Calculations

Calculations

• Joint merge

  Reuses an existing joint when a new one is asked for at the same place.

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Member length and angle

  The centerline length and the slope angle of a member between two joints.

  len = √(Δx² + Δz²); angle = |atan2(Δz, Δx)| in degrees

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Frame of a named truss type

  The joints and members of a king, queen, Howe, Pratt, Fink, scissor, mono or attic truss from span, pitch and overhang.

  rise(x) = min(x, span − x) × tan(pitch); panel points at span × i ÷ n

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• 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

• Member lines for the picture

  The 3D end points of every member, for drawing.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• View projection

  Turns 3D points into picture coordinates for a view direction.

  x′ = x cos A − y sin A; y′ = −(z cos E + (x sin A + y cos A) sin E)

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Picture output

  Scales the projected lines to the picture size and writes them as SVG.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Height of a roof face over a point

  The height of a face's plane above a plan point.

  z = start + (n·p − c) ÷ speed

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Solver tolerance

  Sets the tolerance every merge, split and overlap test in the roof solver uses.

  scale = max(1, width, depth of the outline); eps = 1e-7 × scale

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Edge lines

  The direction, inward normal and line offset of each eave edge.

  u = (b − a) ÷ |b − a|; n = (−u_y, u_x); c = n·a

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Corner velocity

  How a corner of the shrinking polygon moves per unit of height.

  n_a·v = v_a; n_b·v = v_b; determinant = n_a × n_b

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Next event height

  Finds the height at which the polygon next changes: an edge starts to move, an edge shrinks to nothing, or a reflex corner reaches another edge.

  collapse: t = T + length ÷ closing rate; split: t = T + distance ÷ approach rate

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Advance to the event

  Moves every corner to the event height and records its path as a roof line and a face boundary.

  p′ = p + v × (t_next − T)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Clean-up after an event

  Merges corners that met, removes edges folded onto each other as ridges, splits a loop a corner has cut, and closes loops with no area left.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Shared part of two folded edges

  The stretch two opposite edges on one line have in common, which becomes a ridge.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Face boundaries chained into polygons

  Joins the boundary pieces of a face into closed loops.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Collinear points removed from a face

  Drops points of a face polygon that lie on the line between their neighbors.

  removed when |u × v| ÷ max(|u|, |v|) ≤ tolerance

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Roof lines joined end to end

  Joins the pieces of one ridge, hip or valley into a single line.

  joined when ends meet within tolerance and cos θ ≥ 1 − 1e-9

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Faces kept

  Builds each face's plan polygon and drops slivers.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit