Calculations

Calculations

• World transform

  The transform of an object in the scene, through all its parents.

  W = M_root × … × M_parent × M_own

  USD transforms and placement usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Scene units and up axis

  The transform from the scene's own units and up axis to meters with Z up.

  scale by metersPerUnit; Y-up scenes: rotate 90° about X

  USD transforms and placement usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Placement of instanced copies

  The transform of each copy of a point instancer from its position, orientation and scale.

  M = translate(p) × rotate(q) × scale(s)

  USD transforms and placement usd/scene.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Writing an object's transform

  Stores an object's placement in the exported scene.

  USD transforms and placement usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Attribute value to its storage type

  Converts a list of numbers to the number type its USD attribute type calls for.

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Mesh points and extent

  Stores the points of a mesh and its bounding box in the scene.

  extent = [min x, min y, min z, max x, max y, max z] of the points

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Lamp intensity

  Converts a lamp's lumens to the intensity a renderer reads.

  intensity = lumens ÷ (683 × area × π)

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit, display only

• Single values in the binary file

  Writes one number, tuple or matrix into the binary USD file.

  USD mesh coordinates in saved and exported files usd/usdc-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arrays in the binary file

  Writes an array of numbers into the binary USD file.

  USD mesh coordinates in saved and exported files usd/usdc-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Reading a mesh

  The points, faces and attached values of a mesh read from a USD scene.

  USD mesh coordinates in saved and exported files usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Built-in shapes as meshes

  A cube, sphere, cylinder, cone, capsule or plane of a USD scene as a mesh.

  ring point = (r·cos θ, r·sin θ, z), θ = 2π·j ÷ 24

  USD mesh coordinates in saved and exported files usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Frame of a member

  The origin, the unit direction, the two section axes and the length of a member line.

  x = (e − s) ÷ |e − s|; v = unit(Z − x·x_z); u = v × x; u′ = cos a·u + sin a·v, v′ = −sin a·u + cos a·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Local point to model point

  The model coordinates of a point given along the member and across its section.

  p = o + x·x̂ + u·û + (v + voff)·v̂

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Model point to local point

  Where a model point lies along a member and across its section.

  d = p − o; x = d·x̂, u = d·û, v = d·v̂ − voff

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• End face position on a plane-cut end

  How far along the part its end face is at a given point of the section, for square ends and mitre cuts.

  x = x0 + ku·u + kv·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Section outline clipped at a height

  The part of a section outline below or above a line, used for coped ends.

  t = (limit − a_v) ÷ (b_v − a_v); new point = (a_u + (b_u − a_u)·t, limit)

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Node merging

  One analysis node for every group of points that lie within 1 mm of each other.

  same node when |p − n| ≤ 1 mm

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Splitting a member at the points on it

  The stations along a drawn member where another member's end or a node load lies on it.

  s = (q − start)·u; foot = start + u·s; cut when |foot − q| ≤ 2 mm and 2 mm < s < L − 2 mm

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• End points of each piece

  The two points of every piece a split member becomes.

  p = start + u·s

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Section properties per profile

  Area, second moments of area and torsion constant of each profile in use, with the reduced bending stiffness of cracked concrete.

  Iy′ = f·Iy, Iz′ = f·Iz

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Which column feet are supports

  Decides which column feet are held: those with a base plate, or with no member going lower at that node.

  support when lowest z at the node ≥ node z − 1 mm

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Point load on a split member

  Moves a point load from its distance along the drawn member to the piece it falls on.

  a′ = max(0, a − s0)

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Distributed load on a split member

  Cuts a uniform or linearly varying load into the part that falls on each piece.

  w(s) = w + (w₂ − w)·(s − a) ÷ (b − a)

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• Sections the drawn members use

  The area and second moments of area listed for each profile in the model.

  Analytical frame model from the drawn members analysis.js

  • DetailCraft
  64-bit

• One bolt's shear strength

  The single-shear design strength of one bolt in kN.

  φRn = 0.75 × Fnv × (π·d² ÷ 4) ÷ 1000

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• End shear from a uniform load

  The end shear of a beam when only a uniform load per meter is given.

  R = w × L ÷ 1000 ÷ 2

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• Shear tab rows and plate

  Bolt diameter, number of rows, edge distance and plate thickness for a shear tab.

  clear = d − 2(tf + r); maxRows = ⌊(clear − 2·edge) ÷ 75⌋ + 1; need = max(2, ⌈R ÷ φRn⌉)

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• End plate rows and plate

  Bolt rows, plate width, thickness and gauge for an end plate.

  rows wanted = max(4, 2·⌈R ÷ φRn ÷ 4⌉); width = max(150, bf rounded up to 10); gauge = max(90, round(0.55·bf ÷ 5)·5)

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• Base plate size and rod spacing

  Plate length and width, rod diameter, hole and rod spacing for a column base.

  length = max(300, (depth + 150) rounded up to 25); sx = length − 100

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• Rounding up to a step

  Rounds a size up to the next multiple of a step.

