2c:null 2d:["$","title",null,{"children":"Concrete Column Interaction Diagram | Ron Kok | Observable"}] 32:T9c4,viewof input = { const form = html`

item	unit
f_c′	ksi	Rectangle Circle Octagon
f_y	ksi
width	inches
depth	inches
bar size
bar pattern
clear cover	inches	Ties Spirals
tie or spiral size		Ties Spirals

`; form.oninput = () => form.value = { fc: form.fc.value, fy: form.fy.value, width: form.width.value, depth: form.depth.value, barSize: form.barSize.value, barPattern: form.barPattern.value, cover: form.cover.value, tieSize: form.tieSize.value, crossSection: form.crossSection.value, confiner: form.confiner.value }; form.oninput(); return form; }33:T410a,diagram = { // Standard US reinforcing bar properties const barDiameter = { "#3": 0.375, "#4": 0.5, "#5": 0.625, "#6": 0.75, "#7": 0.875, "#8": 1.0, "#9": 1.128, "#10": 1.27, "#11": 1.41, "#14": 1.693, "#18": 2.257 } const barArea = { "#3": 0.11, "#4": 0.2, "#5": 0.31, "#6": 0.44, "#7": 0.6, "#8": 0.79, "#9": 1.0, "#10": 1.27, "#11": 1.56, "#14": 2.25, "#18": 4.0 } // Helper function const error = msg => { return html`

Error. ${msg}

` } // Do some input validity checks if (isNaN(input.fc)) { return error(`f_c′ must be numeric.`) } if (isNaN(input.fy)) { return error("f_y must be numeric.") } if (isNaN(input.width)) { return error("Width must be numeric.") } if (isNaN(input.cover)) { return error("Cover must be numeric.") } const isCircle = input.crossSection === "Circle" const isOctagon = input.crossSection === "Octagon" const isRectangle = !(isCircle || isOctagon) const gotSpirals = input.confiner === "Spirals" const depthStr = input.depth let H = 0 if (isCircle || isOctagon) { // Depth is irelevant. We'll use width. } else if (isNaN(depthStr)) { return error("Depth must be numeric or blank.") } else { H = Number(depthStr) } const rebarPattern = /^([0-9]+) *x *([0-9]+)$/ let barPattern = input.barPattern.trim() if (isCircle || isOctagon || gotSpirals) { if (isNaN(barPattern)) { return error("A circular bar pattern must be entered as a single integer, e.g., “12”.") } } else if (!isNaN(barPattern)) { if (Number(barPattern) % 4 !== 0) { return error("The bar pattern should be an integer evenly divisible
by 4 or it should be written in the format
𝐦 x 𝐧, where 𝐦 and 𝐧 are integers ≥ 2.") } } else if (!rebarPattern.test(barPattern)) { return error("Invalid input for number of bars.") } // Collect the input data const fPrimeC = Number(input.fc) const fy = Number(input.fy) const b = Number(input.width) const barSize = input.barSize const cover = Number(input.cover) const tieSize = input.tieSize.trim() // More column data const barDia = barDiameter[barSize] if (!barDia) { return error("Not a valid bar size.") } const barRadius = barDia / 2 const areaPerBar = barArea[barSize] const tieDia = barDiameter[tieSize] if (!tieDia) { return error("Not a valid tie size.") } const tieIR = 2 * tieDia // inside radius of tie bending curve const tieOR = 3 * tieDia const Ag = isRectangle ? b * H : isOctagon ? 0.8284271247 * b ** 2 : Math.PI * b ** 2 / 4 // Get the number of bars let numTopBars = 0 let numSideBars = 0 let numBars = 0 if (isNaN(barPattern)) { const pos = barPattern.indexOf("x") numTopBars = Number(barPattern.slice(0, pos)) numSideBars = Number(barPattern.slice(pos + 1)) numBars = 2 * numTopBars + 2 * (numSideBars - 2) } else { numBars = Number(barPattern) if (!