31:[] 2f:{"title":"Design of a short reinforced concrete column","cells":[{"id":0,"value":"md`## Design of a short reinforced concrete column\n#### Using CSA A23.3-2014 *Design of Concrete Structures*`\n\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":266,"value":"md`This notebook shows an example calculation of a short concrete column axial capacity using the Canadian concrete design standard CSA A23.3. Short is used to describe a column in which slenderness effects can be safely ignored.\n\nAll values are in kips, inches, and ksi.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":262,"value":"md`---\n## Inputs`","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"viewof Pf = number({title: \"Factored Axial Force Demand\", value: 165})","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"viewof b = number({title: \"Column width\", value: \"24\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"viewof d = number({title: \"Column Depth\", value: 36})","pinned":false,"hidden":false,"mode":"ojs"},{"id":355,"value":"viewof fc = number({value: 6.5, title: \"Concrete Compressive Strength\", step: 0.1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":96,"value":"viewof nb = slider({title: \"Number of verts\", value: 8, min: 0, max: 40, step: 1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":93,"value":"viewof bsize = select({\n options: BarNames,\n value: \"25M\",\n title: \"Size of Verts\",\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":309,"value":"viewof fy = number({value: 58, title: \"Reinforcing Yield Strength\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":274,"value":"md`---\n## Calculations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":40,"value":"md`Gross Area`","pinned":false,"hidden":false,"mode":"ojs"},{"id":170,"value":"tex`A_g = (b) (d) = (${b}) (${d}) = ${b*d}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":241,"value":"md`Steel Area`","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"tex`A_s = (n_b)(A_b) = (${nb})(${Ab(bsize)}) = ${nb * Ab(bsize)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":377,"value":"md`Concrete Area`","pinned":false,"hidden":false,"mode":"ojs"},{"id":378,"value":"tex`A_c = A_g - A_s = (${Ag()}) - (${As()}) = ${Ag()-As()}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":457,"value":"md`Equivalent Stress Block Factor`","pinned":false,"hidden":false,"mode":"ojs"},{"id":459,"value":"tex`\\alpha_1 = 0.85 - 0.0015(f_c) = 0.85 - 0.0015(${fc}) = ${a1()}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":104,"value":"md`Column Axial Capacity`","pinned":false,"hidden":false,"mode":"ojs"},{"id":396,"value":"tex`P_r = 0.8(\\phi_c\\alpha_1 f_c A_c + \\phi_s A_s f_y)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":248,"value":"tex`P_r = 0.8[(0.65)(${a1()})(${fc})(${Ac()}) + (0.85)(${As()})(${fy})]`","pinned":false,"hidden":false,"mode":"ojs"},{"id":450,"value":"tex`P_r = ${Pr(Ag(),As(),fc,fy)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":278,"value":"md`---\n## Summary`","pinned":false,"hidden":false,"mode":"ojs"},{"id":293,"value":"tex`P_r = ${Pr(Ag(),As(),fc,fy)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":297,"value":"tex`P_f = ${Pf}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":130,"value":"Pr(Ag(),As(),fc,fy) > Pf ? md`P_r > P_f ---> OK` : md`P_r < P_f ---> NOT OK`","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"md`\n---\n### Misc info and helper functions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":548,"value":"md`Normalized Capacity Table`","pinned":false,"hidden":false,"mode":"ojs"},{"id":559,"value":"table(data)","pinned":false,"hidden":false,"mode":"ojs"},{"id":550,"value":"data = {\n let Ag = 100;\n let fy = 58;\n let r = [0.01,0.02,0.03,0.04];\n let fc = [35,45,55,65];\n let data = [];\n for(let bb=0; bb < 4; bb++){\n for(let aa=0; aa<4; aa++){\n data.push({fc: fc[bb], r: r[aa], Pr: Math.round(Pr(Ag, r[aa]*Ag, fc[bb]/6.895, fy)/Ag*100)/100});\n }\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"value":"md`Array of Canadian rebar information`","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"BarOptions = ([{name: '10M', db: 0.39, A:0.155}, {name: '15M', db: 0.59, A:0.31}, {name: '20M', db: 0.79, A:0.465}, {name: '25M', db: 0.98, A:0.775},{name: '30M', db: 1.18, A:1.085},{name: '35M', db: 1.38, A:1.55}])","pinned":false,"hidden":false,"mode":"ojs"},{"id":108,"value":"table(BarOptions)","pinned":false,"hidden":false,"mode":"ojs"},{"id":155,"value":"BarNames = ['10M','15M','20M','25M','30M','35M']","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"//function to look up bar diameter\nfunction db(size) {\n let bar = BarOptions.find(o => o.name === size)\n return bar.db\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"// function to look up bar area\nfunction Ab(size) {\n let bar = BarOptions.find(o => o.name === size)\n return bar.A\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":411,"value":"// gross area\nfunction Ag() { return b*d}","pinned":false,"hidden":false,"mode":"ojs"},{"id":415,"value":"//steel area\nfunction As() { return nb * Ab(bsize)}","pinned":false,"hidden":false,"mode":"ojs"},{"id":427,"value":"// Net concrete area\nfunction Ac() { return Ag() - As() }","pinned":false,"hidden":false,"mode":"ojs"},{"id":441,"value":"// equivalent concrete stress block factor\nfunction a1() { return Math.round((0.85-0.0015*fc*6.895)*1000)/1000 }","pinned":false,"hidden":false,"mode":"ojs"},{"id":452,"value":"// Pr calculates axial capacity\nfunction Pr(Ag,As,fc,fy) { \n const Ac = Ag - As\n const a1 = 0.85-0.0015*fc*6.895\n return Math.round(0.8*(0.65*fc*a1*Ac + 0.85*As*fy)*10)/10\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":113,"value":"md`---\n### Imports for notebook`","pinned":false,"hidden":false,"mode":"ojs"},{"id":111,"value":"import {table} from \"@tmcw/tables@444\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":151,"value":"import {select, number, slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}