Calculations

Calculations

• Friction rate and velocity of a drawn section

  The friction rate and velocity of a duct section as drawn, in the units typed.

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

  • CadCraft
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• Loads at the joints

  Turns roof, snow and ceiling loads in kPa into forces in kN at the joints of the frame.

  top chord: w = (dead × L + snow × Δx) × spacing; bottom chord: w = ceiling × Δx × spacing; half to each end

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Wind and uplift forces at the joints

  Forces at the top-chord joints from wind pressure normal to the roof and from a net uplift on plan.

  F = p × spacing × L; n = (−Δz, Δx) ÷ L; joint force = −n F ÷ 2

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Load across each chord member

  The load per meter across each chord member, per load case, used for bending between panel points.

  c = |Δx| ÷ L; dead: w c; snow and uplift: w c²

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Linear solve

  Solves a square system of linear equations.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Member forces by the method of joints

  The axial force in every member and the support reactions for one set of joint loads.

  Σ member pulls + reactions = load at every joint; members + 3 = 2 × joints

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Member check

  The utilization of one member under an axial force and a bending moment.

  tension: T ÷ (Ft·CD·A); compression: fc ÷ (Fc·CD·Cp), Cp = q − √(q² − α ÷ c), q = (1 + α) ÷ 2c, α = FcE ÷ (Fc·CD), FcE = 0.822 Emin ÷ (le ÷ d)²

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Governing combination for a member

  The load combination that gives a member its highest utilization, with the largest and smallest force over all combinations.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Smallest sizes that pass

  The smallest timber size for the top chord, the bottom chord and the webs that keeps every member at or under a utilization of 1.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Deflection estimate

  The largest vertical deflection at a bottom-chord joint and the span-to-deflection ratio.

  δ = Σ N n L × 1000 ÷ (E A)

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Frame member stiffness

  The stiffness of each member of the attic frame, turned into the frame's axes and added to the whole.

  EA = E b d; EI = E b d³ ÷ 12; K = Tᵀ k T

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Uniform load on a level beam

  The joint forces and moments that stand in for a uniform load on the floor or ceiling tie.

  end force = w L ÷ 2; end moment = w L² ÷ 12

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Frame displacements, forces and moments

  Solves the frame and reads each member's axial force and each beam's largest moment.

  N = (EA ÷ L)(u_b − u_a); M = max(|Ma|, |Mb|, |w L² ÷ 8 − (|Ma| + |Mb|) ÷ 2|)

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Frame support reactions

  The reactions at the two supports of the attic frame.

  R = Σ K·D − F for the support's row

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Load combinations

  Member forces, chord moments and reactions for each combination of the load cases.

  force = Σ factor × case force; M = |w| L² ÷ momentDiv

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Point loads from carried trusses

  Adds point loads, such as the reactions of jack trusses on a girder, at the nearest top-chord joint.

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Attic frame sizing passes

  Repeats the frame solve and the sizing of an attic truss until the sizes settle.

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Stub forces and the governing force per member

  The force in each bearing stub and, for the joints and the drawing, the force of largest size in each member over all combinations.

  stub force = −vertical reaction; governing = value with the largest |force|

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Forces used for the deflection

  Chooses the member forces the deflection estimate is based on.

  service force = dead case + snow case

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Bearing reactions

  The largest and smallest vertical reaction at each bearing and the largest horizontal reaction, over the combinations.

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• Ceiling and floor loads of an attic truss

  The load on each bottom-chord member of an attic truss in a combination.

  w = f_D × ceiling dead × spacing + f_S × floor live × spacing (room floor only)

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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
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• OBJ export

  The truss set written as an OBJ file.

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

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• 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

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• 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

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• Force labels in the force diagram

  The force written beside each member.

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

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• 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

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• 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

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• 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

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• 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

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• 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

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