(isOctagon || isCircle || gotSpirals)) { numTopBars = numBars / 4 + 1 numSideBars = numTopBars } } if (numBars < 4 ) { return error("ACI 318 section 10.7 requires at least 4 vertical bars.") } if (numBars < 6 && gotSpirals) { return error("ACI 318 section 10.7 requires at least 6 vertical bars in a spiral.") } const steelArea = numBars * areaPerBar const rho = steelArea / Ag if (rho < 0.005 || rho > 0.08) { return error("ACI 318 sections 10.6.1 and 10.3.1.2 require ρ to be between 0.5% and 8%.") } const scale = 100 / Math.max(b, H) // Draw the column in a box 100px wide. // We'll create an SVG. First write the input data. let svg = ` Concrete Column fc′ fy ACI 318- ${isCircle ? "Diameter" : (isOctagon ? "Width across flats" : "Width")} ${String(fPrimeC)} ${String(fy)} 14 ${b} ksi ksi inches inches ` if (isRectangle) { // Write the depth svg += `Depth${H}inches` } // Write bar size, bar pattern, cover, and tie size const yBarSize = isRectangle ? 140 : 120 svg += `Bar size${barSize}` svg += `${isNaN(barPattern) ? "Bar pattern" : "# of bars"}${barPattern}` svg += `Clear cover${cover}inches` svg += `${gotSpirals ? "Spiral" : "Tie"} size${tieSize}` // Draw the column cross-section if (isRectangle) { svg += `\n` } else if (isCircle) { svg += `\n` } else { // An octagon const angleIncrement = 2 * Math.PI / 16 const cx = 210 + b / 2 * scale const cy = 20 + b / 2 * scale const R = (b / 2 / Math.cos(angleIncrement)) * scale svg += `\n` } // Draw the ties/spirals if (isCircle || isOctagon || gotSpirals) { svg += `\n\n` } else { svg += `\n \n` } // Draw the vertical bars const brp = (barRadius * scale).toFixed(2) // bar radius in px let topSpacing = 0 let sideSpacing = 0 if (isCircle || isOctagon || gotSpirals) { const angleIncrement = 2 * Math.PI / numBars const cx = 210 + b / 2 * scale const cy = 20 + b / 2 * scale const R = (b / 2 - cover - tieDia - barRadius) * scale - 1 const adjustment = numBars === 6 ? 0 : Math.PI / (numBars === 4 ? 4 : 2) for (let i = 1; i <= numBars; i++) { const theta = (i - 1) * angleIncrement + adjustment const xbar = (cx + Math.cos(theta) * R).toFixed(2) const ybar = (cy - Math.sin(theta) * R).toFixed(2) svg += `\n` } } else { // Rectangular column const margin = ((1 - 0.7071) * tieIR - (1 - 0.7071) * barRadius > 0) ? cover + tieDia + (1 - 0.7071) * tieIR - (1 - 0.7071) * barRadius + barRadius : cover + tieDia + barRadius + 0.0625 topSpacing = (b - 2 * margin) / (numTopBars - 1) sideSpacing = (H - 2 * margin) / (numSideBars - 1) for (let i = 0; i < numTopBars; i++) { svg += `\n` svg += `\n` } for (let i = 1; i < numSideBars - 1; i++) { svg += `\n` svg += `\n` } } // Check if we want to draw the centerlines if (isRectangle && (b !== H || numTopBars !== numSideBars)) { svg += `\n` svg += `\n` // Write x's on the horizontal axis svg += `x\n` svg += `x\n` } // Write in the Ag, As, and rho values svg += `Ag = ${Ag.toFixed(1)} in²\n` svg += `As = ${steelArea.toFixed(2)} in²\n` svg += `ρ = ${(rho * 100).toFixed(2)}%\n` // Write in the bar spacing if (isCircle || isOctagon || gotSpirals) { const spacing = (b - 2 * cover - 2 * tieDia - barDia) * Math.PI / numBars svg += `bar spacing = ${spacing.toFixed(2)}″\n` } else { svg += `bar spacing = ${topSpacing.toFixed(2)}″ × ${sideSpacing.toFixed(2)}″ c/c\n` } if (rho < 0.01 || rho > 0.06) { svg += `Check if ACI 318 section 18.7.4 allows this ρ value.