EN1992: Design of Concrete Structures

Formula sheet for the design of rectangular concrete sections e.g. beams and slabs.

School of Civil Engineering

Job No. Section Sheet No. Revision
# # # #
Engineer # Checked #
Date # Rev. Date #

Concrete Design, Formulae and Design Charts to EN1992

When K ≤ K' (0.168), then

$Z=\frac{d}{2}\left[1+\sqrt{1-3.53K}\right]\le 0.95d$

When K > K' (0.168), then

$Z=\frac{d}{2}\left[1+\sqrt{1-3.53{K}^{\text{'}}}\right]\le 0.95d$

Area of Compression Reinforcement

${A}_{s2,req\text{'}d}=\frac{\left(K-{K}^{\text{'}}\right){f}_{ck}b{d}^{2}}{{f}_{sc}\left(d-{d}_{2}\right)}$

When K ≤ K' (0.168), then

${A}_{s,req\text{'}d}=\frac{{M}_{Ed}}{{f}_{yd}Z}$

Maximum & Minimum Reinforcement Requirement

${A}_{s,\mathrm{max}}=0.04{A}_{c}$
${A}_{s,\mathrm{min}}=\frac{0.26{f}_{ctm}{b}_{t}d}{{f}_{yk}}$
fck fctm Minimum
percentage
28 2.8 0.14%
30 2.9 0.15%
32 3.0 0.16%
35 3.2 0.17%
fck & fctm in N/mm2

Design Shear Stress

${v}_{Ed}=\frac{{V}_{Ed}}{{b}_{w}Z}$

Shear Stress Capacity

$\begin{array}{l}{v}_{Rd,c}=0.12k{\left(100{\rho }_{1}{f}_{ck}\right)}^{1}{3}}\ge 0.035{k}^{1.5}{f}_{ck}^{0.5}\end{array}$

Where

$\theta =0.55{\mathrm{Sin}}^{-1}\left[\frac{{v}_{Ed}}{0.20{f}_{ck}\left(1-{f}_{ck}/250\right)}\right]$
fck vRd,max cotθ=2.5 vRd,max cotθ=1.0
28 3.43 1.97
30 3.64 5.28
32 3.84 5.58
35 4.15 6.02
All figures are in N/mm2

Maximum Spacing or Shear Reinforcement

${s}_{L,\mathrm{max}}=0.75d$

Area of Shear Reinforcement

${A}_{sw}=\frac{{v}_{Ed}{b}_{w}{S}_{l}}{{f}_{ywd}Cot\theta }$

Reference Reinforcement Ratio

${\rho }_{0}=\frac{{f}_{ck}^{0.5}}{1000}$

Tension Reinforcement Ratio

$\rho =\frac{{A}_{s,req\text{'}d}}{bd}$

Compression Reinforcement Ratio

$\rho \text{'}=\frac{{A}_{s2,req\text{'}d}}{bd}$

Basic Span to Effective Depth Ratios

$ρ≤ ρ 0$ $\frac{l}{d}=K\left[11+\frac{1.5\sqrt{{f}_{ck}}×{\rho }_{0}}{\rho }+3.2\sqrt{{f}_{ck}}{\left(\frac{{\rho }_{0}}{\rho }-1\right)}^{1.5}\right]$

K = 0.4 for cantilevers

$ρ> ρ 0$ $\frac{l}{d}=K\left[11+\frac{1.5\sqrt{{f}_{ck}}×{\rho }_{0}}{\left(\rho -\rho \text{'}\right)}+\frac{\sqrt{{f}_{ck}}}{12}\sqrt{\frac{\rho \text{'}}{{\rho }_{0}}}\right]$