Calculations

Calculations

• Outlet condition

  Sets the last column of a flow-through box from its neighbor.

  f_out = f_eq(1, u_nb) + (f_nb − f_eq(ρ_nb, u_nb))

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Velocity at a point

  The velocity reported at a position in the grid.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Result fields

  A copy of the velocity, speed, density or tracer field for reading or plotting.

  speed = √(u_x² + u_y²)

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Mixing time

  The number of steps until the tracer is evenly spread.

  deviation = max |C − mean|; reached when deviation ≤ level × starting deviation

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Residence time distribution

  The distribution of times a pulse of tracer takes to leave a flow-through box, with its mean, variance and the nominal time.

  E = flux ÷ Σ(flux × Δt); mean = Σ t E Δt; variance = Σ t² E Δt − mean²; nominal = V ÷ Q

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• VTK export

  Writes the velocity and tracer fields as a legacy ASCII VTK file.

  2D mixing solver (lattice Boltzmann) cfd/lbm.js

  • CadCraft
  64-bit

• Lineweight to the file's lineweight index

  Picks the stored lineweight that is nearest to the one the layer or object has.

  index = the i with the smallest |table[i] − lineweight|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Ellipse with a ratio above 1

  Rewrites an ellipse whose minor axis is longer than its major axis so the file holds a ratio of 1 or less.

  major′ = (−m_y, m_x) × ratio; ratio′ = 1 ÷ ratio; start and end − π ÷ 2

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Ray and construction line direction

  Writes the direction of a ray or construction line as a unit vector.

  d′ = d ÷ |d|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Drawing extents

  The lower left and upper right corner of model space written to the file header.

  min and max of x, y, z over the defining points

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Default angles of a light

  The hotspot and falloff angles written for a light that has none of its own.

  hotspot = π ÷ 4; falloff = π ÷ 4 + 0.0872664626

  Values changed when a DWG is written dwg/solid-write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Standard gravity

  The acceleration that turns a member's or plate's mass into its own weight.

  g = 9.80665 m/s²

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  Exact

• Member length and local axes

  The length of a member and the three unit vectors its forces and section are measured in.

  L = |P_j − P_i|; x = (P_j − P_i) ÷ L; z = unit(Z − (Z·x) x); y = z × x; then y and z turned by the roll

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Zero-length member test

  Removes a member whose two ends are at the same place.

  |P_j − P_i| < 1e-6 mm

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Area and second moments of a polygon section

  Area, centroid, second moments about the centroid, principal moments and their angle for a section outline with holes.

  A = ½ Σ cᵢ; Iyy = (1 ÷ 12) Σ (v₀² + v₀v₁ + v₁²) cᵢ − A c_v²; cᵢ = u₀v₁ − u₁v₀; I₁,₂ = (Iyy + Izz) ÷ 2 ± √(((Iyy − Izz) ÷ 2)² + Iyz²)

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Torsion constant

  The Saint-Venant torsion constant J of a catalog section or of an outline.

  I with fillets: J = ⅔ B T³ + ⅓ (D − 2T) t³ + 2 α D₁⁴ − 0.420 T⁴; open: Σ b t³ ÷ 3; tube: 4 Am² t ÷ p; round tube: π (D⁴ − (D − 2t)⁴) ÷ 32

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Section properties for the analysis

  Chooses the area, the two second moments, J and the roll a drawn section is analyzed with.

  A = the profile's exact area if given, else the polygon's; Iy, Iz = Iyy, Izz, or I₁, I₂ with roll = the principal angle

  Member axes and section properties frame/frame-model.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Internal forces at a cut

  N, Vy, Vz, T, My and Mz at a distance x from the member's start.

