Calculations

Calculations

• Cables and pipes under an overhead line

  The cable routes and pipes an overhead line crosses in plan, with the line's chainage and the level of the top of each.

  cable top = ground − cover ÷ m per unit; pipe top = invert at the crossing + diameter

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Joints from the drum length

  How many joints each cable needs and where along the route they fall.

  run = length × (1 + slack %); joints per cable = ⌈run ÷ drum⌉ − 1; at = k × drum ÷ (1 + slack %)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• Trench quantities

  Trench length, excavation, bedding and backfill volumes, duct length and cable length of a route.

  excavation = width × depth × length; bedding = width × bedding × length; backfill = excavation − bedding − ducts × π(d ÷ 2)² × length; cable = (length × slack + 2 × depth) × count

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• Cubic meters per cubic yard

  The factor used to give volumes in cubic yards in a feet project.

  1 yd³ = 0.764554857984 m³

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  Exact

• Stringing table rows

  Tension, span length, sag and conductor length per section and temperature, in project units.

  length ÷ m per unit; force ÷ 10 for daN or ÷ 4.4482216152605 for lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Stringing table CSV

  The stringing table as CSV text.

  lengths and sags round(v, 2); tension round(v, 1)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Support table rows

  Ground, attachment, load, nominal load, foundation and swing per support, in project units.

  attach height = attach z − ground z; load = worst F_eq in daN or lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Conductor length to buy

  The conductor length of a line with an allowance for jumpers and waste.

  length = Σ catenary lengths × phases × circuits × 1.02 ÷ m per unit

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Lengths and volumes in project units

  Converts meters and cubic meters to feet and cubic yards for the quantity rows.

  LF = m ÷ 0.3048; CY = m³ ÷ 0.764554857984

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Quantities file for TakeoffCraft

  The quantity rows in the format TakeoffCraft reads.

  qty = round(qty, 2)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• 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

  • CivilCraft
  64-bit

• Meters per unit

  The length of each supported unit in meters.

  ft = 0.3048; US survey ft = 1200 ÷ 3937; in = 0.0254; yd = 0.9144; mi = 1609.344

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  Exact

• Scale from two points

  Project units per pixel from two points on the scan and the true distance between them.

  units per pixel = distance ÷ √(Δpx² + Δpy²)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Scale from a stated scale

  Project units per pixel from the scan's resolution and a scale such as 1 inch = 50 feet or 1:500.

  per ÷ dpi, or ratio × 0.0254 ÷ (m per unit) ÷ dpi

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Placement from a scale, origin and rotation

  The transform that puts the sheet's lower-left corner at a point, turned by an angle, at a given scale.

  c = s·cos θ, d = s·sin θ; X = x₀ − d·h + c·px + d·py; Y = y₀ + c·h + d·px − c·py

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Pixel to project coordinates

  The project position of a pixel.

  X = g₀ + g₁·px + g₂·py; Y = g₃ + g₄·px + g₅·py

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Inverse placement

  The transform from project coordinates back to pixels.

  det = g₁·g₅ − g₂·g₄; inverse = adjugate ÷ det

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Scale of a placement

  The project units per pixel a placement stands for, reported with every fit.

  scale = √|g₁·g₅ − g₂·g₄|

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Rotation of a placement

  The angle a placement turns the sheet by, in degrees.

  rotation = atan2(g₄, g₁) × 180 ÷ π

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• 3 × 3 linear solve

  Solves the normal equations of the affine fit.

  Gauss-Jordan elimination with partial pivoting

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Least-squares fit to matched points

  The placement that best matches points picked on the scan to their project coordinates, with each point's residual and the root mean square.

  similarity: c = Σ(u·X + v·Y) ÷ Σ(u² + v²), d = Σ(u·Y − v·X) ÷ Σ(u² + v²); rms = √(Σ r² ÷ n)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Traced arc to points

  Turns an arc found on the scan into points for a line layer.

  n = max(2, ⌈|sweep| ÷ 5°⌉); point = center + r·(cos t, sin t)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Traced lines in project coordinates

  The lines and arcs traced on the scan as one line layer in project coordinates.

  each end point through the placement; kept when its length > the minimum

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Frame of a member

  The origin, the unit direction, the two section axes and the length of a member line.

  x = (e − s) ÷ |e − s|; v = unit(Z − x·x_z); u = v × x; u′ = cos a·u + sin a·v, v′ = −sin a·u + cos a·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Local point to model point

  The model coordinates of a point given along the member and across its section.

  p = o + x·x̂ + u·û + (v + voff)·v̂

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Model point to local point

  Where a model point lies along a member and across its section.

  d = p − o; x = d·x̂, u = d·û, v = d·v̂ − voff

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• End face position on a plane-cut end

  How far along the part its end face is at a given point of the section, for square ends and mitre cuts.

  x = x0 + ku·u + kv·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Section outline clipped at a height

  The part of a section outline below or above a line, used for coped ends.

  t = (limit − a_v) ÷ (b_v − a_v); new point = (a_u + (b_u − a_u)·t, limit)

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit

• 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

  • DetailCraft
  64-bit