Calculations

Calculations

• Shear tab: plate and bolt row

  The tab's two end points, its rotation, and the position of each bolt in the row.

  length = (rows − 1)·pitch + 2·edge; v_i = ev + ((rows − 1) ÷ 2 − i)·pitch; s_bolt = s_face + eh

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

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• Shear tab: skew and slope

  The beam's skew in plan and its slope, reported with the connection.

  skew = acos(min(1, away·n)); slope = asin(min(1, |dir_z|))

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

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• Base plate and anchor rods

  The base plate's position under the column and the four rod positions and lengths.

  rod = B ± ĉ_v·sx ÷ 2 ± ĉ_u·sy ÷ 2; rod length = embed + grout + tp + projection

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

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• Plate washers on the rods

  The size, thickness and position of each plate washer and the hole in it.

  hole = rod + 25.4 ÷ 16; z = top of plate + thickness ÷ 2

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

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• Splice: joint middle and cut-backs

  The middle of the joint between two spliced members and how far each is cut back to leave the joint gap.

  mid = J + out·(dJ·out) ÷ 2; setback = max(0, gap ÷ 2 − (dJ·out) ÷ 2)

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

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• Splice: flange plates and bolts

  The length of the flange cover plates and the position of every flange bolt.

  L_F = gap + 2·(2·edge + (n − 1)·pitch); s = ±(gap ÷ 2 + edge + i·pitch); gauge = bf − 80 when not given

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

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• Splice: web plates and bolts

  The height and length of the web cover plates and the position of every web bolt.

  clear = d − 2·(tf + r); H_W = ⌊(clear − 20) ÷ 5⌋·5 when not given; L_W = gap + 2·(2·edge + (cols − 1)·pitch_x)

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

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• Gusset: plane of the plate

  The gusset's normal and the direction across it, from the brace and the support.

  n_P = unit(d × x̂_S); w = unit(n_P × x̂_S)

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

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• Gusset: brace cut-back

  How far the brace is cut back to clear every member at the joint and a base plate there.

  need = max over corners of (off + gap − c·n) ÷ (d·n); setback = largest need

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

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• Gusset: bolt line

  The position of each bolt along the brace and its matching hole in the gusset.

  s_k = setback + edge + k·pitch; Q = P + n_P·(o − (P − N)·n_P)

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

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• Gusset: plate size

  How far the gusset runs along and across its support, and the width in its profile name.

  a0 = min a − margin, a1 = max a + margin; width = round(w1 − w0)

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

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• Mitre: where the two center lines meet

  The closest points of the two members' center lines and the joint point between them.

  s_A = (b·e − d) ÷ (1 − b²), s_B = (e − b·d) ÷ (1 − b²); b = x̂_A·x̂_B, d = x̂_A·r, e = x̂_B·r; J = (P_A + P_B) ÷ 2

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

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• Mitre: cut plane

  The angle between the two members and the plane that halves it.

  angle = acos(clamp(ê_A·ê_B, −1, 1)); n = unit(ê_B − ê_A); out = unit(−(ê_A + ê_B)); w = unit(ê_A × ê_B)

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

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• Mitre: the two cut faces

  The point each member's cut plane passes through, set back for the gap and the plates.

  face_A = J − n·off, face_B = J + n·off; off = gap ÷ 2 + plate thickness

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

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• Mitre: where a section edge meets the cut

  Where a line along the member through a point of its section crosses the cut plane, in the plane's own two directions.

  k = n·(face − Q) ÷ (n·x̂); X = Q + x̂·k − face

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

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• Mitre: bolt rows and gauge

  The rows of bolts between the flanges of the two end plates and their gauge.

  rows spread from c0 + weld + d0 to c1 − weld − d0; gauge = max(⌈2.4·d0 ÷ 5⌉·5, round(width ÷ 2 ÷ 5)·5) when not given

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

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• Mitre: weld length round the cut section

  The length of the all-round weld between a member's slanted end and its plate.

  length = perimeter ÷ |n·x̂|

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

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• Mitre: stiffener position and size

  Where the pair of web stiffeners sits past the cut and how big each is.

  at = far + dist + t ÷ 2; height = d − 2·tf; width = (bf − tw) ÷ 2

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

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• Two directions across an axis

  Two unit directions square to a bolt or torch axis, used to lay out the sample grid.

  u = unit(a × h); v = a × u

  Constructability checks constructability.js

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• Socket access to a bolt

  Whether a socket over a bolt head or nut runs into another part, and how much free length there is.

