Calculations

Calculations

• Bearing stubs under a raised heel

  Adds a vertical stub under each heel joint when the heel is raised.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/geometry.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Heel depth and raise

  The heel depth the chords need at the outer face and how far a taller stated heel raises the truss.

  needed = d_bottom ÷ 2 + d_top ÷ (2 cos pitch); raise = max(0, heel − needed)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/geometry.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Roof section along a truss line

  The height of the roof's underside along the line a truss stands on.

  z = start + (n·p − c) ÷ speed on each face; highest face wins

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/profile.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Profile simplification

  Removes repeated points and points that lie on a straight line between their neighbors.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/profile.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Height of a profile at x

  The profile's height at a distance along the truss.

  z = z₀ + (z₁ − z₀)(x − x₀) ÷ (x₁ − x₀)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/profile.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• What a profile is

  Decides whether a roof section is a plain triangle, has a flat top, has a valley across it, and is symmetric.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/profile.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Frame from a roof profile

  The joints and members of a truss whose top chord follows the roof's section.

  pitch = atan(slope of the first panel), or atan(steepest profile slope) when the left end stands on a post

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/profile.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Chord pieces

  Joins chord members that run straight on through a joint into one piece of timber, with its length.

  joined when acos(|u·v|) < 0.5°; len = √(Δx² + Δz²)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cutlist.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Cut length and end angles

  The length to cut each piece and the angle of each end cut.

  cut = joint length − set_A − set_B + (d ÷ 2)(tan A + tan B); web set = (host depth ÷ 2) ÷ max(0.2, sin φ)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cutlist.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Member list values

  The length, angle, force and utilization shown for each member.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cutlist.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Joint schedule and plate choice

  The members meeting at each joint with their angles and forces, and the first plate of the table that fits.

  plate: capacity ≥ largest |force| and min(w, h) ≥ min(deepest member + 25, 152)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cutlist.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Bird's mouth cut

  The plumb cut of a rafter seat and the depth left above it.

  plumb = seat × tan(pitch); left = depth − plumb × cos(pitch)

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cutlist.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Jig drawing at full size

  The outline of every member on the 1:1 jig sheet.

  corner = joint ± (−Δz, Δx) ÷ L × d ÷ 2

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/fab.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Stock plan

  Nests the cut pieces of a truss set onto stock lengths and lists them as CSV.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/fab.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Member as a solid

  A closed box for one member from its two end points, depth and thickness, with its volume.

  V = |Σ a · (b × c) ÷ 6| over the 12 triangles

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/bodies.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Members placed in plan and height

  The 3D end points of every member of a laid-out truss.

  p = a + x × (b − a) ÷ span; z = z₀ + node z + raise + base

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/bodies.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• STL export

  The truss set written as an ASCII STL file.

  text = round(v × 1000) ÷ 1000

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/bodies.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• OBJ export

  The truss set written as an OBJ file.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/bodies.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Millimeters to drawing coordinates

  Places truss drawings in a CadCraft drawing at a point and a scale.

  X = at_x + x × k; Y = at_y + y × k

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cadplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Member outlines in the elevation

  The closed outline drawn for each member in the truss elevation.

  corner = joint ± (−Δz, Δx) ÷ L × d ÷ 2

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cadplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Force labels in the force diagram

  The force written beside each member.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cadplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Schedule rows in the drawing

  The cut list and joint schedule as rows of a table drawn in CadCraft.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/cadplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Dimension labels on the elevation picture

  The span, overhang, pitch, rise and heel written on the truss elevation.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/drawing.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Outline area

  The signed area of the roof outline.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Where a truss line crosses the outline

  The points where a station line enters and leaves the roof outline.

  v = a_v + (u − a_u) ÷ (b_u − a_u) × (b_v − a_v)

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Trusses along an outline

  The station, end points and span of each truss over a plain outline, and the actual spacing.

  bays = ceil(length ÷ spacing); step = length ÷ bays; span = v₁ − v₀

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Ridge direction

  The direction the ridge runs, which the trusses span across.

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Valley pairs of a roof plan

  Finds pairs of valley lines that meet at a wing's ridge, with the wing's axis and reach.

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Valley truss set

  The span, rise, base height and position of each valley truss of a wing roof over a main roof.

  ridge height = (W ÷ 2) tan(wing pitch); rise = d × tan(main pitch); span = 2 d tan(main pitch) ÷ tan(wing pitch)

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Stations along the ridge

  The truss stations of a roof and the stretches of each station that lie inside the outline.

  bays = ceil(length ÷ spacing); u = u₀ + inset + i × step

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• A truss from a roof section

  Decides the form of the truss at a station, its design key, and the values stored for it.

  common truss pitch = atan(2 × apex ÷ span)

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Jack trusses in a hip end

  The jack and corner trusses between the end wall and a girder truss, and where each bears on the girder.

  count = ceil((width − 2 × inset) ÷ spacing); v = v₀ + inset + k × step

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Velocity beyond a wall

  The value used just outside the region so that the velocity at a wall equals the wall's own.

  u_ghost = 2 × u_wall − u_inside

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Value at a cell face

  The value carried across a cell face by the flow.

  central ½(a + b) when |u| h ÷ ν ≤ 2, else the upwind value

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Time step

  The largest stable time step for the current velocities.

  dt = min(0.4 h ÷ u_max, 0.2 h² ÷ ν, 0.8 ν ÷ u_max²)

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Momentum step for u

  The predicted x velocity at each face after one time step.

  u* = u + dt (−convection + ν ∇²u + source)

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Pressure equation

  Sets up the pressure equation that makes the velocity field divergence-free.

  ∇²p = (∇·u*) ÷ dt

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Pressure solve

  Solves the pressure equation by conjugate gradient.

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Velocity correction

  Removes the pressure gradient from the predicted velocities.

  u = u* − dt (p_right − p_left) ÷ h

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Tracer transport

  Moves a tracer with the flow and lets it diffuse, one time step.

  limiter φ(r) = (r + |r|) ÷ (1 + |r|); C′ = C − dt (∇·flux) + dt × source

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Run to a steady state

  Steps the flow until it stops changing or a limit is reached.

  change = max |u′ − u| ÷ dt

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Velocity at cell centers

  The velocity at the center of each cell.

  u_c = ½(u_left + u_right); v_c = ½(v_bottom + v_top)

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Velocity at a point

  The velocity at any point of the region.

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Stream function

  The stream function at the cell corners.

  ψ(i, j) = ψ(i, j − 1) + U(i, j − 1) × h_y

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• VTK export

  Writes velocity, pressure and tracer fields as a legacy ASCII VTK file.

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Mixing time

  The time at which a tracer's spread falls below a target.

  CV = √(Σ (c − mean)² ÷ n) ÷ mean

  2D flow solver (finite volume) cfd/fv.js

  • CadCraft
  64-bit

• Lattice directions and weights

  The nine directions of the lattice and the weight of each.

  w = 4/9, 1/9 (×4), 1/36 (×4)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Mixer set-up

  Creates the grid, the solid mask, the force field and the starting distributions.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Equilibrium distributions

  The equilibrium the flow and the tracer relax toward.

  f_eq = w ρ (1 + 3 c·u + 4.5 (c·u)² − 1.5 u²); g_eq = w C (1 + 3 c·u)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Collision step

  Density, velocity and tracer value of each cell, and the relaxation of its distributions.

  ρ = Σ f; u = (Σ f c + ½ F) ÷ ρ; f ← f − (f − f_eq) ÷ τ + source

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit