Calculations

Calculations

• 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

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• Point inside a section outline

  Whether a point lies inside a closed outline.

  Clash check between parts clash.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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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