  R_s = 1.96·d ÷ 2 + wall; grid step = max(2.5, R_s ÷ 8); stations at 0, ¼, ½, ¾ and 1 × socket length

  Constructability checks constructability.js

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• Room between neighboring bolts

  Whether the socket over one bolt touches the head of the next.

  lat = |dv − A·(dv·A)|; need = 1.96·d_max ÷ 2 + wall + 1.96·d_min ÷ 2

  Constructability checks constructability.js

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• Fillet weld size limits

  The smallest and largest fillet weld allowed for the thinner of the two parts joined.

  min = 3, 5, 6 or 8 mm for thickness up to 6.35, 12.7, 19.05 mm or more; max = t when t < 6.35, else t − 1.6

  Constructability checks constructability.js

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• Torch access along an all-round weld

  The share of an all-round fillet weld's line where a torch on the 45 degree bisector is blocked.

  start s0 = r·√2 + 1; direction = unit(outward + away); tested every 5 mm for the reach

  Constructability checks constructability.js

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• Slope of a hollow section

  The slope of a tube, used to decide whether an open upper end lets rain in.

  slope = asin(|Δz| ÷ length) × 180 ÷ π

  Constructability checks constructability.js

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• Steel and bar weight in the status line

  The total weight of all steel parts and of all reinforcing bars, shown under the drawing.

  steel = Σ part weight; bars = Σ row total weight

  Weight totals in the status line and panels detailcraft.js

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• Steel weight of a selection

  The weight of the selected members plus the main plate of each selected connection.

  steel = Σ weight of selected members and connection plates

  Weight totals in the status line and panels detailcraft.js

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• Cut length and weight of one part

  The cut length, weight and weight per meter shown for a selected member.

  Weight totals in the status line and panels detailcraft.js

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• A dimension figure

  The number printed on a dimension line, and the value recorded for the sheet.

  figure = round(value)

  Dimensions and views on drawing sheets drawings.js

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• A chain of dimensions with its overall

  The run of dimensions between successive positions and the overall dimension beside it.

  step_i = v_i − v_{i−1}; overall = v_n − v_0

  Dimensions and views on drawing sheets drawings.js

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• Positions to dimension

  The sorted list of distinct positions a chain is drawn through.

  keep v when v − previous kept > 0.5 mm

  Dimensions and views on drawing sheets drawings.js

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• Sheet scale

  The largest standard scale at which a view fits its room on the paper.

  first n in the list with size ÷ n ≤ room

  Dimensions and views on drawing sheets drawings.js

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• Model to paper

  The scale and offset that place a view on the sheet.

  paper = origin + model ÷ s

  Dimensions and views on drawing sheets drawings.js

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• Part of a member inside a view's slab

  The stretch of a member's axis that lies inside the band a plan or elevation shows.

  a = (lo − s0) ÷ k, b = (hi − s0) ÷ k; k = x̂·A

  Dimensions and views on drawing sheets drawings.js

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• Corners of a part's box

  The eight corners of a part's section box, moved onto the cut faces at mitre ends.

  Dimensions and views on drawing sheets drawings.js

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• Outline of a projected part

  The convex outline of a part's projected box corners.

  pop while cross(o, a, b) ≤ 1e-9

  Dimensions and views on drawing sheets drawings.js

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• Hidden parts of a line

  Splits a drawn line into the runs that show and the runs behind a part in front.

  Dimensions and views on drawing sheets drawings.js

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• Where two paper lines cross

  The position along one segment where it crosses another.

  t = ((c − a) × q) ÷ (r × q), u = ((c − a) × r) ÷ (r × q)

  Dimensions and views on drawing sheets drawings.js

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• A hole's center and axis

  Where a hole is in the model and which way it goes through the part.

  flange hole: v = ±(depth ÷ 2 − t ÷ 2)

  Dimensions and views on drawing sheets drawings.js

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• An assembly in its main part's coordinates

  The welded-on parts, holes and overall extents of an assembly, measured along and across its main part.

  Dimensions and views on drawing sheets drawings.js

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• Weights in an assembly's part list

  The weight of each part, of each line and of the whole assembly in the part list.

  total = Σ n × weight

  Dimensions and views on drawing sheets drawings.js

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• Rounding to six decimals

  The rounding applied to every number written to the file.

  round(v × 10⁶) ÷ 10⁶

  Drawing sheets as DWG and DXF dwgout.js

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• Text position and height

  Where a line of text sits and how tall it is in the DWG model.

  height = size × 0.718

  Drawing sheets as DWG and DXF dwgout.js

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• Line and polyline vertices

  The points of each line, polyline and solid fill in the DWG model.

  Drawing sheets as DWG and DXF dwgout.js

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• Outline of a filled circle

  The polygon used as the boundary of a filled circle.

  (c_x + r·cos(2π·i ÷ 48), c_y + r·sin(2π·i ÷ 48))

  Drawing sheets as DWG and DXF dwgout.js

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• A number in the DXF text

  How each coordinate is printed in the DXF file.

  Drawing sheets as DWG and DXF dwgout.js

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• Line weight of a pen

  The line weight written for a layer, in hundredths of a millimeter.

  round(w × 100)

  Drawing sheets as DWG and DXF dwgout.js

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• Model point to screen

  Where a model point is drawn on the canvas.

  Erection movie player erection-html.js

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• Where a pick is at a given minute

  The offset of a lifted piece from its final place while the movie plays.

  Erection movie player erection-html.js

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• Load chart cleaned

  The chart rows kept: sorted by radius, with a capacity that never rises as the radius grows.

  Erection plan: picks, crane loads and times erection.js

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• Capacity at a radius

  The chart capacity that applies at a given radius.

  capacity = kg of the first row with radius ≥ r; 0 beyond the last row

  Erection plan: picks, crane loads and times erection.js

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  Exact