Calculations

Calculations

• Plant sizes in project units

  The factor that turns a plant's mature height and spread in meters into project units.

  project units per meter = 1 ÷ (1200 ÷ 3937) for feet

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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• Tree canopy as a ring

  The outline of a plant's canopy used to find where a span passes over it.

  12 points on the circle of radius r: (x + r·cos(2πk ÷ 12), y + r·sin(2πk ÷ 12))

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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• A plant as an obstacle

  A single plant's canopy radius, height and ground level as an obstacle under a line.

  radius = max(spread ÷ 2, 0.1); height = mature height

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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• Foundation volume shown in cubic yards

  The foundation volume in the support's properties, in cubic yards for a feet project.

  yd³ = m³ × 1.307951

  Overhead line checks: clearances, support loads and sizing powerline/powerline-ui.js

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• Length of a span in the network

  The electrical length of each overhead span.

  length = √(Δx² + Δy²) × m per unit

  Power network: load current and voltage drop powerline/network.js

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• Snapping to the nearest node

  Finds the support or equipment a route end or a piece of equipment connects to.

  nearest node with distance × m per unit ≤ snap + 1e−9

  Power network: load current and voltage drop powerline/network.js

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• Resistance, reactance and ampacity of an edge

  The electrical data of a span or cable route, with parallel cables counted.

  R = R₂₀ ÷ n; X = X ÷ n (0.08 or 0.35 Ω/km by default); ampacity × n

  Power network: load current and voltage drop powerline/network.js

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• Loads summed upstream

  The active and reactive power each edge carries, and the current each load draws.

  Q = P·tan(acos pf); I = √(P² + Q²) ÷ (√3·U)

  Power network: load current and voltage drop powerline/network.js

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• Current, voltage drop and node voltage

  The current and voltage drop in each edge and the voltage and cumulative drop at each node.

  ΔU = √3·I·(L ÷ 1000)·(R·cos φ + X·sin φ); drop % += ΔU ÷ (U × 1000) × 100; U node = U·(1 − drop ÷ 100)

  Power network: load current and voltage drop powerline/network.js

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• Numbers in the file

  Turns a value into the fixed-decimal text the file carries, and newtons into decanewtons.

  text = v.toFixed(d); daN = N ÷ 10, 2 decimals

  Line study file (.DON) export and import powerline/don.js

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• Signed line angle at each support

  The turn of the line at each support in degrees, counter-clockwise positive.

  turn = atan2 of the span ahead − atan2 of the span behind, wrapped to ±180°

  Line study file (.DON) export and import powerline/don.js

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• Support coordinates and heights written

  Each support's position, ground level, pole length, height above ground and line angle as written to the file.

  X = x × m per unit, 3 decimals; Hauteur = typed height × m per unit + embedment

  Line study file (.DON) export and import powerline/don.js

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• Section tension and catenary parameter written

  The reference temperature, horizontal tension and catenary parameter of each section as written to the file.

  Parametre = H ÷ w, 3 decimals; TensionIni = H ÷ 10 daN, 2 decimals

  Line study file (.DON) export and import powerline/don.js

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• Reading a number

  Turns a field's text into a number, accepting a decimal comma.

  Line study file (.DON) export and import powerline/don.js

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• Angles in grades

  Converts a line angle given in grades to degrees.

  degrees = grades × 0.9

  Line study file (.DON) export and import powerline/don.js

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• A study file into a line

  Turns the supports read from a file into a line in project units.

  x = X (m) ÷ m per unit; voltage kV = V ÷ 1000

  Line study file (.DON) export and import powerline/don.js

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• Clear-sky beam and diffuse irradiance

  The irradiance outside the atmosphere, the beam transmittance, and the beam and diffuse irradiance at the ground.

  τ_b = a₀ + a₁·exp(−k ÷ cos Z); G_on = 1367·(1 + 0.033·cos(2πn ÷ 365)); G_bn = G_on·τ_b; τ_d = 0.271 − 0.294·τ_b

  Clear-sky solar irradiance pv/daylight-bim-sky.js

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• Node merging

  One analysis node for every group of points that lie within 1 mm of each other.

  same node when |p − n| ≤ 1 mm

  Analytical frame model from the drawn members analysis.js

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• Splitting a member at the points on it

  The stations along a drawn member where another member's end or a node load lies on it.

  s = (q − start)·u; foot = start + u·s; cut when |foot − q| ≤ 2 mm and 2 mm < s < L − 2 mm

  Analytical frame model from the drawn members analysis.js

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• End points of each piece

  The two points of every piece a split member becomes.

  p = start + u·s

  Analytical frame model from the drawn members analysis.js

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• Section properties per profile

  Area, second moments of area and torsion constant of each profile in use, with the reduced bending stiffness of cracked concrete.

  Iy′ = f·Iy, Iz′ = f·Iz

  Analytical frame model from the drawn members analysis.js

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• Which column feet are supports

  Decides which column feet are held: those with a base plate, or with no member going lower at that node.

  support when lowest z at the node ≥ node z − 1 mm

  Analytical frame model from the drawn members analysis.js

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• Point load on a split member

  Moves a point load from its distance along the drawn member to the piece it falls on.

  a′ = max(0, a − s0)

  Analytical frame model from the drawn members analysis.js

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• Distributed load on a split member

  Cuts a uniform or linearly varying load into the part that falls on each piece.

  w(s) = w + (w₂ − w)·(s − a) ÷ (b − a)

  Analytical frame model from the drawn members analysis.js

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• Sections the drawn members use

  The area and second moments of area listed for each profile in the model.

  Analytical frame model from the drawn members analysis.js

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• One bolt's shear strength

  The single-shear design strength of one bolt in kN.

  φRn = 0.75 × Fnv × (π·d² ÷ 4) ÷ 1000

  Connection autopilot starting sizes autopilot.js

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• End shear from a uniform load

  The end shear of a beam when only a uniform load per meter is given.

  R = w × L ÷ 1000 ÷ 2

  Connection autopilot starting sizes autopilot.js

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• Shear tab rows and plate

  Bolt diameter, number of rows, edge distance and plate thickness for a shear tab.

  clear = d − 2(tf + r); maxRows = ⌊(clear − 2·edge) ÷ 75⌋ + 1; need = max(2, ⌈R ÷ φRn⌉)

  Connection autopilot starting sizes autopilot.js

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• End plate rows and plate

  Bolt rows, plate width, thickness and gauge for an end plate.

  rows wanted = max(4, 2·⌈R ÷ φRn ÷ 4⌉); width = max(150, bf rounded up to 10); gauge = max(90, round(0.55·bf ÷ 5)·5)

  Connection autopilot starting sizes autopilot.js

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• Base plate size and rod spacing

  Plate length and width, rod diameter, hole and rod spacing for a column base.

  length = max(300, (depth + 150) rounded up to 25); sx = length − 100

  Connection autopilot starting sizes autopilot.js

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• Rounding up to a step

  Rounds a size up to the next multiple of a step.

  ⌈v ÷ step − 1e-9⌉ × step

  Connection autopilot starting sizes autopilot.js

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• Box round each part and footing

  The center, axes and half sizes of the box used for the first, coarse test.

  c = o + x̂·L ÷ 2 + v̂·voff; h = (L ÷ 2, width ÷ 2, depth ÷ 2)

  Clash check between parts clash.js

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• 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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• 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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