Concrete Beam Load & Reinforcement Calculator
Calculate bending moment capacity and reinforcement ratios for rectangular concrete beams. Checks against ACI 318 minimum/maximum limits.
1. Beam Geometry
2. Materials
About
This structural calculator assesses the flexural strength of a simply supported, singly reinforced concrete beam. It determines whether a proposed beam design is safe by comparing the Nominal Moment Capacity (Mn) against required loads, while simultaneously validating that the reinforcement ratio falls within the brittle failure safety limits defined by ACI 318 and Eurocode 2.
The tool highlights under-reinforced sections (ductile failure, preferred) versus over-reinforced sections (sudden brittle failure, dangerous). It assumes a rectangular cross-section with tension reinforcement only, using the Whitney Stress Block method for analysis. Standard concrete strengths (3000-6000 psi) and steel grades (40, 60) are supported.
Formulas
The depth of the equivalent compressive stress block (a) is calculated from the equilibrium of tension and compression forces:
The Nominal Moment Capacity (Mn) is derived from the couple formed by the tension steel and concrete compression:
To ensure safety, the design moment (φMn) applies a strength reduction factor (φ, typically 0.9 for tension-controlled sections):
Reference Data
| Parameter | Symbol | Typical Value (Imp) | Typical Value (Met) |
|---|---|---|---|
| Concrete Strength | f′c | 3000 - 5000 psi | 20 - 35 MPa |
| Steel Yield Strength | fy | 60,000 psi (Gr 60) | 420 - 500 MPa |
| Concrete Cover | cc | 1.5″ (Interior) | 40 mm |
| Modulus of Elasticity | Es | 29,000 ksi | 200 GPa |
| Beta Factor | β1 | 0.85 | 0.85 |