takes the previous tangent to the next.

  angle = atan2(|a × b|, a · b); v' = R(a × b, angle) v, made square to b

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Swept disk

  A round bar or tube along a path, such as rebar, with an optional inner radius and bend radius.

  section = 36-sided polygon of the radius; swept on the path's frames

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Bends of a swept path

  Rounds the corners of a 3D polyline with arcs of a given radius.

  d = min(r ÷ tan(half), 0.999 × each leg); center = corner + bisector × r' ÷ sin(half)

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Sphere

  The mesh of an IfcSphere.

  (r sin θ cos φ, r sin θ sin φ, r cos θ), θ = π i ÷ 12, φ = 2π j ÷ 24

  IFC swept solids, primitives and faceted shapes ifc/geo-solid.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Outer bound of a face

  Picks the largest loop of a face as its outer bound when the file marks none.

  size = |Σ ((yₐ − y_b)(zₐ + z_b), (zₐ − z_b)(xₐ + x_b), (xₐ − x_b)(yₐ + y_b))| (twice the area)

  IFC swept solids, primitives and faceted shapes ifc/geo-brep.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Repeated points of a loop

  Drops consecutive points of a face loop that coincide, and a closing point equal to the first.

  IFC swept solids, primitives and faceted shapes ifc/geo-brep.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Point on a clothoid

  The point at a length along a clothoid from its origin.

  x = ∫₀ˢ cos(k u²) du, y = ∫₀ˢ sin(k u²) du, k = sign(A) ÷ (2A²); Simpson's rule

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Points of a curve segment

  Samples one alignment segment from its parent curve and places it at the segment's start.

  n = max(2, min(400, ceil(|length| ÷ 2))); p_i = T · f(start + length × i ÷ n)

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Distance along the alignment

  The horizontal distance of each sampled point from the start.

  d_i = d_{i−1} + √(Δx² + Δy²)

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Height from the vertical profile

  The height of each horizontal point from the alignment's vertical profile.

  z = z_lo + (z_hi − z_lo) × (d − d_lo) ÷ (d_hi − d_lo)

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Point at a station

  The position and direction on a curve at a distance along it.

  p = p_{i−1} + (p_i − p_{i−1}) × (d − d_{i−1}) ÷ (d_i − d_{i−1})

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Placement along an alignment

  The matrix of an element placed at a station with lateral, vertical and longitudinal offsets.

  origin = p + left × lateral + (0, 0, vertical) + heading × longitudinal

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Solid between cross sections

  The solid of an IfcSectionedSolidHorizontal: cross sections placed across the alignment at their stations and joined.

  ring point = o + x × ((1 − f) a_x + f b_x) + y × ((1 − f) a_y + f b_y), f = (d − d₀) ÷ (d₁ − d₀)

  IFC alignment curves and stations ifc/geo-align.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cylinder and cone

  A point on a cylindrical or conical surface from (u, v), and (u, v) from a point.

  p = o + (r + v tan α)(x cos u + y sin u) + z v; u = atan2(d · y, d · x), v = d · z

  IFC faces on curved surfaces ifc/geo-nurbs.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Swept curve by length

  The generating curve of an extruded or revolved surface as a polyline with a length parameter.

  s_i = s_{i−1} + |p_i − p_{i−1}|; point at s by linear interpolation

  IFC faces on curved surfaces ifc/geo-nurbs.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• B-spline basis functions

  The non-zero basis functions of a B-spline at a parameter.

  Cox-de Boor: N_r = saved + right × N_r ÷ (right + left)

  IFC faces on curved surfaces ifc/geo-nurbs.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit