Calculations › EC2 Deflection

EC2 Deflection

EN 1992-1-1

Rigorous long-term deflection check for a simply-supported RC beam or slab strip to EN 1992-1-1 §7.4.3.

Example inputs

Span5000 mm

Section width b200 mm

Section depth h400 mm

Effective depth d350 mm

Tension steel As1500 mm²

Compression steel As20 mm²

Depth to comp. steel d250 mm

Quasi-permanent load w_qp8 kN/m

Total load w_total12 kN/m

Concrete gradeC25/30

Creep coefficient φ(∞,t₀)2 —

Shrinkage strain ε_cs0.0003 —

National annexUK

Results

EC2 Deflection — 200×400mm

C25/30 · 5000mm span · φ=2 · EN 1992-1-1

Results

✓ Cracking Moment PASS

util 1.8325.00EN 1992-1-1 §7.4.2(5)

fctm mean tensile strength = 0.30 × fck^(2/3)	2.565	N/mm²	EN 1992-1-1 Table 3.1
Ecm mean elastic modulus = 22000 × ((fck+8)/10)^0.3	31475.81	N/mm²	EN 1992-1-1 Table 3.1
αe modular ratio = Es / Ecm	6.354	—
I_gross gross inertia = b × h³ / 12	1066666666.67	mm⁴
Mcr cracking moment = fctm × I_gross / (h/2)	13.68	kNm	EN 1992-1-1 §7.4.2(5)
MEd quasi-permanent = w_qp × L² / 8	25	kNm

✓ Long-term Deflection PASS

util 0.5510.92EN 1992-1-1 §7.4.1(4)

x cracked neutral axis depth = quadratic solution	141.1	mm
I₁ uncracked 2nd moment	1281114166.67	mm⁴
I₂ cracked 2nd moment	603204612.58	mm⁴
ζ distribution coefficient = 1 − 0.5(Mcr/MEd)²	0.85	—	EN 1992-1-1 §7.4.3(4)
I_eff effective 2nd moment = ζ·I₂ + (1−ζ)·I₁	704891045.69	mm⁴
1/r_lt long-term curvature = (1+φ_ef)·MEd/(Ecm·I_eff)	3.38	×10⁻⁶ mm⁻¹
1/r_cs shrinkage curvature = ε_cs·S_eff/I_eff	0.812	×10⁻⁶ mm⁻¹
δ_total long-term deflection = (5/48)·(1/r_total)·L²	10.92	mm	EN 1992-1-1 §7.4.3
δ_limit span/250	20	mm

✓ After Finishes PASS

util 0.959.46EN 1992-1-1 §7.4.1(5)

δ_imm immediate deflection = (5/48)·(1/r_el)·L²	2.93	mm
δ_after post-finishes deflection = δ_total − 0.5·δ_imm	9.46	mm
δ_limit span/500	10	mm

Try it yourself

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