Special moment frame members
The beam and the column of a reinforced concrete special moment frame by ACI 318-19 18.6 and 18.7, in one frame direction: the dimensional limits, longitudinal bar limits and strengths, the hoops of the beam hinge zones and the column confinement over ℓo, the strong-column rule at the joint above the column, and the capacity-design shears from the probable moments Mpr. The joint itself is the Beam-column joint type.
Inputs of the special moment frame members #
- Materials: f'c, Grade 60 or 80; Mpr and Mn by strain compatibility with all the bars (default: counting the compression bars gives a slightly larger Mpr and so the safer shear) or as a singly reinforced rectangle.
- Beam: width, depth, clear span, bar centroid from the faces, top and bottom bars (continuous over the span), the slab bars inside the effective width (they count in Mnb− for 18.7.3.2 when developed), hoops and spacings.
- Beam loads: dead and live load per foot for the 18.6.5.1 gravity shear with Ev = 0.2SDS D, the live load factor (1.0, or 0.5 where 2.3.6 permits it), and the factored face moments of your analysis.
- Column below the joint: c1 (in the frame direction), c2, clear height, bars per face, cover, hoops with the number of legs (hoop legs and crossties) in each direction, the spacings within and beyond ℓo.
- Column forces: the range of factored axial force with E, the factored moment and shear of the analysis, and the axial force range of the column above (same section) for the strong-column check; interior or exterior joint.
Auto-design varies the column bar size and the hoop spacings of the beam and the column; sections, beam bars and forces are kept.
Checks performed #
| Check | Basis |
|---|---|
| Beam span, width, projection | 18.6.2.1 (a) to (c) |
| Beam bars | Two continuous bars each face, As,min (9.6.1.2), ρ ≤ 0.025 / 0.02 (18.6.3.1); Mn+ ≥ Mn−/2 (18.6.3.2) |
| Beam flexure at the face | φMn ≥ Mu, φ by Table 21.2.2 |
| Beam hoops | s ≤ d/4, 6 in., 6db / 5db within 2h (18.6.4.4); d/2 beyond (18.6.4.6) |
| Beam shear | Ve = (Mpr− + Mpr+)/ℓn + wu ℓn/2 (18.6.5.1); Vc = 0 where the earthquake part ≥ Ve/2 (18.6.5.2) |
| Column dimensions and steel | 18.7.2.1; 0.01 to 0.06 Ag (18.7.4.1) |
| Column axial and flexure | φPn,max; φMn at the axial force of the range that governs (strain compatibility) |
| Strong column | ΣMnc ≥ 6/5 ΣMnb (Eq. 18.7.3.2), Mnc at the least-strength axial force, slab bars in Mnb− |
| Confinement | ℓo (18.7.5.1); hx ≤ 14 in. or 8 in. (18.7.5.2); s ≤ b/4, 6db / 5db, so (18.7.5.3); Ash of Table 18.7.5.4 (a), (b), (c) with kf, kn, both directions; spacing beyond ℓo (18.7.5.5) |
| Column shear | Ve = 2Mpr/ℓu over the Pu range, not more than ΣMpr,b/ℓu, not less than Vu (18.7.6.1); Vc = 0 per 18.7.6.2.1 |
The drawings are the beam section at the joint face and the column section within ℓo with the bars and hoops checked.
Limitations #
- One frame direction, rectangular sections, the beam's two ends equal; circular columns, walls and prestressed beams are not covered.
- The joint, lap splice locations, bar development, hooks and crosstie details and the frame analysis are yours.
- For 18.6.5.2 (b) the beam axial force is taken as below Ag f'c/20 (enter beams with larger axial force elsewhere); for 18.7.6.2.1 (b) the least column axial force of the range is used.
Verification examples #
Verification status: 13 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 13 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: the provisions it uses were read in the target edition.
No published special moment frame example with these numbers is on disk. Hand calculations (closed form) check the beam Mn and Mpr of a singly reinforced section, wu and Ve, ℓo, hx and so, the Table 18.7.5.4 ratios and kf, kn.