Rectangular RC Section Check - EC2 & TCVN 5574

What it checks

This tool verifies a rectangular reinforced concrete section to Eurocode 2 or to TCVN 5574. It covers ultimate limit state bending, combined axial force and bending through the N-M interaction, shear with the variable strut inclination method, and the serviceability checks - stress limits, crack width and deflection.

Both codes are full engines rather than one being a translation of the other: EC2 and TCVN use different material models, different partial factor systems and a different shear formulation, so switching code changes the answer rather than just the labels.

The rectangular stress block

Eurocode 2 idealises the concrete compression zone as a uniform rectangular stress block rather than the true parabolic-rectangular distribution. Two parameters define it: lambda sets the depth of the block as a fraction of the neutral axis depth, and eta scales the stress. For concrete up to C50/60 these are 0.8 and 1.0, and both reduce for higher strength classes because high-strength concrete is more brittle and its stress-strain curve is less full.

The design compressive strength itself is f_cd = alpha_cc f_ck / gamma_C. The alpha_cc factor - commonly 0.85, though it is a National Annex parameter - accounts for long-term effects and the difference between cylinder strength and sustained in-situ strength. Combining these, the uniform stress used in the block is eta f_cd, so the familiar 0.85 f_ck / 1.5 for ordinary concrete.

Variable strut inclination for shear

EC2 shear design uses a truss model where the compression strut angle is chosen by the designer within limits, normally between about 21.8 and 45 degrees, rather than fixed at 45. A shallower strut engages more links across the crack and so reduces the shear reinforcement required, but it increases the compression in the strut and the tension in the longitudinal steel.

The consequence is that the strut angle is a design lever, not a given. Optimising it can significantly cut link quantities on a heavily loaded beam, but two things must then be checked: the strut crushing limit, which is what stops you from taking the angle arbitrarily shallow, and the additional longitudinal tension force, which has to be anchored.

Formula reference

Design concrete strength

$f_{cd} = \dfrac{\alpha_{cc}\,f_{ck}}{\gamma_C}$

Design steel strength

$f_{yd} = \dfrac{f_{yk}}{\gamma_S}$

Stress block, up to C50/60

$\lambda = 0.8,\quad \eta = 1.0$

Compression force in the block

$F_c = \eta\,f_{cd}\,b\,\lambda x$

Moment resistance

$M_{Rd} = F_c\left(d - \dfrac{\lambda x}{2}\right)$

Shear reinforcement

$V_{Rd,s} = \dfrac{A_{sw}}{s}\,z\,f_{ywd}\cot\theta$

Strut crushing limit

$V_{Rd,\max} = \dfrac{\alpha_{cw} b_w z \nu_1 f_{cd}}{\cot\theta + \tan\theta}$

Shear without links

$V_{Rd,c} = \dfrac{0.18}{\gamma_C}k(100\rho_l f_{ck})^{1/3} b_w d$

Assumptions and limits

The section is rectangular with reinforcement in defined layers, and plane sections are assumed to remain plane. Bond is assumed adequate - the tool checks the section, not the anchorage or lap lengths that make the assumed steel force developable, and those are a separate detailing exercise.

Deflection and crack width are serviceability checks whose results depend heavily on creep, shrinkage and the assumed degree of cracking. They are inherently less precise than the ULS numbers, and the long-term values are typically two to three times the instantaneous ones. Treat them as design guidance rather than as precise predictions.

Second-order effects for slender members, torsion, punching shear, fatigue, fire resistance and seismic detailing are outside the scope. The tool checks a section, not a member, so buckling of a slender column is not addressed here.

FAQ