` } // Draw the x & y axis for the diagram const baseX = 450 const baseY = 180 svg += `\n` svg += `\n` // øPn label on the y-axis svg += `ϕPn (kips)\n` // 0 at the origin svg += `0` // øMn label on the x-axis svg += `ϕMn (kip·ft)\n` // Do the math to find the curve points let [Px, Mx, Mxb, Pmax, MxMax, PatMxMax, MxAtPmax] = curveArray(fPrimeC, fy, b, H, Ag, areaPerBar, barRadius, barPattern, cover, tieDia) let needTwoCurves = false let Py =0 let My = 0 let Myb = 0 let MyMax = 0 let MyatPmax = 0 let PatMyMax = 0 let MyAtPmax = 0 if (H !== 0 && (b !== H || numTopBars !== numSideBars)) { needTwoCurves = true; if (isNaN(barPattern)) { // The bar pattern is written as `m x n`, where m and n are integers. // So we reverse the order to look at moments about the y axis. const parts = barPattern.match(rebarPattern) barPattern = parts[2] + " x " + parts[1] } [Py, My, Myb, Pmax, MyMax, PatMyMax, MyAtPmax] = curveArray(fPrimeC, fy, H, b, Ag, areaPerBar, barRadius, barPattern, cover, tieDia) } // find scales and find the max M const vertScale = 170 / (1.05 * Pmax) const topOfGraph = baseY - vertScale * Pmax let Mb = 0 let Mmax = 0 let PatMmax = 0 let MatPmax = 0 let biggerMAxis = "" if (MxMax > MyMax) { Mmax = MxMax PatMmax = PatMxMax Mb = Mxb MatPmax = MxAtPmax biggerMAxis = "x" } else { Mmax = MyMax PatMmax = PatMyMax Mb = Myb MatPmax = MyAtPmax biggerMAxis = "y" } let horizScale = 200 / (1.05 * Mmax) svg += ` Pmax ? Pmax : Px[i])).toFixed(2) } svg += path + `"/>\n` // Write Mpure let xPos = baseX + horizScale * Mb let align = (Mb > Mx[Mx.length - 2]) ? "start" : "end" svg += `${Math.round(Mb / 12)}\n` if (needTwoCurves) { svg += ` Pmax ? Pmax : Py[i])).toFixed(2) } svg += path + `"/>\n` } // Pmax svg += `${Math.round(Pmax)} kips\n` // PatMmax & Mmax xPos = baseX + horizScale * Mmax + 10 const sPatMmax = Math.round(PatMmax) const sMmax = Math.round(Mmax / 12) svg += `ϕPn = ${sPatMmax} kips\n` svg += `ϕMn = ${sMmax} kip·ft\n` if (needTwoCurves) { svg += `(${biggerMAxis} axis)\n` } // M at Pmax svg += `ϕMn = ${Math.round(MatPmax / 12)} kip·ft\n` // Draw the background lines const iVert = backgroundLineSpacing(Pmax) const iHoriz = backgroundLineSpacing(Mmax / 12) const endX = baseX + 200 horizScale = horizScale * 12 for (let i = 1; i < 20; i++) { if (baseY - i * iVert * vertScale < topOfGraph) { break } svg += `\n` svg += `${Math.round(i * iVert)}\n` } for (let i = 1; i < 20; i++) { if (i * iHoriz * horizScale > 200) { break } svg += `\n` svg += `${Math.round(i * iHoriz)}\n` } svg = "" // We want to display an element, not an element. // Start by escaping all the characters that are not allowed in a data-uri. svg = svg.replace(/"/g, `'`) // Single quotation marks don't need to be escaped. const symbols = /[\r\n%#()<>?[\\\]^`{|}]/g const uri = svg.replace(symbols, encodeURIComponent) // Finally, return the . return html `

