Column Alignment-Chart Stiffness Ratio G (from member EI/L)
The joint stiffness ratio G from member sizes, the input an effective-length-factor calculation needs.
Example
You enter
- Column 1 moment of inertia Ix (in⁴) 800
- Column 1 length (ft) 12
- Column 2 Ix (in⁴, continuing column; 0 to skip) 800
- Column 2 length (ft, 0 to skip) 12
- Girder 1 moment of inertia Ix (in⁴) 1200
- Girder 1 length (ft) 24
- Girder 2 Ix (in⁴, 0 to skip) 1200
- Girder 2 length (ft, 0 to skip) 24
- Girder far-end condition rigid
You get
- Stiffness ratio G (feed the K tile) 1.333
- Col stiffness 133.333
- Girder stiffness 100
Details, formula, and sources
At a joint G = sum(EI/L)_columns / sum(EI/L)_girders; E is the same steel throughout and cancels, so G = sum(I/L)_columns / sum(I/L)_girders. Girder stiffness carries the standard far-end modifier: braced frame x1.5 (far pinned) / x2.0 (far fixed), moment frame x0.5 (far pinned) / x0.67 (far fixed), rigid x1.0. Two columns (Ix 800 in^4, 12 ft) over two girders (Ix 1,200 in^4, 24 ft), rigid, give G 1.33; feed it as GA or GB to the effective-length calculation (G 10 at a pin, 1 at a fixed base). AISC 360 Commentary App. 7 / Salmon & Johnson. A design aid, not the engineer of record's stamped design.
G = sum(I/L)_columns / (m * sum(I/L)_girders), E cancels; girder modifier m = 1.5 (braced far-pinned), 2.0 (braced far-fixed), 0.5 (moment far-pinned), 0.67 (moment far-fixed), 1.0 (rigid).
The AISC alignment-chart joint stiffness ratio G computed from member sizes, with the standard girder far-end stiffness modifiers, as compiled in AISC 360 Commentary Appendix 7 / Salmon & Johnson, by name.
The stiffness-ratio definition and the girder far-end modification factors are public results in the AISC Commentary and the standard steel-design references; the member I and L are the user's own section and framing data.
Estimate. AHJ and licensed professional govern.
Field names used by the API: ic1, lc1, ic2, lc2, ig1, lg1, ig2, lg2, girder_far_end, g_ratio, col_stiffness, girder_stiffness
- Stiffness ratio G = sum(I/L)_columns / sum(I/L)_girders (E cancels for all-steel frames)AISC Commentary alignment charts
- Girder far-end modifier braced 1.5 (pin) / 2.0 (fix); moment 0.5 (pin) / 0.67 (fix); 1.0 rigidAISC 360 Commentary App. 7 / Salmon & Johnson
- End-condition convention G = 10 at a pin support, G = 1 at a fixed baseAISC Commentary
- Feeds supplies GA or GB to the steel-effective-length-k tilescope of this tile