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The uniformly distributed ceiling load carried by the bottom chord.
Include ceiling drywall dead load plus any applicable attic live load, converted to a load per linear meter of chord. This field does NOT follow the unit toggle: it stays newtons per linear metre whatever system the span and modulus fields above are showing. A US figure is quoted in plf (lbf per linear foot), and the WHOLE unit converts, not just its denominator — 1 lbf is 4.4482216152605 N and it is spread over 0.3048 m, so 1 plf is 14.5939 N/m. Multiply a plf figure by 14.5939 before entering it; the default 500 N/m is 34.26 plf. Typing the plf number raw is never refused, it is silently mishandled, in one of two ways. Below 50 plf it is under this field's minimum and is CLAMPED up to 50 rather than rejected, then graded as though 50 had been typed: the default's own 34.26 plf becomes 50 N/m, a tenth of the load meant, and the deflection falls from 5.50 mm to 0.55 mm. From 50 plf up it lands inside the 50-5000 range and is simply accepted, understated by the full 14.5939. Deflection is proportional to this load, so both outcomes understate the answer and bias the L/240 comparison toward the inside of the limit: on this page's other defaults (3 m chord bay, E 11 000 MPa, I 8.71 x 10^6 mm^4) the limit is 12.50 mm, and a chord loaded at 100 plf, which is 1,459.4 N/m, really deflects 16.07 mm, past the 12.50 mm limit, while typing 100 here returns 1.10 mm and sits well inside it.
The bottom chord's span between panel points — where the webs pick it up — not the truss's overall clear span.
Panel point to panel point, which is much shorter than the truss span and is the length that actually bends. Entering the truss's clear span here reports a deflection several times too large, because deflection goes with the fourth power of the span: a chord panel of a third the truss span deflects about one eightieth as much under the same load.
The bottom chord lumber's modulus of elasticity.
The chord timber's E, from the design values for its species and grade — bottom chords are frequently a higher grade than the webs, so the truss's general species is not necessarily the right table row. If the truss drawing names the chord material, use that; if it does not, the truss designer's own deflection figure is a better answer than a value assumed here.
The bottom chord's cross-sectional moment of inertia.
For a rectangular timber chord, I = b x d^3 / 12 about the axis resisting the load, then divided by 10^6 to give the units this field wants. A 38 x 89 mm (nominal 2x4) chord is 2.23, a 38 x 140 mm (2x6) is 8.71, and a 45 x 145 mm is 11.43. The depth is cubed, so chord depth dominates: going from a 2x4 to a 2x6 is not 57% stiffer but almost four times stiffer. Metal-web and steel chords come from the fabricator's published section properties instead, since the section is not a plain rectangle. THE FLOOR ON THIS FIELD USED TO BE 5, which excluded the 2x4, 35 x 97 and 47 x 97 chords that are among the most common sections in the answer. A value below the floor was not refused — it was raised to the floor, which made the chord more than twice as stiff as the one entered, halved the deflection and moved the answer from past the limit to inside it. It is 0.5 now.
Bottom chord deflection
0.231 in
The deflection this bottom chord works out to is below the L/240 ceiling deflection limit for this span shown with it — The L/240 convention the building codes use for a ceiling gives it. Being under one limit is not a design. Nothing else is checked here — not the other limit states, not the connections, not the member the load arrives from.
- L/240 ceiling limit
- 0.5 in
They open the calculator with your figures already in it
Truss Bottom Chord Deflection Calculator: 0.2309 in — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Uniformly-loaded simple beam deflection D = 5wL^4/(384EI), applied to the truss bottom chord acting as a ceiling joist, checked against the standard L/240 ceiling deflection limit
Inputs used
- Ceiling Uniform Load (N/m)
- 500
- Span
- 10 ft
- Modulus of Elasticity E
- 1595415.12 psi
- Moment of Inertia I (×10⁶ mm⁴)
- 8.71
Intermediate steps
- L/240 ceiling limit
- 0.5 in
Confidence note: The deflection this bottom chord works out to is below the L/240 ceiling deflection limit for this span shown with it — The L/240 convention the building codes use for a ceiling gives it. Being under one limit is not a design. Nothing else is checked here — not the other limit states, not the connections, not the member the load arrives from.
What this calculation does not cover
- The bottom chord is modelled as a simply supported beam spanning the full width of the truss, which is not how a truss carries its load. Web members tie the chord to the top chords at panel points and the chord runs continuously past them, so the local bending is over a panel length rather than the whole span, and the L⁴ term alone puts a 6 m (20 ft) span at 81 times a 2 m (6.5 ft) panel before any credit for that continuity. The overall deflection of the truss, which comes from every member stretching and shortening and is what the ceiling below actually follows, is not calculated anywhere on this page.
- The load field is a line load along one chord, not a ceiling pressure, and it can only be uniform. A 0.5 kN/m² ceiling on trusses at 600 mm (24 in) centres works out at 300 N/m of chord, and the page does no tributary-width conversion, so a figure quoted per square metre has to be converted before it is typed in. A water tank or a stack of stored boxes cannot be entered as what it is either, and the same total weight concentrated at mid-span deflects a simple span 1.6 times as much as it does spread evenly.
- Nothing here is a strength check. A bottom chord carries the truss's tension force at the same time as this bending, and what usually governs its size is the combined tension-and-bending interaction rather than a deflection ratio. Chords are spliced with toothed metal plates where the timber runs out, and the plate at a splice or at the heel joint is often the limiting component of the whole truss.
- This is the instantaneous elastic deflection, and almost all of a bottom chord's load is permanent, since plasterboard, insulation and self-weight sit there for the life of the roof. The value that eventually opens a ceiling joint is the crept one, which Eurocode 5 obtains by multiplying the permanent share by (1 + kdef) — around 1.8 for solid timber in a roof space treated as service class 2 — while other codes apply their own multiplier, so the factor is jurisdictional.
- Downward deflection is not the only way a bottom chord moves a ceiling. In a cold loft the chord sits buried in insulation while the timber above it dries and moves, and the differential arches the chord upward in winter, opening a gap along the top of internal partitions. That is a seasonal moisture effect with no term in this formula, and the remedy is slip fixings at the partition head rather than a stiffer chord.
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Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-06 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- Uniformly-loaded simple beam deflection D = 5wL^4/(384EI), applied to the truss bottom chord acting as a ceiling joist, checked against the standard L/240 ceiling deflection limit
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