  ⌈v ÷ step − 1e-9⌉ × step

  Connection autopilot starting sizes autopilot.js

  • DetailCraft
  64-bit

• Box round each part and footing

  The center, axes and half sizes of the box used for the first, coarse test.

  c = o + x̂·L ÷ 2 + v̂·voff; h = (L ÷ 2, width ÷ 2, depth ÷ 2)

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Do two boxes overlap

  Whether two oriented boxes overlap by more than the tolerance.

  separated on axis l when |T·l| > r_A + r_B − tol

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Point inside a section outline

  Whether a point lies inside a closed outline.

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Distance to the nearest outline edge

  The shortest distance from a point to any edge of an outline.

  t = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); d = |p − a − t·(b − a)|

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• How far a point is inside a part

  The distance from a point to the outside of a part, zero when it is outside.

  depth = min(x, L − x, distance to each outline edge)

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Ray to the far side of the material

  How far a ray from an edge runs before it meets another edge of the section, to place a sample point in the middle of a flange or web.

  t = (w × e) ÷ (d × e), u = (w × d) ÷ (d × e)

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Sample points across and along a part

  The points of one part that are tested inside the other.

  stations n = clamp(⌈(t1 − t0) ÷ 10⌉, 2, 40)

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Stretch of a part that can reach the other

  The range along one part's axis where it can meet the other part's box.

  t0 = max(0, min x − pad), t1 = min(L, max x + pad); pad = √(h_u² + h_v²)

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Reported depth and location

  The depth and the point each clash is reported with.

  depth = round(depth × 10) ÷ 10

  Clash check between parts clash.js

  • DetailCraft
  64-bit

• Distance from a point to a member line

  The shortest distance from a point to the segment between a member's two ends.

  k = clamp((P − a)·(b − a) ÷ |b − a|², 0, 1); d = |P − (a + k·(b − a))|

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Is a member vertical

  Whether a member stands vertical, the condition for a column to take a connection.

  |Δx| < 1 mm and |Δy| < 1 mm and |Δz| ≥ 1 mm

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Members end to end in line

  Pairs of member ends that meet in line, with the gap between them.

  along = d·d̂_a; off = |d − d̂_a·along|; in line when |d̂_a·d̂_b| ≥ 0.9999, off ≤ 1 mm, |d| ≤ 50 mm

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Beam end at a column

  Which beam ends land on a column, and whether they meet its flange, its web or come in skewed.

  flange when |away·v̂| > 0.9999; web when |away·û| > 0.9999; else skew

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Members meeting at an angle

  Pairs of I-shaped member ends that share a point and are not in line, with the angle between them.

  angle = acos(clamp(ê_A·ê_B, −1, 1)) × 180 ÷ π

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Plate size written into the profile name

  The thickness and width digits of a plate's profile name, which is how a connection plate's section reaches the built part.

  text = Number(v.toFixed(1))

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  64-bit

• Bolt length rounded up to 5 mm

  The length of a bolt from its grip and the allowance.

  length = ⌈(grip + allowance) ÷ 5 − 1e-9⌉ × 5

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  64-bit

• Anchor rod hole and washer sizes

  The hole diameter, washer size and washer thickness for an anchor rod, from the table in AISC Design Guide 1.

  mm = inches × 25.4

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  Exact

• End plate, its holes and bolts

  Where an end plate sits against the column and where each bolt row goes.

  center = N + away·(faceOff + tp ÷ 2); z_i = z_c + ((rows − 1) ÷ 2 − i)·pitch; hole = face ± ŵ·gauge ÷ 2

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  64-bit

• Edge distance and spacing checks

  Warnings when bolt edge distances, pitch or gauge are under the EN 1993-1-8 Table 3.3 minimums.

  e1, e2 ≥ 1.2·d0; p1 ≥ 2.2·d0; p2 ≥ 2.4·d0

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  64-bit

• Shear tab: beam cut-back

  How far a square, skewed or sloped beam is cut back so every corner of its end clears the column face by the gap.

  setback = max over corners of (faceOff + gap − c·n) ÷ cos A; cos A = dir·n

  Connection plates, holes, bolts and cut-backs connections.js

  • DetailCraft
  64-bit