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Generation from JSON database
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‎assets/db/equations.json‎

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{
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"Cylinder": {
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"title": "Cylinder",
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"legend": [
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"D : diameter",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = D /cdot /pi/]",
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"/[A = /pi r^{2}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{/pi /cdot D^{4}}{64}/]",
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"/[W = /frac{/pi /cdot D^{3}}{32}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Hollow Cylinder": {
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"title": "Hollow Cylinder",
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"legend": [
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"D : diameter",
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"d : internal diameter",
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"t : thickness",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[d = D - 2t/]",
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"/[P = D /cdot /pi + d /cdot /pi = /pi (D + d)/]",
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"/[A = /pi r^{2} - /pi (r - t)^{2} = /pi t (D - t)/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{/pi /cdot (D^{4} - d^{4})}{64}/]",
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"/[W = /frac{/pi /cdot (D^{3} - d^{3})}{32}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Rectangle Bar": {
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"title": "Rectangle Bar",
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"legend": [
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"B : base length",
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"H : height",
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"R : corner radius",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = 2 (B + H - 4R) + 2 /pi R/]",
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"/[A = B (H - 2R) + 2R (H - 2R) + /pi R^{2}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I /approx /frac{B H^{3}}{12}/]",
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"/[W /approx /frac{B H^{2}}{6}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Rectangular Tube": {
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"title": "Rectangle Tube",
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"legend": [
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"B : base length",
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"H : height",
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"R : outer radius",
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"r : inner radius",
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"t : thickness",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[r = max /left /{ 0 ; R - t /right /} /]",
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"/[P_{inner} = 2 (B + H - 4t - 4r) + 2 /pi r/]",
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"/[A_{inner} = (B - 2t)(H - 2t - 2r) + 2r (B - 2t - 2r) - /pi r^{2}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I /approx /frac{B H^{3} - (B - 2t)(H - 2t)^{3}}{12}/]",
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"/[W /approx /frac{B H^{3} - (B - 2t)(H - 2t)^{3}}{6 H}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Triangle Prism": {
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"title": "Triangular Prism",
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"legend": [
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"B : base length",
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"H : height",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = B + 2 /sqrt{/frac{B^2}{4} + H^2}/]",
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"/[A = /frac{B H}{2}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{B H^3}{36}/]",
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"/[W = /frac{B H^2}{24}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Trapezius Prism": {
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"title": "Trapezius Prism",
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"legend": [
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"B : major base length",
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"b : minor base length",
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"H : height",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = B + b + 2 /sqrt{/frac{(B - b)^{2}}{4} + H^2}/]",
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"/[A = /frac{H (B + b)}{2}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{H^3 (b^3 + 4Bb + B^2)}{36 (B + b)}/]",
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"/[W = /frac{H^2 (b^2 + 4Bb + B^2)}{12 (B + 2b)}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Hexagon Prism": {
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"title": "Hexagonal Prism",
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"legend": [
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"H : height (side to side)",
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"e : edge length",
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"s : circumscribed diameter",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[e = /frac{H}{2 sin/frac{/pi}{3}}/]",
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"/[s = 2e/]",
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"/[P = 6e/]",
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"/[A = /frac{P /cdot H}{4}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{5 /sqrt{3}}{16} /cdot e^4/]",
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"/[W_{A} = /frac{2 I}{H}/]",
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"/[W_{B} = /frac{2 I}{s}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Octagonal Prism": {
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"title": "Octagonal Prism",
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"legend": [
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"H : side to side dimension",
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"e : edge length",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[e = H /sqrt{2} - H = /frac{H}{1 + /sqrt{2}}/]",
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"/[P = 8e/]",
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"/[A = 2 (/sqrt{2} - 1) /cdot H^2/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{/sqrt{2} - 1}{6} /cdot H^4/]",
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"/[W = /frac{2 I}{H} = /frac{/sqrt{2} - 1}{3} /cdot H^3/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Elliptic Bar": {
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"title": "Elliptic Bar",
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"legend": [
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"A : horizontal diameter",
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"B : vertical diameter",
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"a : horizontal radius",
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"b : vertical radius",
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"h : circularity factor",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[a = /frac{A}{2} /; , /; b = /frac{B}{2}/]",