` }34:T2d98,function curveArray(fPrimeC, fy, b, H, Ag, areaPerBar, barRadius, barPattern, cover, tieDia) { // Calculate the interaction diagram for a concrete column. // Return the results in a pair of arrays. const isCircle = input.crossSection === "Circle" const isOctagon = input.crossSection === "Octagon" const isRectangle = input.crossSection === "Rectangle" const gotSpirals = input.confiner === "Spirals" const phiB = 0.9 // ACI 318 strength reduction factor for bending const phiC = gotSpirals ? 0.7 : 0.65 // ditto for compression const tieIR = 2 * tieDia // inside radius of tie bending curve let numLayers = 0 // number of layers of reinforcing steel let y // y-coordinate of each layer of reinforcing steel let A // area of each layer of reinforcing steel const P = [] // axial strength const M = [] // bending strength const beta1 = fPrimeC <= 4 ? 0.85 : fPrimeC >= 8 ? 0.65 : 0.85 - (fPrimeC - 4) / 20 // Get the number of bars let numTopBars = 0 let numSideBars = 0 let numBars = 0 if (!isNaN(barPattern)) { numBars = Number(barPattern) if (isRectangle && !gotSpirals) { numTopBars = numBars / 4 + 1 numSideBars = numTopBars } } else { const pos = barPattern.indexOf("x") numTopBars = Number(barPattern.slice(0, pos)) numSideBars = Number(barPattern.slice(pos + 1)) numBars = 2 * numTopBars + 2 * (numSideBars - 2) } const steelArea = numBars * areaPerBar const rho = steelArea / Ag // find the locations of the layers of steel bars if (isRectangle && !gotSpirals) { numLayers = numSideBars y = new Array(numLayers).fill(0) A = new Array(numLayers).fill(0) const margin = ((1 - 0.7071) * tieIR - (1 - 0.7071) * barRadius > 0) ? cover + tieDia + (1 - 0.7071) * tieIR - (1 - 0.7071) * barRadius + barRadius : cover + tieDia + barRadius const spacing = (H - 2 * margin) / (numSideBars - 1) for (let i = 0; i < numLayers; i++) { y[i] = i === 0 ? margin : y[i - 1] + spacing const numBarsInLayer = i === 0 || i === numLayers - 1 ? numTopBars : 2 A[i] = numBarsInLayer * areaPerBar } } else { // Circular bar pattern const theta = 2 * Math.PI / numBars const r = b / 2 - cover - tieDia - barRadius // radius to center of bar if (numBars === 6) { numLayers = 3 y = new Array(numLayers).fill(0) A = new Array(numLayers).fill(0) y[0] = b / 2 - r * Math.cos(theta / 2) A[0] = 2 * areaPerBar y[1] = b / 2 A[1] = 2 * areaPerBar y[2] = b / 2 + r * Math.cos(theta / 2) A[2] = 2 * areaPerBar } else if (numBars % 2 === 0) { numLayers = 2 + (numBars - 2) / 2 y = new Array(numLayers).fill(0) A = new Array(numLayers).fill(0) y[0] = cover + tieDia + barRadius A[0] = areaPerBar y[numLayers - 1] = b - cover - tieDia - barRadius A[numLayers - 1] = areaPerBar let alpha = 0 for (let i = 1; i < numLayers - 1; i++) { alpha = alpha + theta y[i] = b / 2 - r * Math.cos(alpha) A[i] = 2 * areaPerBar } } else { numLayers = 1 + (numBars - 1) / 2 y = new Array(numLayers).fill(0) A = new Array(numLayers).fill(0) let alpha = -theta / 2 for (let i = 0; i < numLayers - 1; i++) { alpha = alpha + theta y[i] = b / 2 - r * Math.cos(alpha) A[i] = 2 * areaPerBar } y[numLayers - 1] = b - cover - tieDia - barRadius A[numLayers] = areaPerBar } } // Find maximum compression, where moment = 0 const Po = 0.85 * fPrimeC * (Ag - steelArea) + fy * steelArea let Pmax = (gotSpirals ? 