Truss Member Force Coefficients — Reference
Maximum member forces as a multiple of the total uniform gravity load W on the truss. Multiply by W = pressure × spacing × span. Positive = tension, − = compression.
Pitched roof trusses — load on the top chord
| Truss | Pitch | Top chord max C | Bottom chord max T | Web max T | Web max C |
|---|---|---|---|---|---|
| King post | 4/12 | −0.791 | 0.750 | 0 | 0 |
| 6/12 | −0.559 | 0.500 | 0 | 0 | |
| 8/12 | −0.451 | 0.375 | 0 | 0 | |
| 12/12 | −0.354 | 0.250 | 0 | 0 | |
| Queen post | 4/12 | −1.054 | 1.000 | 0.354 | −0.250 |
| 6/12 | −0.745 | 0.667 | 0.300 | −0.250 | |
| 8/12 | −0.601 | 0.500 | 0.280 | −0.250 | |
| 12/12 | −0.471 | 0.333 | 0.264 | −0.250 | |
| Fink (W) | 4/12 | −1.186 | 1.125 | 0.265 | −0.265 |
| 6/12 | −0.839 | 0.750 | 0.225 | −0.225 | |
| 8/12 | −0.676 | 0.562 | 0.210 | −0.210 | |
| 12/12 | −0.530 | 0.375 | 0.198 | −0.198 | |
| Howe roof 6 panels | 4/12 | −1.318 | 1.250 | 0.354 | −0.250 |
| 6/12 | −0.932 | 0.833 | 0.300 | −0.250 | |
| 8/12 | −0.751 | 0.625 | 0.280 | −0.250 | |
| 12/12 | −0.589 | 0.417 | 0.264 | −0.250 | |
| Pratt roof 6 panels | 4/12 | −1.318 | 1.250 | 0.333 | −0.300 |
| 6/12 | −0.932 | 0.833 | 0.333 | −0.236 | |
| 8/12 | −0.751 | 0.625 | 0.333 | −0.208 | |
| 12/12 | −0.589 | 0.417 | 0.333 | −0.186 | |
| Scissor bottom pitch = ½ top | 4/12 | −2.372 | 2.281 | 0.839 | −0.250 |
| 6/12 | −1.677 | 1.546 | 0.625 | −0.250 | |
| 8/12 | −1.352 | 1.186 | 0.530 | −0.250 | |
| 12/12 | −1.061 | 0.839 | 0.500 | −0.250 |
Load W is applied uniformly on plan along the top chord and lumped at the top panel points; the half-panels at the heels go directly to the supports. King post: one top joint (apex). Queen post: top joints at the third points. Fink: top joints at the quarter points, bottom joints at the third points.
Parallel-chord trusses — 6 panels, load on the top chord
| Truss | Depth | Top chord max C | Bottom chord max T | Web max T | Web max C |
|---|---|---|---|---|---|
| Pratt | L/8 | −1.000 | 0.889 | 0.694 | −0.500 |
| L/10 | −1.250 | 1.111 | 0.810 | −0.500 | |
| L/12 | −1.500 | 1.333 | 0.932 | −0.500 | |
| Howe | L/8 | −0.889 | 1.000 | 0.250 | −0.694 |
| L/10 | −1.111 | 1.250 | 0.250 | −0.810 | |
| L/12 | −1.333 | 1.500 | 0.250 | −0.932 | |
| Warren | L/8 | −1.000 | 1.000 | 0.401 | −0.601 |
| L/10 | −1.250 | 1.250 | 0.434 | −0.651 | |
| L/12 | −1.500 | 1.500 | 0.471 | −0.707 | |
| Warren + verticals | L/8 | −0.889 | 1.000 | 0.417 | −0.694 |
| L/10 | −1.111 | 1.250 | 0.486 | −0.810 | |
| L/12 | −1.333 | 1.500 | 0.559 | −0.932 |
Load W/6 at each interior top panel point and W/12 at each end top joint; supports at the bottom-chord ends. Pratt: max web compression is the end vertical (the full reaction W/2). Howe: max web compression is the end diagonal.
What the coefficients leave out
| Effect | What to do |
|---|---|
| Ceiling load on the bottom chord | Add it as a second case; it changes the web forces and adds bending to the bottom chord |
| Chord bending between panel points | Combine axial force with panel bending (NDS Eq. 3.9-1 / 3.9-3); it often governs the top chord |
| Unbalanced or drift snow, point loads | Analyze the actual loading; webs near midspan can reverse |
| Wind uplift | Every force reverses under net uplift; check members that were in tension for buckling |
Coefficients computed by PE-Calc with the stiffness solver in the truss calculator (pin-jointed, linear elastic) and checked against the method of joints; determinate trusses, so independent of member size. Spans and panel layouts as stated; values are rounded to three decimals.
Related cheat sheets and tools
Pair with the unit weights card for dead loads, the Euler buckling tool for compression members, and 3D frame analysis when the truss is part of a frame.
Frequently asked questions
How do I use truss force coefficients?
Multiply the coefficient by the total uniform load on the truss, W = pressure × spacing × span (for example 30 psf × 2 ft × 28 ft = 1,680 lb). A Fink truss at 6/12 has a top-chord coefficient of −0.839, so the maximum top-chord compression is 0.839 × 1,680 = 1,410 lb. Negative values are compression.
Why does a lower pitch increase truss forces?
The chords resist the bending moment of the whole truss as a couple, and the lever arm is the truss rise. Halving the pitch roughly halves the rise and doubles the chord forces. A king post truss at 4/12 has 1.5 times the bottom-chord force of the same truss at 6/12.
Which web carries the most compression in a flat Pratt truss?
The end vertical over each support carries the whole reaction, W/2, in compression. The interior verticals carry less, and the diagonals are in tension. In a Howe truss, the pattern reverses: the end diagonals carry the largest compression and the verticals are in tension.
Are these coefficients accurate enough for design?
They are exact for the stated geometry and loading, a pin-jointed truss under uniform gravity load at the panel points. They are not a substitute for an analysis with the actual loads (ceiling load on the bottom chord, unbalanced snow, point loads, uplift), the bending of loaded chords, and the member checks. Use them for preliminary sizing and to check software output.