Masonry beam and deep beam
A fully grouted reinforced concrete masonry beam on two bearings, or an interior span of a continuous beam, to TMS 402-22 strength design or allowable stress design (the switch in the toolbar). Where the effective span is short for the depth, the beam is designed as a deep beam (TMS 402-22 5.3.2) with the internal lever arm of Table 5.3.2.2 and distributed flexural bars. US and metric units. For a lintel with arching action and point loads in the wall above, use the masonry lintel calculation.
Edition. TMS 402-22 is not on hand. The beam and deep beam provisions were read in the 402-16 text (5.2, 5.2.2, Table 5.2.2.2, 9.3.4.2) and carry the 402-22 numbers of the TMS cross-reference list (5.3, 5.3.2, 9.3.3.2); the MDG-2022 sample example 12.4-2A, written to 402-22, is the published check. Items still to confirm against the 2022 text are marked in the steps.
Inputs of the masonry beam #
- Beam: nominal width; depth from the courses (8n − 3/8 in.) or entered; f′m; the mortar (it sets the modulus of rupture of Table 9.1.9.2 for Mcr); Grade 60 or 40; coarse or fine grout.
- Reinforcement: bottom bar size, bars per course and courses with bars, the soffit to the lowest bars; for a deep beam the spacing of the distributed bars over the lower half (bond-beam courses or joint reinforcement, at most dv/5 and 16 in.); top bars for a continuous span; single-leg stirrups and their spacing; the bar embedment past the face of the support.
- Span and loads: simple span or interior span of a continuous beam; the clear span and the bearing lengths (span = clear span plus half the bearing at each end, 5.3.1.1); for a continuous span the moment coefficients and the shear factor are yours (1/16, 1/11 and 1.15 prefilled, ACI 318-19 6.5 style); the lateral support spacing of the compression face (0 = braced continuously); the self-weight (81 psf for a fully grouted 8 in. medium-weight wall) and uniform dead, live, roof live and snow loads.
- Code options: the shear design section (d/2 from the face, 5.3.1.5, or the face); Mu/(Vu dv) taken as 1.0 or computed; whether the beam supports unreinforced masonry (the l/600 limit of 4.6), the limit and the 8d exemption.
Auto-design (editor toolbar) varies the courses, the courses with bars, bars per course, bar size and the stirrups. Objective: the shallowest beam, then the least steel. Span, loads, width, f′m and code options are kept.
Checks performed #
| Check | Basis |
|---|---|
| Deep beam classification | leff = min(centre to centre, 1.15 ln); deep when leff/dv < 2 (simple) or < 3 (continuous) (5.3.2.1, 2.2) |
| Flexure (beam) | Strain compatibility, 0.80 f′m block, φ of Table 9.1.4 (9.3.2); cracked transformed section with Fs and 0.45 f′m (8.3) |
| Tension controlled | c at most the depth for εt = εty + 0.003 (9.3.3.2.4), εty = 0.002 for Grade 60 |
| Minimum flexural strength | Mn ≥ 1.3 Mcr, Mcr = fr b h²/6 with fr parallel to the bed joints, unless As ≥ 4/3 of the required area (9.3.3.2.2.2, .3) |
| Flexure (deep beam) | Mn = As fy z (Ma = As Fs z), z of Table 5.3.2.2; distributed bars over the tension half at most dv/5 and 16 in. apart (5.3.2.3) |
| Negative moment (continuous) | Top bars, by the same methods |
| Shear | Vn = Vnm + Vns, Anv = b d, Vns with dv = h, upper limits of 9.3.3.1.2; 8.3.5 in allowable stress |
| Stirrups | Required above φVnm; Av/s ≥ 0.0007 b; s ≤ dv/2 and 48 in. (9.3.3.2.3), or dv/5 and 16 in. in a deep beam with horizontal shear steel at least half the vertical (5.3.2.4) |
| Total reinforcement (deep beam) | ρh + ρv ≥ 0.001 (5.3.2.5) |
| Lateral support, bearing | Compression face braced at most min(32b, 120b²/d) (5.3.1.3); bearing at least 4 in. (5.3.1.4) |
| Development | Bottom bars past the face of the support at least ld of Eq. 6-1 (6.1.6.3.1) |
| Bar limits | db ≤ b/8 and 1/3 of the grout space, area per course ≤ 4 % of the grout space (6.1.3) |
| Deflection | l/600 under service dead plus live with Ieff of Eq. 5-1 (5.3.1.6, 4.6), where the beam supports unreinforced masonry and the span exceeds 8d |
The drawings are the beam elevation with its loads and bars and the beam section.
Limitations #
- Uniform loads only; no point loads, no axial load (9.3.3.2.1 limits it to 0.05 An f′m), no torsion.
- Fully grouted beams in running bond; partially grouted beams, stack bond and clay masonry are not covered.
- The bearing stress on the supporting masonry is not checked (masonry bearing calculation); arching action is not taken (masonry lintel calculation).
- Deflection is calculated for simple spans only; for continuous spans the averaged Ieff is yours.
- Deep beams: the minimum vertical shear reinforcement and the total reinforcement are read as ratios (Av/(b s) and ρh + ρv); the 402-16 text prints 0.0007 b d and 0.001 b dv (to confirm against the 2022 text).
Verification examples #
Verification status: 18 values compared in 4 examples (2 published, 2 hand calculations from the cited equations): 18 within tolerance, 0 recorded deviations. Thin: only 2 published examples. Code basis: not yet recorded for this module.
Published: MDG-2022 Example 12.4-2A (on hand as a sample chapter): factored load, moment, required steel, cracking moment, nominal strength, maximum reinforcement ratio, lateral support limit, and in the rework the moment, design strength (printed as "Mn", the value is φMn), shear at d/2 and Vnm. Hand calculations: the allowable moment of the same beam and a deep beam (lever arm, Mn, shear).