What the tool checks
The tool checks one beam span between two column faces with three sections: top steel at the left and right supports (negative moment) and bottom steel at midspan (positive moment). For each section it lays the bars out in layers (minimum clear spacing per 25.2.1, 25 mm between layers), finds the effective depth, and calculates the design strength φMn with the rectangular stress block. ACI 318-19 requires beams to be tension-controlled (εt ≥ εty + 0.003), so a section in the transition zone is reported as failing.
Shear is designed in two zones at each end: an end zone of length 2h from the face, and the span region beyond it. The concrete contribution uses the new ACI 318-19 Table 22.5.5.1, which depends on the longitudinal steel ratio ρw. The tool also covers torsion (22.7), crack-control bar spacing (24.3.2), minimum steel (9.6.1.2), development and lap lengths (25.4, 25.5) and deflection (24.2).
SMRF capacity design in short
In a special moment frame the beam must yield in flexure before it fails in shear. So the design shear is not the analysis shear; it is the shear that develops when both ends reach their probable moment strength Mpr (1.25fy, φ = 1), plus the gravity shear: Ve = (Mpr,1 + Mpr,2)/ln + wu·ln/2 (18.6.5.1). The tool checks both sway directions. Within 2h of each face the concrete shear Vc is set to zero when the earthquake part of Ve is at least half of the total (18.6.5.2). Hoops in that zone start within 50 mm of the face and are spaced at no more than d/4, 6db (Grade 420) or 150 mm (18.6.4.4).
What changed in ACI 318-19
- Shear: Vc = max(0.17, 0.66ρw1/3)·λ√f′c·bw·d when at least minimum stirrups are provided (Table 22.5.5.1). Lightly reinforced members get less concrete shear than before.
- Strain limit: beams must be tension-controlled; the old εt ≥ 0.004 transition zone is gone (9.3.3.1).
- Deflection: Ie uses Bischoff's equation with (2/3)Mcr (Table 24.2.3.5). Deflections of lightly reinforced members are larger than with the old Branson equation.
- Development: new grade factor ψg, and a new hooked-bar equation with db1.5 (25.4.3.1).
Worked example
The default inputs are a 300 × 600 mm SMRF beam, f′c 34.5 MPa, fy 415 MPa, clear span 6.0 m. Top 4Ø25 at each support (one layer, d = 537.5 mm) gives a = 92.6 mm, εt = 0.011 (tension-controlled) and φMn = 360.2 kN·m. Bottom 5Ø25 needs two layers (3 + 2), so d = 517.5 mm and φMn = 421.3 kN·m. Probable moments are 488.5 kN·m (top) and 566.8 kN·m (bottom), so Vp = (488.5 + 566.8)/6.0 = 175.9 kN. With Vg = 70 kN, Ve = 245.9 kN. Vp is more than half of Ve, so Vc = 0 in the end zones. Two-leg Ø10 hoops need s ≤ 106.9 mm, and the tool adopts 1 @ 50 then 11 @ 100 mm over 2h = 1200 mm. In the span region (Vu = 217.9 kN at 2h, Vc allowed) stirrups at 240 mm are adequate.
How to use
- Choose the frame type, materials and section size.
- Enter the clear span, the factored gravity load wu and the analysis shears at both faces (from ETABS, SAP2000 or hand analysis).
- Enter the provided bars and factored moments at the two supports and at midspan.
- Enter service moments for the deflection check.
- Read the status and checks, then review the drawings and the step-by-step working. Print the report for your calculation package.
Limits of this tool
- Rectangular sections only (no T-beam flange), normalweight concrete (λ = 1), uncoated bars.
- Flexural strength ignores compression steel (conservative). As′ is used in the deflection check.
- Axial force in the beam is taken as zero.
- Bar cut-off points and the beam–column joint shear check are not included.
FAQ
Why is my SMRF design shear larger than the ETABS shear?
ACI 318-19 18.6.5 requires capacity design. The beam must be able to carry the shear that occurs when both ends develop their probable moments Mpr (with 1.25fy). This is usually larger than the analysis shear, especially when extra flexural steel is provided.
Why is Vc zero near the supports?
In SMRF beams, when the earthquake-induced shear is at least half of the total design shear and the axial force is small, the concrete contribution must be neglected within 2h of the face (18.6.5.2), because cyclic loading degrades it.
My section fails "tension-controlled" but φMn is enough. Why?
ACI 318-19 9.3.3.1 requires nonprestressed beams with low axial load to be tension-controlled (εt ≥ εty + 0.003). Increase the depth or f′c, or reduce the tension steel. Compression steel also helps, but this tool does not count it.
Which deflection limits are used?
Table 24.2.2: immediate live-load deflection ≤ L/360 for floors, and the long-term plus live-load deflection after partitions are installed ≤ L/480 (partitions likely to be damaged) or L/240 (not likely to be damaged).
How is the hook length into the column found?
For SMRF joints the tool uses 18.8.5.1, ℓdh = max(fy·db/(5.4√f′c), 8db, 150 mm). For other frames it shows the 25.4.3.1 equation with conservative factors (ψr = 1.6, ψo = 1.25).