Rectangular RC Section Design Theory - TCVN 5574:2018

A rectangular reinforced-concrete section - a beam or a column - is checked to TCVN 5574:2018 at the ultimate limit state (bending, eccentric compression, shear and torsion) and at the serviceability limit state (crack width and deflection). TCVN 5574 follows the limit-state tradition of the Russian SNiP code, so its method differs from Eurocode 2 in several ways set out below.

Materials - design strengths come straight from the tables

Unlike Eurocode 2, which divides a characteristic strength by a partial factor ($\gamma_C = 1.5$, $\gamma_S = 1.15$), TCVN 5574 tabulates the design strengths directly - the material reliability factor is already applied in the published value. For concrete B30 the design strengths are $R_b = 17.0$ MPa and $R_{bt} = 1.20$ MPa; for CB500 steel $R_s = R_{sc} = 435$ MPa. The only further multipliers are the optional working-condition coefficients $\gamma_{bi}$ / $\gamma_{si}$ (casting position, sustained action, etc.), which default to 1.0.

The ductility limit is the relative boundary height $\xi_R$, found from the steel yield strain and the ultimate concrete strain $\varepsilon_{b2} = 0.0035$:

ULS bending - the rectangular stress block

TCVN 5574 uses a rectangular concrete stress block of the full design strength $R_b$ acting over the whole compression depth $x$ (there is no $0.8x$ / $\eta f_{cd}$ reduction as in EC2). With effective depth $h_0 = h - a$, axial equilibrium of a singly-reinforced section gives the compression depth, and the moment is taken about the tension steel:

If $\xi > \xi_R$ the concrete crushes before the steel yields, so the capacity is capped at $\xi_R$ and compression reinforcement $A_s'$ is added; the calculator sizes both layers and adds the term $R_{sc} A_s' (h_0 - a')$.

ULS eccentric compression - longitudinal bending

A column carries axial force $N$ together with moment $M$. The first-order eccentricity combines the load eccentricity $e_1 = M/N$ with the accidental eccentricity $e_a = \max(h/30,\ l_0/600)$, giving $e_0$. The slenderness (second-order) effect is the longitudinal-bending factor $\eta$, applied when $\lambda = l_0/h > 8$:

The lever $e$ (to the tension steel) and the compression depth $x$ from axial equilibrium decide the case: large eccentricity ($x \le \xi_R h_0$, steel yields, $\sigma_s = R_s$) or small eccentricity (the steel does not yield, $\sigma_s < R_s$). The section is safe when $N e \le M_{gh}$, the capacity about the tension steel:

ULS shear - the inclined section

Shear is checked on an inclined section of horizontal projection $C$ (§8.1.3). The resistance is the sum of a concrete term $Q_b$ and a stirrup term $Q_{sw}$, with $q_{sw} = R_{sw} A_{sw}/s_w$ the transverse intensity and $C$ taken at the governing value within $[h_0,\ 2h_0]$:

The compressed concrete strut between cracks is also checked against $0.3\,R_b\,b\,h_0$, which caps how much shear the stirrups can develop.

ULS torsion - the spatial section

Torsion is resisted on a spatial (skew) section formed by a helical crack (§8.1.4). With the core dimensions $Z_1, Z_2$ and $\delta = Z_1/(2Z_2 + Z_1)$, the torsional resistance combines the closed stirrups and the longitudinal bars:

A concrete-strut limit $0.1\,R_b\,b^{2} h$ bounds the torsion the section can carry before the concrete crushes.

SLS - crack width and deflection

The section first cracks when the moment reaches $M_{crc} = 1.3\,W_{red}\,R_{bt,ser}$ (§8.2.2), using the serviceability tensile strength $R_{bt,ser}$. Beyond that, the crack width is:

Deflection (§8.2.3) follows from the curvature $1/r = M/D$, where the flexural rigidity $D$ uses the reduced steel modulus $E_{s,red} = E_s/\psi_s$ for a cracked section; the deflection is $f = s\,(1/r)\,L^{2}$ with the scheme coefficient $s$. Both $a_{crc}$ and $f$ are compared with the code limits.

Minimum reinforcement, detailing and the working-condition coefficients $\gamma_{bi}$ / $\gamma_{si}$ always govern the final design.