REINFORCED CONCRETE SECTION CHECK
M_Rd · V_Rd,c · V_Rd,s — rectangular section · EN 1992-1-1
Compression reinforcement
Optional. Leave the bar count at 0 for a singly reinforced section. Bars close to the neutral axis rarely reach yield — the calculation reads their actual stress from the strain, it does not assume f_yd.
Tool information
What this calculator checks
The calculator verifies a rectangular reinforced-concrete section in bending and shear, according to EN 1992-1-1. It returns three design resistances:
- \(M_{Rd}\) — the bending moment resistance, using the rectangular stress-block model (§3.1.7 and §6.1)
- \(V_{Rd,c}\) — the shear resistance without shear reinforcement (§6.2.2, expr. 6.2)
- \(V_{Rd,s}\) and \(V_{Rd,max}\) — with links: the reinforcement resistance and the crushing of the compression struts (§6.2.3, expr. 6.8 and 6.9)
Bending: the stress block
At Ultimate Limit State, the compressed concrete is idealised by a block of constant stress \(f_{cd}\) over a depth \(\lambda x\), and the tension reinforcement yields at \(f_{yd}\). Equilibrium of the concrete compression force with the steel tension force gives the depth of the compression zone, then the lever arm \(z\) and the moment resistance:
\(M_{Rd} = A_s \cdot f_{yd} \cdot z\)
For \(f_{ck} \le 50\) MPa the factors are \(\lambda = 0.8\) (block depth) and \(\eta = 1.0\) (intensity).
Shear: two regimes
Without links, the resistance \(V_{Rd,c}\) comes from the concrete and the longitudinal reinforcement (dowel action and aggregate interlock), with the empirical term of expr. 6.2. If \(V_{Ed} \le V_{Rd,c}\), minimum shear reinforcement is sufficient.
With links, the truss analogy applies: the force is carried by the concrete compression struts and the steel ties. The resistance is the lesser of:
- \(V_{Rd,s}\) — yielding of the links (expr. 6.8)
- \(V_{Rd,max}\) — crushing of the concrete struts (expr. 6.9)
If the struts crush before the links yield, adding reinforcement does not help — the section or the concrete class must be increased.
Input data
- Concrete class — \(f_{ck}\), from which \(f_{cd} = \alpha_{cc} f_{ck} / \gamma_c\).
- Geometry — the width \(b\), depth \(h\), cover to the bar centres.
- Longitudinal tension reinforcement — the number and diameter of bars.
- Links — the number of legs, diameter, spacing, and the grade of the transverse steel.
- Partial factors \(\gamma_c\) (recommended 1.5) and \(\gamma_s\) (recommended 1.15).
Assumptions and limitations
- Singly reinforced in tension: compression reinforcement and axial force do not enter \(M_{Rd}\). For columns with axial load, see the N·M interaction diagram.
- Vertical links (\(\alpha = 90°\)) and \(f_{ck} \le 50\) MPa.
- Biaxial bending and torsion are not treated.
- The crack-width (Serviceability) check is not covered — see crack-width verification.
- Concrete cover is determined separately — see concrete cover.
Related calculations
- Concrete cover — \(c_{nom}\), from which the effective depth \(d\) follows
- Crack-width verification — the SLS check of the same section
- N·M interaction diagram — for sections with axial force
- Punching shear — shear at slabs on columns