Continuous concrete beam
A nonprestressed rectangular or T-beam over two or more spans by ACI 318-19: moment and shear envelopes by analysis with the live-load patterns of 6.4.2, or by the coefficients of 6.5 where they apply; flexure at every span and support, shear, an optional torsion check, the cutoff points of the top bars (9.7.3) and the deflection of each span.
Inputs of the continuous beam #
- Materials: f'c, the bar grade, the concrete type and density, Ec, the stirrup grade, the bar coating.
- Section: rectangular or T-beam (flange width by Table 6.3.2.1 from the least clear span, or entered), bw, h, cover to the stirrups, aggregate size.
- Spans: centre-to-centre lengths with the uniform superimposed dead and live loads (service) and the bottom bars of each span; top bars at the supports (one row per support from the left; a missing row repeats the last). The support width sets the faces. The web self-weight is added to D (the slab of a T-beam belongs in wD).
- Analysis: with the 6.4.2 patterns (the live load on the span and alternate spans, on adjacent spans, and on all spans), end supports pinned or fixed, interior supports as knife edges; or the coefficients of 6.5 with the exterior support condition and the stiff-column case (wu ℓn²/12).
- Shear and torsion: stirrups (bar, legs, spacing), shear at d from the face, Tu with the torsion type, Al and θ.
- Deflection: your limits (Table 24.2.2), the sustained part of the live load and its duration.
Auto-design varies the overall depth (2 in. steps) and the stirrup spacing with the bars as you laid them out.
Checks performed #
| Check | Basis |
|---|---|
| Demands | Analysis with the 6.4.2 patterns and the ASCE 7-22 combinations, or Tables 6.5.2 / 6.5.4 with 6.5.1 (checked: two spans or more, adjacent clear spans within 20 %, L ≤ 3D) |
| Flexure | Each span (bottom bars, T-section) and each support face (top bars), strain compatibility (22.2), φ by εt, tension-controlled (9.3.3.1), As,min (9.6.1.2) |
| Shear | Vu at d from the face (9.4.3.2), Vc of Table 22.5.5.1, Vs, the section limit 22.5.1.2, Av,min (9.6.3.1), spacing (Table 9.7.6.2.2) |
| Torsion | 22.7 (threshold, compatibility reduction, section limit, At/s, Al, minimums, spacing) |
| Cutoff points | Top bars: the inflection point of the negative envelope, one-third of the bars extended max(d, 12db, ℓn/16) beyond it (9.7.3.8.4), the others to where the continuing bars suffice plus max(d, 12db) (9.7.3.3), all at least ℓd from the face (9.7.3.4); bottom bars per 9.7.3.8.1 / 9.7.3.8.2 stated |
| Deflection | Table 9.3.1.1 reported; Ie (Table 24.2.3.5) at midspan applied to the analysis deflection with the live load on the span and alternate spans, λΔ (24.2.4) |
The drawings show the beam elevation with its loads and the factored moment and shear envelopes.
Limitations #
- Uniform dead and live loads only; columns are not modelled (knife-edge supports), so column moments and the restraint of the exterior columns come from the end condition you choose. No moment redistribution (6.6.5).
- One stirrup layout and one torsion moment for the whole beam; the governing span's shear is checked.
- The deflection scales the elastic deflection by Ig/Ie of the span (Ie at midspan, 24.2.3.7): an approximation the code permits in principle (24.2.3) but not a prescribed method.
- Cutoffs are computed lengths for the detailing; 9.7.3.5 for bars cut in a tension zone is yours.
Verification examples #
Verification status: 12 values compared in 3 examples (1 published, 2 hand calculations from the cited equations): 12 within tolerance, 0 recorded deviations. Thin: only 1 published example. Code basis: the provisions it uses were read in the target edition.
| Example | What it checks | Published | ILX Calcs |
|---|---|---|---|
| StructurePoint continuous T-beam (ACI 318-14) | Flange width, Ib of the T-section, minimum depth of the end span | 130.5 in., 40,634 in⁴, 25.94 in. | same |
The StructurePoint moments come from a frame with columns, which this calculation does not model, so they are not compared. Hand calculations (closed form): two equal spans with the patterns (Mu+ = 1.15² ℓ² w / 5.6, Mu− = wu ℓ²/8, Vu at d), the coefficients of Tables 6.5.2 and 6.5.4 for three spans, and the embedment of the top bars beyond the point of inflection (9.7.3.8.4).