0.85 : 0.8) * phiC * Po // Load the initial values of axial strength, P, and bending strength, M P.push(Pmax) M.push(0) // get ready to start the while loop that will find axial and moment strengths let phiHasChanged = false let iWhenPhiChanged = 0 let gotMatPmax = false let MatPmax = 0 const concreteStrain = 0.003 const d = y[numLayers - 1] // depth from compression face to max steel layer // definition: steelStrain = strain at "d" let steelStrain = 0.003 // initial value, starting at max compression // The upcoming loop will iterate with varying locations of the neutral axis. // That varies the steel strain, starting at max compression, and adding tension // to the steel in increments. At each iteration, we calculate column axial strength // and bending strenth. We'll iterate until we reach the pure bending condition // for the column. let delta = -(fy / 29000 + concreteStrain) / 50 // delta strain per step // Before we start the while loop, we're going to jump ahead to the point where a = h // a = h = beta1*c = beta1*d * (0.003 / (-steelStrain + 0.003)), so from algebra: steelStrain = 0.003 - 0.003 * beta1 * d / (isRectangle ? H : b) steelStrain = steelStrain - delta // correct for the first increment while (true) { steelStrain = steelStrain + delta const c = d * (0.003 / (-steelStrain + 0.003)) // distance to neutral axis const s = (0.003 - steelStrain) / d // slope of strain line const a = beta1 * c // distance to edge of Whitney stress block let Cc = 0 // concrete compression chord force let Mc = 0 // moment about center of column due to Cc if (isRectangle) { // We have a rectangular cross section Cc = 0.85 * fPrimeC * b * (a < H ? a : H) // Concrete compression chord force (first pass) Mc = a < H ? (Cc * (H / 2 - a / 2)) : 0 // Moment about center of column due to Cc } else if (isOctagon) { const sideLength = 0.414213562 * b const chamferLength = (b - sideLength) / 2 if (a < b) { let Aregion = 0 let Yregion = 0 if (a < 0.2928932 * b) { Aregion = sideLength * a + a ** 2 Yregion = (0.5 * sideLength * a ** 2 + 2 / 3 * a ** 3) / Aregion } else if (a < 0.5 * b) { const Aquarter = sideLength * chamferLength + chamferLength ** 2 const Yquarter = (0.5 * sideLength * chamferLength ** 2 + 2 / 3 * chamferLength ** 3) / Aquarter const Aslice = b * (a - chamferLength) const Yslice = chamferLength + (0.5 * b * (a - chamferLength) ** 2) / Aslice Aregion = Aquarter + Aslice Yregion = (Aquarter * Yquarter + Aslice * Yslice) / Aregion } else if (a < 0.5 * b + chamferLength) { const Ahalf = 0.82842712 * b ** 2 / 2 const Yhalf = (0.5 * sideLength * chamferLength ** 2 + 2 / 3 * chamferLength ** 3 + b * sideLength / 2 * (chamferLength + sideLength / 4)) / Ahalf const Aslice = b * (a - b / 2) const Yslice = b / 2 + (0.5 * b * (a - b / 2) ** 2 / Aslice) Aregion = Ahalf + Aslice Yregion = (Ahalf * Yhalf + Aslice * Yslice) / Aregion } else { const AthreeQuarters = b * sideLength + sideLength * chamferLength + chamferLength ** 2 const YthreeQuarters = (b * sideLength * (chamferLength + sideLength / 2) + 0.5 * sideLength * chamferLength ** 2 + 2 / 3 * chamferLength ** 3) / AthreeQuarters const aPrime = a - sideLength - chamferLength const Aslice = b * aPrime - aPrime ** 2 const Yslice = (b * aPrime * (chamferLength + sideLength + aPrime / 