All-in-one concrete beam calculator for the USA — calculate minimum beam size (width × depth), required flexural reinforcement (As), shear capacity check (Vn vs Vu), and effective depth (d) per ACI 318-19. Covers simply supported, continuous, and cantilever beams using Grade 60 steel and normal-weight concrete for all US structural concrete projects.
Select a calculation tab — Beam Sizing, Required Flexural Steel, or Shear Capacity Check — all per ACI 318-19.
Enter the clear span between faces of supports in feet
Both-ends continuous is typical for interior beams in cast-in-place concrete frames
Number of main tension bars in the single bottom layer — typically 2–6 for standard beams
ASTM A615 Grade 60 — #8 is most common for standard US commercial beams
#3 stirrups are standard for most US beams up to 24 in. deep
Cover measured to the outside face of the stirrup per ACI 318 Table 20.6.1.3
M_u = factored design moment from structural analysis (1.2D + 1.6L per ASCE 7 / ACI 318)
Web width (b_w) of the beam — use minimum beam width calculator above if unknown
Effective depth = h − cover − stirrup dia. − d_b/2 — use effective depth calculator if unknown
4,000 psi (4 ksi) is the most common US commercial concrete specification
Grade 60 (ASTM A615 or A706) is the standard US structural rebar specification
Calculator will determine how many bars of this size are needed to satisfy M_u
V_u = factored design shear from structural analysis (1.2D + 1.6L per ASCE 7) at face of support
Web width of the beam cross-section in inches
Effective depth from compression face to centroid of tension steel
Specified 28-day compressive strength of concrete
Two-legged (closed) stirrups assumed — standard for US beam shear reinforcement
Center-to-center spacing of stirrups in inches — ACI 318 max spacing = d/2 or 24 in., whichever is less
Yield strength of the stirrup steel — Grade 60 is most common for US stirrups
Factored axial compression — enter 0 for beams with no significant axial force
A complete US concrete beam design per ACI 318-19 involves five interdependent checks: (1) minimum depth from ACI 318 Table 9.3.1.1 for deflection control, (2) minimum width from Section 25.2 for rebar fit, (3) required flexural tension steel area (As) from the factored moment Mu using the rectangular stress block method of ACI 318 Section 22.2–22.3, (4) shear capacity check per ACI 318 Section 22.5, and (5) verification that the provided steel satisfies both the minimum steel ratio (ρmin) and the maximum steel ratio (ρmax) for tension-controlled ductile failure. This calculator covers the three most frequently needed checks — size, flexure, and shear — that define the beam's cross-section and reinforcement for any US structural concrete project.
ACI 318-19 Section 22.2 uses the Whitney rectangular stress block model for flexural design. The concrete compressive stress distribution at ultimate is idealized as a uniform block of intensity 0.85 × f'c over a depth of a = β1 × c, where β1 = 0.85 for f'c ≤ 4,000 psi (reduced by 0.05 for each 1,000 psi above 4,000 psi, minimum 0.65). The nominal moment capacity is Mn = As × fy × (d − a/2), where a = As × fy / (0.85 × f'c × bw). The design must satisfy φMn ≥ Mu with φ = 0.90 for tension-controlled sections.
US structural beam design uses ASCE 7-22 factored load combinations to compute Mu and Vu: the governing combination for most floor beams is 1.2D + 1.6L (ACI 318 Section 5.3.1a). For beams supporting roof loads: 1.2D + 1.6W + 1.0L; for seismic: 1.2D + 1.0E + 1.0L. Service-level loads (unfactored D + L) are used only for deflection and crack control checks. Always determine Mu and Vu from a proper structural analysis before entering values into this beam calculator.
ACI 318-19 Section 9.6.1.2 requires a minimum steel ratio ρmin = max(3√f'c, 200) / fy — for Grade 60 steel with 4,000 psi concrete: ρmin = max(3×63.2, 200)/60,000 = 200/60,000 = 0.00333. The maximum steel ratio for tension-controlled beams (φ = 0.90) is derived from ACI 318 Section 21.2.2 net tensile strain εt ≥ 0.004: ρmax = 0.85β1 × f'c/fy × [0.003/(0.003+0.004)]. For Grade 60 / 4,000 psi: ρmax ≈ 0.0181. Design steel ratio should stay between these limits.
The ACI 318-19 simplified shear formula (Section 22.5.5.1 Table 22.5.5.1 — Method 1 for members with Av ≥ Av,min) gives the concrete shear contribution as: Vc = [8λ(ρw)1/3(f'c)1/3 + Nu/6Ag] × bw × d. The more commonly used legacy simplified equation (still used for preliminary design) is Vc = 2λ√f'c × bw × d (in pounds). Stirrup contribution: Vs = Av × fyt × d / s. Total: φVn = φ(Vc + Vs) ≥ Vu, with φ = 0.75.
The three sets of formulas below cover the complete preliminary beam design sequence used on US structural concrete projects — from initial sizing through steel selection and shear check. All formulas are per ACI 318-19 with ASTM A615 Grade 60 reinforcement and normal-weight concrete.
ACI 318-19 introduced a revised detailed shear equation (Table 22.5.5.1) that replaces the legacy 2√f'c formula for members with minimum shear reinforcement. The updated formula: Vc = [8λ(ρw)1/3(f'c)1/3 + Nu/6Ag] × bw × d — this is more accurate but requires knowledge of the longitudinal steel ratio ρw. The simplified legacy formula Vc = 2√f'c × bw × d remains widely used for preliminary design. This calculator uses the simplified legacy method — use the ACI 318-19 detailed method for final design.
