How the concrete beam calculator works
This free reinforced concrete beam calculator analyzes and checks a single-span rectangular beam that is either simply supported (pinned–pinned) or fixed at both ends, using ACI 318-19. Enter the span, width, depth and cover, f'c and fy, uniform and point dead and live loads, up to two layers of top and bottom bars, and the stirrup size, legs and spacing. Self-weight at 150 pcf can be included, and results update as you type.
What it calculates
- Factored shear (Vu) and moment (Mu) diagrams for 1.2D + 1.6L or 1.4D, and the factored support reactions
- Positive and negative design moment strength φMn, with φ from the net tensile strain εt
- Shear strength φVn = 0.75(Vc + Vs), with Vc = 2λ√f'c·bwd and Vs = Avfyd/s limited to 8√f'c·bwd
- Minimum flexural steel, minimum shear reinforcement Av,min and maximum stirrup spacing (d/2 or d/4)
- Immediate service deflection compared with L/240 (total load) and L/360 (live load), with a deflection diagram
Method
Shears, moments and deflections come from closed-form beam formulas for a uniform load plus one point load, superposed. Flexural strength uses the rectangular stress block, a = Asfy/(0.85f'c·b), with the effective depth taken at the centroid of each bar group.
Deflection uses the effective moment of inertia Ie from Branson's equation, with cracking moment Mcr = frIg/yt (fr = 7.5√f'c), a cracked transformed section with n = Es/Ec and Ec = 57,000√f'c. The smallest Ie along the span is applied to the whole beam, which is conservative.
Assumptions and limitations
- Single span with uniform loads and one point load. Continuous beams and live-load patterning are not covered.
- Rectangular sections only. T-beam flanges are not included.
- Branson's Ie equation (ACI 318-14) is used. ACI 318-19 Table 24.2.3.5 uses a revised expression that predicts larger deflections for lightly reinforced beams. Long-term deflection from creep and shrinkage is not included.
- Vc uses the simplified 2λ√f'c·bwd without the ACI 318-19 size-effect factor λs.
- Development length, bar spacing and crack control are not checked.
Frequently asked questions
Which load combinations does the beam calculator use?
You can choose 1.2D + 1.6L or 1.4D, the basic gravity combinations of ASCE 7 and ACI 318-19. Dead load includes the beam self-weight when that option is on.
What deflection limits does it check?
It compares the immediate deflection under total service load with L/240 and under live load with L/360, typical limits from IBC Table 1604.3. Confirm the limits that apply to your project.
Can I model a beam with fixed ends?
Yes. Choose Fixed - Fixed as the support condition. The calculator then reports negative moments at the supports, so add top bars and check the negative moment card.
Does it include the beam's self-weight?
Yes, when Include Self-Weight is checked. It adds the weight of the rectangular section at 150 pcf to the dead load.
Related calculators
For educational and preliminary design purposes only. Always verify results with a licensed PE.