2) - aPrime ** 2 * (chamferLength + sideLength + 2 / 3 * aPrime)) / Aslice Aregion = AthreeQuarters + Aslice Yregion = (AthreeQuarters * YthreeQuarters + Aslice * Yslice) / Aregion } Cc = 0.85 * fPrimeC * Aregion Mc = Cc * (b / 2 - Yregion) } else { Cc = 0.85 * fPrimeC * Ag Mc = 0 } } else { const Ycircle = b / 2 const Acircle = Math.PI * b ** 2 / 4 if (a < b) { if (a > b / 2) { const nearSide = a - b / 2 // one side of a triangle, for the trig const alpha = Math.acos(nearSide / (b / 2)) const Asegment = b ** 2 * (alpha - Math.sin(alpha) * Math.cos(alpha)) / 4 // segment of a circle const Qsegment = b ** 3 * (Math.sin(alpha)) ** 3 / 12 const Ysegment = Qsegment / Asegment + b / 2 const Aregion = Acircle - Asegment // area of region in compression const Yregion = (Acircle * Ycircle - Asegment * Ysegment) / Aregion Cc = 0.85 * fPrimeC * Aregion Mc = Cc * (b / 2 - Yregion) } else { const nearSide = b / 2 - a const alpha = Math.acos(nearSide / (b / 2)) const Asegment = b ** 2 * (alpha - Math.sin(alpha) * Math.cos(alpha)) / 4 const Qsegment = b ** 3 * (Math.sin(alpha)) ** 3 / 12 const Ysegment = b / 2 - Qsegment / Asegment Cc = 0.85 * fPrimeC * Asegment Mc = Cc * (b / 2 - Ysegment) } } else { Cc = 0.85 * fPrimeC * Ag Mc = 0 } } let Psteel = 0 let Msteel = 0 for (let j = 0; j < numLayers; j++) { // Find forces contributed by each layer of reinforcing bars. const yLocal = c - y[j] const localStrain = s * yLocal // strain in this layer of bars let fs = 29000 * localStrain // steel stress if (fs > fy) { fs = fy } // limited to yield stress if (fs < -fy) { fs = -fy } // ditto const PsLocal = A[j] * fs // area of this layer times steel stress Psteel = Psteel + PsLocal const localArm = (isRectangle ? H : b) / 2 - y[j] Msteel = Msteel + PsLocal * localArm if (a > y[j]) { const CcLocal = A[j] * 0.85 * fPrimeC Cc = Cc - CcLocal Mc = Mc - CcLocal * localArm } } P.push(phiC * (Cc + Psteel)) M.push(phiC * (Mc + Msteel)) if (!gotMatPmax) { if (P[P.length - 1] < Pmax) { // This is where the curve dips below Pmax MatPmax = M[M.length - 1] gotMatPmax = true } } if (!phiHasChanged) { if (steelStrain <= -0.005) { iWhenPhiChanged = P.length - 1 phiHasChanged = true delta = 2 * delta } } if (P[P.length - 1] < 0) { break } } // The last iteration of that loop just barely crossed into a point of negative axial load. // Do a linear interpolation to find M at the pure bending point (where axial load = 0). const numPoints = P.length const n = numPoints - 1 // index of last point M[n] = M[n - 1] + (M[n] - M[n - 1]) / (P[n] - P[n - 1]) * (0 - P[n - 1]) P[n] = 0 // Rework the points after the change in phi const numPointsAfterChange = numPoints - iWhenPhiChanged if (numPointsAfterChange > 0) { const s = ((phiB / phiC) - 1) / numPointsAfterChange for (let i = iWhenPhiChanged; i < numPoints; i++) { const f = s * (i - iWhenPhiChanged) M[i] = M[i] * (1 + f) } } let Mb = M[n] if (rho < 0.01) { // In low seismic areas, ACI 318 sections 10.6.1 and 10.3.1.2 allow rho to less than 1%, but only // if the area of the column is assumed to be small enough to make an effective rho of 1%. // Here, we do that reduction. const r = rho / 0.01 // reduction factor for (let i = 0; i < numPoints; i++) { P[i] = r * P[i] M[i] = r * M[i] } Pmax = r * Pmax Mb = r * Mb } let Mmax = 0 let PatMmax = 0 for (let i = 0; i < numPoints; i++) { if (M[i] > Mmax) { Mmax = M[i] PatMmax = P[i] } } return [P, M, Mb, Pmax, Mmax, PatMmax, MatPmax] } 35:[] 30:{"id":"4d0fa5d0125e1b22","slug":"concrete-column-interaction-diagram","title":"Concrete Column Interaction Diagram","thumbnail":"2e7fc4fd5a82cc96a10d1d474247435ab2f5363fedc18f1cf5fcf831224e8fb6","access_level":"public","create_time":"$D2020-03-26T15:51:32.260Z","update_time":"$D2022-05-13T22:32:24.149Z","view_time":null,"first_public_time":"$D2020-04-02T17:20:09.358Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"f8cea2abc7249eb3","login":"ronkok","name":"Ron Kok","avatar_url":"https://avatars-next.observableusercontent.com/9da9c3ded25c70e265a4953d90d833bf112966f9aedc5aa2f0aa21c5435d6a28","tier":"starter_2024"},"version":1093,"publish_version":1093,"role":null,"authored":false,"authors":[{"type":"individual","id":"b8a040dc9e849ca6","login":"ronkok","name":"Ron Kok","avatar_url":"https://avatars-next.observableusercontent.com/9da9c3ded25c70e265a4953d90d833bf112966f9aedc5aa2f0aa21c5435d6a28","tier":null}],"members":[{"type":"individual","id":"b8a040dc9e849ca6","login":"ronkok","name":"Ron Kok","avatar_url":"https://avatars-next.observableusercontent.com/9da9c3ded25c70e265a4953d90d833bf112966f9aedc5aa2f0aa21c5435d6a28","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Concrete Column Interaction Diagram","cells":[{"id":0,"value":"md`# Concrete Column Interaction Diagram`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"md `This notebook creates a concrete column interaction diagram per ACI 318-14.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":784,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1059,"value":"md `To copy the diagram, right-click it and select the \"Copy image\" option.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1079,"value":"md `In rectangular columns, the bar pattern may be written in the form:
𝐦 x 𝐧
where 𝐦 and 𝐧 are integers ≥ 2.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":587,"value":"md `This diagram is not the last word on column capacity. Slenderness must be addressed elsewhere. Also, ACI 318 has several prescriptive requirements that must be met in order for this diagram to be valid. Such as: maximum bar spacing, minimum ρ values, minimum cover, and requirements for spirals. You are responsible to check those prescriptive requirements.\n\nOnly qualified engineers should use this diagram.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":836,"value":"function backgroundLineSpacing(num) {\n const numStr = num.toExponential(2)\n const pos = numStr.indexOf(\"+\")\n const exponent = Number(numStr.slice(pos + 1))\n const c0 = numStr.charAt(0)\n const c1 = numStr.charAt(2)\n if (c0 === \"1\") {\n const n = { \"0\": 0.2, \"1\": 0.3, \"2\": 0.3, \"3\": 0.3, \"4\": 0.3, \"5\": 0.3, \"6\": 0.4, \"7\": 0.4, \"8\": 0.5, \"9\": 0.5 }[c1]\n return n * 10 ** exponent\n } else {\n const n = { \"2\": 0.5, \"3\": 0.75, \"4\": 1.0, \"5\": 1.0, \"6\": 1.5, \"7\": 2.0, \"8\": 2.0, \"9\": 2.0 }[c0]\n return n * 10 ** exponent\n }\n }\n \n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1"}} 31:"$30:body"