Pre-calculated minimum beam sizes, effective depths, and estimated steel for the most common US beam configurations — all with Grade 60 steel, 4,000 psi concrete, #3 stirrups, 1.5-inch cover, and 3/4-inch aggregate. Use for preliminary design before entering actual loads into the calculator above.
| Span | Support Cond. | Min. h (in.) | Prac. Size (b×h) | Eff. Depth d | Max φVc (kips) | Use |
|---|---|---|---|---|---|---|
| 16 ft | Both Cont. | 9.1→10 in. | 10×12 | 9.6 in. | 14.5 k | Light residential beams |
| 20 ft | Both Cont. | 11.4→12 in. | 12×14 | 11.6 in. | 21.0 k | Residential / light commercial |
| 24 ft | Both Cont. | 13.7→14 in. | 14×16 | 13.6 in. | 28.8 k | Standard commercial floor beams |
| 24 ft | Simply Supp. | 18.0 in. | 14×20 | 17.6 in. | 37.3 k | Simply supported / transfer beams |
| 28 ft | Both Cont. | 16.0→16 in. | 14×18 | 15.6 in. | 33.1 k | Standard commercial frames |
| 32 ft | Both Cont. | 18.3→20 in. | 16×22 | 19.6 in. | 47.5 k | Heavy commercial beams |
| 36 ft | Both Cont. | 20.6→22 in. | 18×24 | 21.6 in. | 58.8 k | Girders / heavy frames |
| 12 ft | Cantilever | 18.0 in. | 12×20 | 17.6 in. | 31.9 k | Balconies / cantilever beams |
ACI 318-19 Section 21.2.2 classifies beam sections based on the net tensile strain εt in the extreme tension steel at nominal strength. Tension-controlled sections (εt ≥ 0.005, but ACI 318 requires εt ≥ 0.004 for φ = 0.90) are ductile and are the target for beam design. Compression-controlled sections (εt ≤ 0.002) are brittle and not permitted for beams. Good US beam design keeps the steel ratio well below ρmax to ensure ductile failure mode under overloading.
ACI 318-19 Section 9.6.3.3 requires minimum shear reinforcement when Vu > φVc/2. The minimum stirrup area is: Av,min/s = max(0.75√f'c/fyt, 50/fyt) × bw. Maximum stirrup spacing: smax = d/2 (for Vu ≤ φVc + 4φ√f'cbwd), reduced to d/4 for higher shear demands. Even when minimum stirrups are not required by shear, most US engineers provide nominal stirrups for bar cage stability and constructability.
When concrete beams are cast monolithically with slabs, they behave as T-beams with an effective flange width per ACI 318-19 Section 6.3.2. The effective overhanging flange width on each side of the web is the lesser of: 8 times the slab thickness, half the clear distance to the next web, or 1/8 of the beam span. T-beam action increases the effective compression area, reducing the required steel area As compared to a rectangular beam of the same depth — use the T-beam design formulas for final design of floor beams.
For beams in Special Moment Frames (SMF) in Seismic Design Categories D–F, ACI 318-19 Chapter 18 requires: maximum steel ratio ≤ 0.025 at any section, minimum 2 bars top and bottom throughout the length, beam width ≥ 10 in. and ≥ 0.3h, hoops (closed stirrups with 135° hooks) in plastic hinge zones with maximum spacing of d/4 or 6×db or 6 inches — whichever is smallest. These seismic requirements significantly affect both beam sizing and detailing compared to ordinary gravity beam design.
Experienced US structural engineers follow this proven preliminary design sequence: Step 1 — Set beam depth using h ≈ L/12 (conservative, usually satisfies both deflection and moment); Step 2 — Set beam width equal to column width (12–18 in. for typical frames); Step 3 — Calculate Mu and Vu using 1.2D + 1.6L load combination; Step 4 — Calculate required As and select bar quantity/size; Step 5 — Check that the selected width can fit the bars (minimum width check); Step 6 — Check shear and provide stirrups. This sequence minimizes iteration and usually produces a final beam in one design cycle.
This tool uses simplified ACI 318-19 formulas for preliminary and intermediate design checks only. It does not perform: T-beam analysis, two-way shear, torsion design (ACI 318 Chapter 22.7), seismic special detailing (Chapter 18), deflection calculations (Section 24.2), crack control (Section 24.3), development length checks (Chapter 25), or lap splice design. All US structural concrete members must be designed, detailed, and stamped by a licensed Professional Engineer (PE) per ACI 318-19, IBC 2021, and all applicable state and local codes before construction.
Official ACI codes, ASTM specifications, and structural engineering references for US concrete beam design
ACI 318-19 is the primary US structural concrete design code. Chapter 9 covers beam design requirements including minimum depth (Table 9.3.1.1) and minimum steel (Section 9.6); Chapter 22 covers flexural and shear strength; Chapter 25 covers reinforcement spacing and development lengths. Required on all US structural concrete projects.
View ACI 318-19The CRSI Design Handbook provides pre-calculated beam capacity tables, bar selection charts, and standard beam details for all common US beam sizes. Includes moment capacity tables for b×h combinations with standard Grade 60 reinforcement — an essential shortcut tool for US structural engineers performing preliminary and final beam design.
Visit CRSI.orgASCE 7-22 Minimum Design Loads for Buildings and Other Structures specifies the factored load combinations used to determine Mu and Vu for ACI 318 beam design. Section 2.3 covers LRFD load combinations; Chapter 4 covers live loads; Chapter 26–31 covers wind loads; Chapter 11–23 covers seismic loads for all US seismic zones.
View ASCE 7-22