How far can a 2x joist, rafter, header or beam span, and which check limits it?

What it found

An open sizing tool for simple-span sawn-lumber members, derived from beam formulas and NDS base design values with no span table copied: bending, shear, deflection and bearing checks, a command line, and the governing check named for every result. For SPF No. 2 floor joists at 16 in the longest clear spans are 9 ft 2 in (2x6), 12 ft 1 in (2x8), 15 ft 3 in (2x10) and 17 ft 8 in (2x12). Bending governs 22 of 32 floor cells and live-load deflection the other 10; total-load deflection governs 31 of 32 ceiling cells; bending governs snow-loaded rafters in 29 of 32. The lightest passing floor joist is the deepest at 24 in, which uses 20–50% less lumber than 2x10 at 16 in, but floor vibration is not checked. A cross-check with house-framing found its header bearing area too generous for a single jack under a 2-ply header. Not validated against published span tables, no engineered lumber, no continuous spans, and not a design anyone should build from without a licensed review.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Open-source residential construction

• Does a floor-vibration frequency limit erase the lumber saved by deep, widely spaced joists?Does a floor-vibration frequency limit erase the lumber saved by deep, widely spaced joists? Beam-theory first-mode frequency on the house-spans checks: limits up to 10 Hz change nothing, 12 Hz shortens a 2x10 at 16 in from 15 ft 3 in to 13 ft 11 in, 15 Hz moves the least-lumber 12 ft joist from 2x10 to 2x12. Joist alone, limit is a policy knob. Stylised. Track 12.
• How much of a floor-vibration penalty does the subfloor's T-beam action recover?How much of a floor-vibration penalty does the subfloor's T-beam action recover? Gamma-method partial-composite stiffness on house-vibration: at a 15 Hz limit a 2x10 at 16 in grows from 12 ft 6 in to 13 ft 2 in–14 ft 6 in, depending on two assumed inputs (connection efficiency and panel modulus). Stylised.
• Does a joist lapped over a middle support span farther than a simple-span joist?Does a joist lapped over a middle support span farther than a simple span? FE beam with pattern loading and NDS checks: two-span peak moment equals a simple span's, so bending-governed floors and snow rafters gain nothing; deflection-governed ceiling joists gain up to 18.5%; 1.5 in bearing on the middle support cuts a 2x10 floor joist to 11 ft 4 in. Not validated against published tables. Follow-up to house-spans.
• How far can the beam under a two-span joist sit from the middle of the house?How far can the beam under a two-span joist sit from the middle of the house? Bending-governed floor joists lose 0.4% of total width at a short/long span ratio of 0.9 and 13% at 0.5 (the short span relieves the long one); deflection-governed ceiling joists lose about 5% per 0.1 of ratio. A 2x10 floor can have its beam 3.5 ft off the middle of a 28 ft house. Stylised; not a design.
• Can a house plan be data, and which plan needs the least framing lumber per square foot?Can a house plan be data, and which plan needs the least lumber per sq ft? Parametric one-storey plan to framing takeoff, bill of materials, room-rule checks and IFC4; best plans use 4.8 to 5.2 bf/sq ft at 640 to 1,024 sq ft with none feasible by stick framing at 1,400; local search hits the exhaustive optimum in 36 of 40 runs where random search hits none. Stylised, not a design.
• Where does a new home's price go, and which levers move it most?Where does a new home's price go, and which levers move it most? Share-anchored model (NAHB 2024): size moves the price most (87.8 to 112.0 for 1,600 to 2,400 sq ft), then storeys, finish level and lot; a 14% framing-lumber cut is worth 0.85% of price (2.4% with labour). Index not dollars, assumed driver splits. Milestone 4 of track 12.

All 41 Open-source residential construction projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.