Coupling beam

A reinforced concrete coupling beam between two special structural walls, ACI 318-19 18.10.7: which reinforcement the code allows for its aspect ratio and shear, and the design of either two intersecting groups of diagonal bars (18.10.7.4) or longitudinal bars and hoops as a special moment frame beam (18.6.3 to 18.6.5, the wall boundary taken as a column). The demands come from the analysis of the coupled walls with the earthquake effects; this type designs the beam, not the walls.

Inputs of the coupling beam #

• Materials: f'c, reinforcement grade, concrete type (λ).
• Beam: width bw (usually the wall thickness), depth h, clear span ℓn between the wall faces, clear cover to the hoops.
• Demands (factored, from the analysis with E): shear Vu; for longitudinal bars also the moment Mu at the face, the factored gravity shear at the face (added to the capacity-design shear Ve) and the axial compression (Vc is taken as zero only when it is below Ag f'c/20, 18.6.5.2(b)).
• Reinforcement: diagonal or conventional. 18.10.7.1 requires conventional reinforcement when ℓn/h ≥ 4; 18.10.7.2 requires diagonals when ℓn/h < 2 and Vu ≥ 4λ√f'c Acw, unless the engineer shows that the loss of the beam does not impair vertical load capacity, egress or nonstructural components (a check box: the engineer's determination); between, either is allowed. For a slender beam the engineer may waive 18.6.2.1(b), (c) by showing lateral stability by analysis.
• Diagonal bars: bar size, bars per group, layers per group, the distance from the beam face to the centroid of each group at the wall face (it sets α: tan α = (h − 2 × distance)/ℓn), and the confinement: each group in its own cage (18.10.7.4(c), cage width and depth out-to-out) or the full section (18.10.7.4(d)).
• Longitudinal bars: top and bottom bars (size, number).
• Hoops: bar, spacing (along the diagonals for group confinement), legs across bw (vertical legs: also the shear legs of a conventional beam) and legs over the depth; the embedment of the bars into each wall.

Auto-design chooses the lightest diagonal bars (size and number per group) or top and bottom bars, then the hoops (size, spacing, legs); the beam size, span, demands and the reinforcement type stay the engineer's. See Auto-design.

Checks performed #

The drawings show the beam elevation between the wall piers (the crossing diagonal groups, or the bars and hoops) and the section at the wall face.

Limitations #

• Rectangular beams; slabs or flanges acting with the beam, steel and composite coupling beams are not covered.
• The walls, their boundary elements and the 18.10.9 ductile coupled wall checks are not part of this type.
• The shear and moment come from the engineer's analysis; the beam's stiffness (effective section properties) is not computed.
• Development uses Eq. 25.4.2.4a with Ktr = 0 (conservative inside a confined boundary element); the 1.25 fy requirement is our reading of 18.10.2.5 (to confirm against the code text).

Verification examples #

Verification status: 13 values compared in 3 examples (1 published, 2 hand calculations from the cited equations): 13 within tolerance, 0 recorded deviations. Thin: only 1 published example. Code basis: the provisions it uses were read in the target edition.

Published worked examples (backend/tests/test_verify_coupling_beam.py):

Hand calculations cover the diagonal option (α from the geometry, 2 Avd fy sin α, the 10√f'c Acw cap) and the Ash of the full-section confinement. No published diagonally reinforced coupling beam example to ACI 318-19 is on disk.