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"/[h = /frac{(a - b)^2}{(a + b)^2}/]",
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"/[P /approx /pi (a + b) /left(1 + /frac{3h}{10 + /sqrt{4 - 3h}} /right)/]",
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"/[A = /pi /frac{A /cdot B}{4}/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I = /frac{/pi A B^3}{64}/]",
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"/[W = /frac{2 I}{B} = /frac{/pi A B^2}{32}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"Hollow Ellipse Bar": {
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"title": "Elliptic Tube",
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"legend": [
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"A : horizontal diameter",
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"B : vertical diameter",
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"a : horizontal external radius",
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"b : vertical external radius",
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"t : thickness",
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"h : circularity factor",
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"h<sub>i</sub> : internal circularity factor",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[a = /frac{A}{2} /; , /; b = /frac{B}{2}/]",
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"/[h = /frac{(a - b)^2}{(a + b)^2} /; , /; h_i = /frac{(a - b)^2}{(a + b)^2}/]",
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"/[P /approx /pi /left[ (a + b) /left(1 + /frac{3h}{10 + /sqrt{4 - 3h}} /right) + (a + b - 2t) /left(1 + /frac{3h_i}{10 + /sqrt{4 - 3h_i}} /right) /right]/]",
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"/[A /simeq /frac{/pi}{4} /left [A B - (A - 2t)(B- 2t) /right ]/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I /simeq /frac{/pi}{64} /left [A B^3 - (A - 2t)(B- 2t)^3 /right ]/]",
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"/[W = /frac{2 I}{B} /simeq /frac{/pi}{32 /cdot B} /left [A B^3 - (A - 2t)(B- 2t)^3 /right ]/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"H Profile": {
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"title": "H Profile",
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"legend": [
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"B : base length",
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"H : height",
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"t : central thickness",
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"h : wings inner height",
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"L : length",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = 2 (2B + H - t)/]",
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"/[A = B (H - h) + ht/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I_{A} = /frac{B H^3 - (B-t) h^3}{12}/]",
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"/[W_{A} = /frac{2 I_{A}}{H} = /frac{B H^3 - (B-t) h^3}{6H}/]",
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"/[I_{B} = /frac{(H - h) B^3 - h t^3}{12}/]",
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"/[W_{B} = /frac{2 I_{B}}{B} = /frac{(H - h) B^3 - h t^3}{6B}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"C / U Profile": {
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"title": "C Profile",
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"legend": [
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"B : base length",
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"H : height",
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"b : inner base",
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"h : wings inner height",
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"L : length",
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"v<sub>1</sub> : barycenter height",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
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"W : strength modulus on vertical load",
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"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = 2 (B + H + b)/]",
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"/[A = B H - b h/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[I_{A} = /frac{B H^3 - b h^3}{12}/]",
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"/[W_{A} = /frac{2 I_{A}}{H} = /frac{B H^3 - b h^3}{6H}/]",
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"/[v_1B = /frac{1}{2} /cdot /frac{(H - h) B^2 + h (B - b)^2}{(H - h) B + h (B - b)}/]",
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"/[I_{B} = /frac{H {v_1B}^3 - h (v_1B - B + b)^3 + (H - h)(B - v_1B)^3}{3}/]",
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"/[W_{B} = /frac{I_{B}}{B - v_1B}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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},
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"T Profile": {
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"title": "T Profile",
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"legend": [
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"B : base length",
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"H : height",
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"t : central thickness",
366+
"h : central height",
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"L : length",
368+
"v<sub>1</sub> : barycenter height",
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"R<sub>m</sub> : braking/ultimate strength",
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"R<sub>eH</sub> : yeld strength",
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"I : moment of inertia relative to horixontal axis",
372+
"W : strength modulus on vertical load",
373+
"F<sub>max</sub> : max traction load"
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],
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"geo": [
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"/[P = 2 (B + H)/]",
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"/[A = B (H - h) - h t/]",
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"/[V = A /cdot L/]",
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"/[if (L = 0) /Rightarrow S = A/]",
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"/[if (L /neq 0) /Rightarrow S = 2A + P /cdot L/]"
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],
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"phi": [
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"/[m = V /cdot /rho/]",
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"/[v_1A = /frac{1}{2} /cdot /frac{t H^2 + (B - t) (H - h)^2}{t H + (B - t) (H - h)}/]",
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"/[I_{A} = /frac{B {v_1A}^3 - (B - t) (v_1A - H + h)^3 + t(H - v_1A)^3}{3}/]",
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"/[W_{A} = /frac{I_{A}}{H - v_1A}/]",
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"/[I_{B} = /frac{(H - h) B^3 - h t^3}{12}/]",
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"/[W_{B} = /frac{2 I_{B}}{B} = /frac{(H - h) B^3 - h t^3}{6B}/]",
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"/[if (R_{s} /neq 0) /Rightarrow F_{max} = /frac{R_{s}}{3} /cdot A/]",
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"/[else /Rightarrow F_{max} = /frac{R_{m}}{4} /cdot A/]"
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]
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}
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}

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