Calculations

Calculations

• 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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• Weight and center of gravity of a pick

  The weight of an assembly and the point its weight acts at.

  W = Σ w_i; cg = Σ w_i·(a_i + b_i) ÷ 2 ÷ W

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

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• Storey a pick belongs to

  Which storey a pick is erected with, for the order of the sequence.

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

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• Load, radius and share of the chart

  The load on the hook, the working radius, the chart capacity there and the share of it used.

  load = W·(1 + rigging% ÷ 100) + deduction; radius = max(r_pick, r_set); share = load ÷ capacity

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

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• Time of a pick

  How long a pick takes and when it starts and ends.

  travel = (plan distance + top height) ÷ 1000; minutes = hook + travel ÷ speed + set + release; start = max(crane free, supports done)

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

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• Status of a pick

  Whether a pick is fine, over the chart, above the chosen limit, out of reach or too high for the hook.

  over when share > 1; high when share > limit

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

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• Plan totals

  The total weight, the total time, the heaviest pick and the pick that uses most of the chart.

  total kg = Σ W; minutes = max end time

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

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• Figures in the plan's warnings

  The numbers quoted when a pick is over the chart, over the limit or too high.

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

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• Data handed to the movie

  The picks, boxes and times saved into the erection movie page.

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

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• Concrete strength from the footing's text

  The concrete strength in MPa read from text such as 4000 psi, 28 MPa or C30/37.

  MPa = psi × 0.00689476

  Footing design checks foundation.js

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• Support reaction as a footing load

  Turns an analysis support reaction into the load on the footing in the footing's own axes.

  P = F_z ÷ 1000; (V_x, V_y) = rot(−F) ÷ 1000; (M_x, M_y) = rot(−M) ÷ 10⁶

  Footing design checks foundation.js

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• Effective depths

  The depth from the top of the footing to the middle of each layer of bottom bars.

  d_X = H − c − d_bX ÷ 2; d_Y = H − c − d_bX − d_bY ÷ 2

  Footing design checks foundation.js

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• Service load and its eccentricity

  The total vertical load on the soil and where it acts.

  W = γ_c·A·h + γ_s·A·fill; N = ΣP + W; e_x = (ΣP·x + ΣM_y + h·ΣV_x) ÷ N

  Footing design checks foundation.js

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• Pressure under a rigid rectangle

  The plane of soil pressure under the footing, with part of the base lifting off when the load is outside the kern.

  q = a + b·x + c·y; inside the kern: a = N ÷ A, b = 12·N·e_x ÷ (A·L²), c = 12·N·e_y ÷ (A·B²)

  Footing design checks foundation.js

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• Three equations in three unknowns

  Solves the Newton step for the pressure plane.

  Footing design checks foundation.js

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• Soil force and moment beyond a cut

  The upward soil force on the part of the base beyond a cut, and its moment about the cut.

  V = Σ q·dw·ds; M = Σ q·dw·ds·(t − cut)

  Footing design checks foundation.js

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• Demand over capacity

  The ratio each check reports and whether it passes.

  ratio = demand ÷ capacity; ok when ratio ≤ 1 + 1e-9

  Footing design checks foundation.js

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• Sliding and overturning

  The safety factors against sliding on the base and against overturning.

  H = √(V_x² + V_y²); sliding: fs·H ≤ μ·N; overturning: FS = 1 ÷ max(|e_x| ÷ (L ÷ 2), |e_y| ÷ (B ÷ 2))

  Footing design checks foundation.js

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• Shear and moment on a cut, and the largest moment

  The shear and moment on a cut across the footing, and the cut with the largest moment.

  V = V_soil − ΣP; M = M_soil − Σ(P·arm + M_col + h·V_col)

  Footing design checks foundation.js

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• Bending steel

  The steel provided per meter, the steel bending needs and the minimum steel.

  M_u per m = |M| ÷ (b ÷ 1000) × 10⁶; A_s provided = A_bar × 1000 ÷ s; A_s,min = ρ_min × 1000 × H

  Footing design checks foundation.js

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• One-way shear

  The largest shear at a distance d from each column face against the concrete's shear strength.

  V_u = max |V| at face ± d; capacity = 0.75 × V_c

  Footing design checks foundation.js

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• Bar development length

  The straight length a bar needs beyond the column face to develop its strength.

  l_d = max(300, f_y ÷ (k·λ·√f′c) × d_b); k = 2.1, 1.7, 1.4 or 1.1

  Footing design checks foundation.js

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• Hooked bar development length

  The length a hooked bar needs.

  l_dh = max(8·d_b, 150, 0.24·f_y ÷ (λ·√f′c) × d_b)

  Footing design checks foundation.js

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• Length available for development

  The length of bar from the farthest column face to the end of the footing, less the cover.

  available = side ÷ 2 − (|x_col| + c_col ÷ 2) − cover

  Footing design checks foundation.js

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• Critical section for punching

  The perimeter at d ÷ 2 from a column, cut off at the footing's edge, with its length, centroid and section properties.

  b_o = Σ l; J = Σ (d·l³ ÷ 12 + l·d³ ÷ 12 along the bending direction) + d·l·arm²

  Footing design checks foundation.js

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• Punching shear

  The shear stress on the critical section against the concrete's punching strength.

  v_u = V_u ÷ (b_o·d) + γ_v·M·c ÷ J (both directions); v_c = min(0.33, 0.17·(1 + 2 ÷ β), 0.083·(2 + α_s·d ÷ b_o))·λ_s·λ·√f′c

  Footing design checks foundation.js

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• Share of the base in contact

  The share of the base still pressing on the soil when part has lifted off.

  share = cells with q > 0 ÷ 1600

  Footing design checks foundation.js

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• Settlement at the corner of a loaded rectangle

  The settlement under the corner of a flexible rectangle carrying a uniform pressure on an elastic half-space.

  w = q·b·(1 − ν²) ÷ (π·E) × (m·ln((1 + √(m² + 1)) ÷ m) + ln(m + √(m² + 1))); m = long side ÷ short side

  Settlement, flexible mats, pile groups and retaining walls foundation.js

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• Settlement at the center and corner of a footing

  The elastic settlement at the middle and at a corner of the footing.

  center = 4 × corner of the quarter rectangle

  Settlement, flexible mats, pile groups and retaining walls foundation.js

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• Mat mesh size and concrete stiffness

  The element size of the plate mesh and the concrete's modulus.

  size = max(min(clamp(min(L, B) ÷ 14, 150, 600), max(100, smallest column ÷ 3)), √(L·B ÷ 8000)); E_c = 4700·√f′c

  Settlement, flexible mats, pile groups and retaining walls foundation.js

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• Soil springs under the nodes

  The spring stiffness under each node from the subgrade modulus and the area the node carries.

  A = |d₁ × d₂| ÷ 2 (the two diagonals); k_node = k_s × 10⁻⁶ × Σ A ÷ 4

  Settlement, flexible mats, pile groups and retaining walls foundation.js

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• A column load spread over its footprint

  The force on each node inside a column's footprint.

  R_i = P ÷ n + M_y·dx_i ÷ Σdx² − M_x·dy_i ÷ Σdy²

  Settlement, flexible mats, pile groups and retaining walls foundation.js

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