  S = −(F_i + ∫₀ˣ q); M = −(M_i + r × F_i + Σ r × q)

  Forces and deflection along a member frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Deflection along the member

  The member's displacement between its ends, from its curvature.

  v″ = M_z ÷ (E I_z); w″ = −M_y ÷ (E I_y); u′ = N ÷ (E A); trapezoids, twice

  Forces and deflection along a member frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Station values and deflection off the chord

  The values kept at each station, and how far the member bows from the straight line between its ends.

  rel = √(v_rel² + w_rel²); v_rel = v − v_end × x ÷ L

  Forces and deflection along a member frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Largest and smallest values along a member

  The maximum and minimum of each internal force, where they occur, and the largest deflection with its span ratio.

  max and min over the stations; ratio = L ÷ deflection

  Forces and deflection along a member frame/frame-solve.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Root fillet constants

  The area of one root fillet over r², and how far its centroid is from the corner over r.

  area ÷ r² = 1 − π ÷ 4; centroid ÷ r = 0.2234

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Section properties for the checks

  Plastic and elastic moduli, radii of gyration, the warping constant and the slenderness ratios of an I-shape.

  Zx = bf tf (d − tf) + tw hc² ÷ 4 + 4 A_f (hc ÷ 2 − 0.2234 r); Cw = Iy ho² ÷ 4; rts = √(√(Iy Cw) ÷ Sx)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Slender-element limits

  Decides whether a flange or web is too slender for the checks that are built.

  bf ÷ 2tf > 0.56 √(E ÷ Fy); h ÷ tw > 1.49 √(E ÷ Fy); bending: 1.0 √(E ÷ Fy), 3.76 √(E ÷ Fy)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Tension strength

  The design strength in tension: yielding of the gross section, and rupture when a net area is given.

  φPn = min(0.90 Fy Ag, 0.75 Fu Ae)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Compression strength

  The design strength in compression for flexural buckling about both axes and torsional buckling.

  Fe = π² E ÷ (KL ÷ r)²; Fcr = 0.658^(Fy ÷ Fe) Fy or 0.877 Fe; φPn = 0.9 Fcr Ag

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Moment gradient factor Cb

  The factor that raises the lateral-torsional buckling strength when the moment is not uniform.

  Cb = 12.5 Mmax ÷ (2.5 Mmax + 3 M_A + 4 M_B + 3 M_C)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Major-axis bending strength

  The design bending strength with lateral-torsional buckling and flange local buckling.

  Lp = 1.76 ry √(E ÷ Fy); Lr by (F2-6); Mn by (F2-1) to (F2-4); φMn = 0.9 Mn

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Minor-axis bending strength

  The design bending strength about the weak axis.

  Mp = min(Fy Zy, 1.6 Fy Sy); noncompact flange: straight line to 0.7 Fy Sy; φMn = 0.9 Mn

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Web shear coefficient

  The reduction of shear strength for a slender web or flange.

  Cv = 1; 1.10 √(kv E ÷ Fy) ÷ (h ÷ t); 1.51 kv E ÷ ((h ÷ t)² Fy)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Shear strength along the web

  The design shear strength in the direction of the web.

  φVn = φ 0.6 Fy d tw Cv; φ = 1.0 when h ÷ tw ≤ 2.24 √(E ÷ Fy), else 0.9

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Shear strength along the flanges

  The design shear strength in the direction of the flanges.

  φVn = 0.9 × 0.6 Fy (2 bf tf) Cv, kv = 1.2

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Bending and axial force together

  The utilization of a member under axial force and bending about both axes.

  Pr ÷ Pc ≥ 0.2: Pr ÷ Pc + 8⁄9 (Mrx ÷ Mcx + Mry ÷ Mcy); else Pr ÷ 2Pc + (Mrx ÷ Mcx + Mry ÷ Mcy)

  Steel member strength to AISC 360-16 frame/frame-design-aisc.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Section properties for the checks

  Plastic and elastic moduli, shear areas, the warping constant and radii of gyration of an I or H section.

  Wpl,y = b tf (h − tf) + tw hc² ÷ 4 + 4 A_f (hc ÷ 2 − 0.2234 r); Avz = A − 2 b tf + (tw + 2r) tf; Iw = Iz (h − tf)² ÷ 4

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Cross-section class

  The class of the flange and web in compression and in bending.

