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RC Beam Design: worked example

A simply supported rectangular reinforced concrete beam checked for bending, shear, crack width and deflection.

EN 1992-1-1:2004 — Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings · SI units · Calculator v1.2

These are the real results of the RC Beam Design for the inputs below, read-only. Open the calculator with these values already loaded to change them.

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Inputs

Section type	Rectangular
Width b	300 mm
Overall depth h	600 mm
Effective depth d	557 mm
Span	6 m
Support condition	simply supported
Concrete	C30/37
Reinforcing steel	B500S
Nominal cover cnom	25 mm
Tension reinforcement	4Ø20
Stirrups	Ø8 @ 200 mm, 2-leg
Design moment MEd	250.0 kN·m
Design shear VEd	150.0 kN

Design checks All checks pass

Check	Required	Provided	Utilisation	Result
Flexure As	1130 mm²	1257 mm²	89.9%	PASS
As,min	252 mm²	1257 mm²	20.1%	PASS
As,max	≤ 7200 mm²	1257 mm²	17.5%	PASS
x/d ratio	≤ 0.450	0.240	53.4%	PASS
VRd,c (links required)¹	VEd = 150 kN	90.6 kN	165.5%	PASS
Stirrup Asw/s	0.275	0.503 mm²/mm	54.8%	PASS
VRd,max	VEd = 150 kN	465.5 kN	32.2%	PASS
Crack width wk	≤ 0.4 mm	0.223 mm	55.8%	PASS
Span/depth l/d	≤ 18.9	10.8	57.0%	PASS

¹ Concrete alone is insufficient for this shear, so shear links are required; the links carry the shear and are checked on the next row.

Calculation steps

Flexural Design (10 steps)

EC2 §3.1.6(1)

Design concrete strength

fcd = αcc · fck / γc

fcd = 0.85 × 30 / 1.5

fcd = 17.00 MPa

EC2 §3.2.7(2)

Design steel strength

fyd = fyk / γs

fyd = 500 / 1.15

fyd = 434.8 MPa

EC2 §6.1(4)

Normalized moment coefficient

K = MEd / (b · d² · fck)

K = 250000000 / (300 × 557.0² × 30)

K = 0.0895

EC2 §6.1(4)

Check: K ≤ Kbal

K = 0.0895 ≤ Kbal = 0.167

Singly reinforced design

✓ Singly reinforced

EC2 §6.1(4)

Lever arm

z = d · (0.5 + √(0.25 − K/1.134)) ≤ 0.95d

z = 557.0 × (0.5 + √(0.25 − 0.0895/1.134))

z = 508.9 mm

EC2 §6.1(4)

Required tension reinforcement

As,req = MEd / (fyd · z)

As,req = 250000000 / (434.8 × 508.9)

As,req = 1130 mm²

EC2 §5.5(4)

Neutral axis depth ratio

x/d = (As·fyd − As2·fyd) / (0.8·b·fcd·d)

x = 133.9 mm

x/d = 0.240 ✓ (limit 0.45)

EC2 §9.2.1.1(1)

Minimum reinforcement

As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d)

As,min = max(0.26×2.9/500×300×557.0, 0.0013×300×557.0)

As,min = 252 mm²

EC2 §9.2.1.1(3)

Maximum reinforcement

As,max = 0.04 · b · h

As,max = 0.04 × 300 × 600

As,max = 7200 mm²

Provided tension steel

As,prov

As,prov = 1257 mm²

Shear Design (7 steps)

EC2 §6.2.2(1)

Size effect factor

k = min(1 + √(200/d), 2.0)

k = min(1 + √(200/557.0), 2.0)

k = 1.599

EC2 §6.2.2(1)

Concrete shear resistance (no reinforcement)

VRd,c = max[CRd,c·k·(100ρl·fck)^⅓·bw·d, vmin·bw·d]

ρl=0.00752, vmin=0.388

VRd,c = 90.6 kN

EC2 §6.2.3(3)

Required shear reinforcement

Asw/s = VEd / (z · fyd · cotθ)

Asw/s = 150×1000 / (501.3 × 434.8 × 2.5)

Asw/s,req = 0.275 mm²/mm

Provided shear reinforcement

Asw/s = nlegs · π·φ²/4 / s

Asw/s = 2×50.3 / 200

Asw/s,prov = 0.503 mm²/mm

EC2 §6.2.3(3)

Maximum shear capacity (strut)

VRd,max = ν₁·fcd·bw·z / (cotθ + tanθ)

ν₁=0.528, fcd=17.0

VRd,max = 465.5 kN

EC2 §9.2.2(5)

Minimum shear reinforcement

ρw,min = 0.08·√fck/fyk

ρw,min = 0.08×√30/500

Asw/s,min = 0.263 mm²/mm

EC2 §9.2.2(6)

Maximum stirrup spacing

smax = min(0.75d, 600)

smax = min(0.75×557.0, 600)

smax = 418 mm ✓

Crack Control (6 steps)

EC2 §7.3.2(3)

Cracked elastic neutral axis

x from b·x²/2 = αe·As·(d−x)

αe = Es/Ecm = 6.06, As = 1257 mm², d = 557.0 mm

x = 144.7 mm

EC2 §7.3.2(3)

Effective tension area

hc,eff = min(2.5(h−d), (h−x)/3, h/2)

hc,eff = min(107.5, 151.8, 300.0)

Ac,eff = 300 × 107.5 = 32250 mm², ρp,eff = 0.0390

EC2 §7.3.4(2)

Steel stress under service load

σs ≈ Ms / (As · 0.87d)

σs = 170000000 / (1257 × 484.6)

σs = 279.2 MPa

EC2 Eq. 7.11

Maximum crack spacing (c = cover to the longitudinal bars)

sr,max = 3.4·c + 0.425·k₁·k₂·φ/ρp,eff

sr,max = 3.4×33 + 0.425×0.8×0.5×20/0.0390

sr,max = 199.5 mm

EC2 Eq. 7.9

Mean strain difference

(εsm−εcm) = max([σs − kt·fct,eff·(1+αe·ρp,eff)/ρp,eff]/Es, 0.6σs/Es)

kt=0.6, αe=6.06

(εsm−εcm) = 1.1198 × 10⁻³

EC2 Eq. 7.8

Calculated crack width

wk = sr,max · (εsm − εcm)

wk = 199.5 × 0.001120

wk = 0.223 mm ✓ (limit: 0.4 mm)

Deflection Check (5 steps)

EC2 §7.4.2(2)

Reference reinforcement ratio

ρ₀ = 10⁻³√fck

ρ₀ = 10⁻³×√30

ρ₀ = 0.00548

EC2 Table 7.4N

Structural system factor

K per support type

Support: simply_supported

K = 1

EC2 Eq. 7.16b

Basic l/d ratio (ρ > ρ₀)

l/d = K·[11 + 1.5·√fck·ρ₀/(ρ−ρ') + √fck/12·√(ρ'/ρ₀)]

ρ=0.00752, ρ'=0.00000

l/d basic = 17.0

EC2 §7.4.2(2)

Steel provision modification

mod = min(As,prov/As,req, 1.5)

mod = min(1257/1130, 1.5)

mod = 1.11

EC2 §7.4.2

Final span/depth check

l/d allowable vs l/d actual

allowable = 17.0 × 1.11 × 1.0 × 1.00

l/d allow = 18.9, l/d actual = 10.8 ✓

Design basis and assumptions

National Annex: none applied as a whole — the EN recommended values are used, except where noted below. There is no National Annex selector; check the values against the annex for your project.
αcc = 0.85 in fcd = αcc·fck/γc (the UK National Annex value; EN 1992-1-1 §3.1.6(1) recommends 1.0). Used for flexure and for the strut capacity VRd,max.
Rectangular-block lever arm z = d·[0.5 + √(0.25 − K/1.134)] ≤ 0.95d, the αcc = 0.85 form.
γc = 1.5 and γs = 1.15 (EN 1992-1-1 Table 2.1N, persistent and transient), editable.

Web-only shear/flexure design for T-beam/L-beam sections — checks use bw alone, not the full flange width, a conservative simplification that doesn’t credit the flange’s extra compression area.
Flange (slab) thickness (hf) is used only to draw the section — it isn’t passed into the flexure, shear, or deflection checks.
Applied design forces (MEd/Mu, VEd/Vu, NEd/Nu) are inputs from your own load combination, unless you use the optional Gk/Qk breakdown, which applies only the code’s standard gravity combination (1.35Gk + 1.5Qk under EC2).
Cover, if not manually overridden, is calculated automatically from exposure/structural class — a manual value below the auto-calculated minimum is accepted without warning.
Crack-width and deflection checks use the serviceability moments (Mk, Mfr, Mqp) you enter directly — this tool doesn’t derive them from the ULS design moment.

Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.