  ε = √(235 ÷ fy); flange c ÷ t ≤ 9ε, 10ε, 14ε; web ≤ 72ε, 83ε, 124ε (bending) or 33ε, 38ε, 42ε (compression)

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Tension resistance

  The design tension resistance of the gross section, and of the net section when one is given.

  Nt,Rd = min(A fy ÷ γM0, 0.9 A_net fu ÷ γM2)

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Shear resistance along the web

  The plastic shear resistance, and the shear buckling resistance of a slender web.

  Vpl,Rd = Av fy ÷ (√3 γM0); λ̄w = hw ÷ (86.4 tw ε); χw = η or 0.83 ÷ λ̄w

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Bending resistance with high shear

  The major-axis bending resistance reduced when the shear exceeds half the plastic shear resistance.

  ρ = (2 V_Ed ÷ Vpl,Rd − 1)²; W = Wpl,y − ρ Aw² ÷ (4 tw)

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Bending and axial force on the cross-section

  The utilization of the cross-section under axial force and bending about both axes.

  class 1–2: (My ÷ M_N,y)² + (Mz ÷ M_N,z)^β, β = max(5n, 1); class 3: σ ÷ (fy ÷ γM0)

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Buckling reduction factor

  The reduction factor χ for a slenderness and a buckling curve.

  Φ = 0.5 (1 + α (λ̄ − 0.2) + λ̄²); χ = 1 ÷ (Φ + √(Φ² − λ̄²)) ≤ 1

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Buckling resistance in compression

  The design buckling resistance for flexural buckling about both axes and torsional buckling.

  Ncr = π² E I ÷ L²; λ̄ = √(A fy ÷ Ncr); Nb,Rd = χ A fy ÷ γM1

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Lateral-torsional buckling resistance

  The design bending resistance of an unrestrained segment.

  Mcr = C1 (π² E Iz ÷ L²) √(Iw ÷ Iz + L² G It ÷ (π² E Iz)); λ̄LT = √(W fy ÷ Mcr); Mb,Rd = χLT W fy ÷ γM1

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Bending and compression on the member

  The left sides of the two member interaction equations (6.61) and (6.62).

  N ÷ (χy N_Rk ÷ γM1) + kyy My ÷ (χLT My,Rk ÷ γM1) + kyz Mz ÷ (Mz,Rk ÷ γM1), and the same with χz, kzy, kzz

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Equivalent uniform moment factor

  The factor Cm of Table B.3 read from a segment's moment diagram.

  straight diagram: max(0.6 + 0.4 ψ, 0.4); loaded span: 0.95 + 0.05 αh or 0.90 + 0.10 αh

  Steel member resistance to EN 1993-1-1 frame/frame-design-en.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Yield and tensile strength of the steel

  The fy and fu used for a member from its grade and thickness.

  table value; EN: the lower pair when the thickest part is over 40 mm

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  Exact

• A diagram value between stations

  Reads a force or moment at any distance along the member from the station values.

  a = aₖ + (x − xₖ) ÷ (xₖ₊₁ − xₖ) × (aₖ₊₁ − aₖ)

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• The diagram on one unbraced segment

  The stations inside a segment plus interpolated values at its two ends.

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Quarter-point moments of a segment

  The largest moment of a segment and the moments at its quarter, middle and three-quarter points.

  |M| at x₀ + 0.25 L, 0.5 L, 0.75 L; max |M| over the stations

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Buckling lengths and segments of a member

  The unbraced length, the number of segments and the effective lengths used in the checks.

  lb = min(L, override or ratio × L); segments = ⌈L ÷ lb − 1e-9⌉; Lcy = ky L; Lcz = kz lb; Lt = lb

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit

• Demands and ratios, AISC 360

  Collects each check's demand, capacity and ratio for one member and combination.

  ratio = demand ÷ capacity; demand = largest station value

  Steel member checks on a solved frame frame/frame-design.js

  • CadCraft
  • BimCraft
  • DetailCraft
  64-bit