Flexure (x)FAIL
As,req
591mm²/m
As,prov
393mm²/m
Utilization150.0%
ShearPASS
VEd
33.2kN/m
VRd,c
92.2kN/m
Utilization36.0%
DeflectionPASS
l/d actual
29.4
l/d allow
39.0
Utilization75.5%
Crack WidthPASS
wk
0.307mm
wmax
0.4mm
Utilization76.6%
Summary
| Check | Dir. | Required | Provided | Util. | Status |
|---|---|---|---|---|---|
| Flexure As | x | 591 mm²/m | 393 mm²/m | 150.4% | FAIL |
| As,min | x | 256 mm²/m | 393 mm²/m | 65.3% | PASS |
| Secondary As | y | 221 mm²/m | 314 mm²/m | 70.3% | PASS |
| Bar spacing | x | ≤ 400 mm | 200 mm | 50.0% | PASS |
| Bar spacing | y | ≤ 450 mm | 250 mm | 55.6% | PASS |
| Shear VRd,c | — | VEd = 33.2 kN/m | 92.2 kN/m | 36.0% | PASS |
| Deflection l/d | x | ≤ 39.0 | 29.4 | 75.5% | PASS |
| Crack width wk | — | ≤ 0.4 mm | 0.307 mm | 76.6% | PASS |
Practical Bar Schedule
X-direction
T10@200
As = 393 mm²/m ✗
Y-direction
T10@250
As = 314 mm²/m ✓
Flexure [EC2 §6.1]▼
Flexural Design
EC2 §3.1.6(1)Design concrete strength
fcd = 0.85·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
Effective depths
dx = h − cnom − φx/2; dy = h − cnom − φx − φy/2
dx = 170.0 mm, dy = 160.0 mm
EC2 TableDesign moment (span)
M⁺Ed = β × ned × lx²
M⁺Ed = 0.1250 × 13.28 × 5.000²
M⁺Ed = 41.48 kN·m/m
EC2 §6.1(4)Flexural design (x-direction, span)
K = MEd/(b·d²·fck)
K = 41484375 / (1000 × 170.0² × 30)
K = 0.0478
EC2 §6.1(4)Lever arm
z = d·min(0.5+√(0.25−K/1.134), 0.95)
z = 170.0 × min(0.5+√(0.25−0.0478/1.134), 0.95)
z = 161.5 mm
EC2 §6.1(4)Required reinforcement (span)
As,req = MEd/(fyd·z)
As,req = 41484375 / (434.8 × 161.5)
As,req,x = 591 mm²/m
EC2 §9.3.1.1(1)Minimum main reinforcement
As,min = max(0.26·fctm/fyk·b·d, 0.0013·b·d)
As,min = max(0.26×2.9/500×1000×170.0, 0.0013×1000×170.0)
As,min = 256 mm²/m
EC2 §9.3.1.1(2)Secondary (transverse) reinforcement
As,sec ≥ 0.2·As,main
As,sec = 0.2 × 591
As,min,y = 221 mm²/m
EC2 §9.2.1.1(3)Maximum reinforcement
As,max = 0.04·b·h
As,max = 0.04 × 1000 × 200
As,max = 8000 mm²/m
Provided reinforcement
As,prov = π·φ²/4 × (1000/s)
As,prov,x = 393 mm²/m, As,prov,y = 314 mm²/m
Shear [EC2 §6.2]▼
Shear Check
EC2 §6.2Design shear force
VEd per support type
ned = 13.28 kN/m², lx = 5.000 m
VEd = 33.19 kN/m
EC2 §6.2.2(1)Size effect factor
k = min(1 + √(200/d), 2.0)
k = min(1 + √(200/170.0), 2.0)
k = 2.000
EC2 §6.2.2(1)Concrete shear resistance
VRd,c = max[CRd,c·k·(100ρl·fck)^⅓·b·d, vmin·b·d]
ρl = 0.00231, vmin = 0.542
VRd,c = 92.18 kN/m
EC2 §6.2.1(4)Shear check (no shear links typical for slabs)
VEd ≤ VRd,c
33.19 ≤ 92.18
✓ No shear reinforcement needed
Bar Spacing [EC2 §9.3]▼
Spacing Check
EC2 §9.3.1.1(3)Maximum main bar spacing
smax = min(3h, 400mm)
smax = min(3×200, 400)
smax,main = 400 mm
EC2 §9.3.1.1(4)Maximum secondary bar spacing
smax = min(3.5h, 450mm)
smax = min(3.5×200, 450)
smax,sec = 450 mm
Spacing check
sx = 200 mm ✓, sy = 250 mm ✓
Deflection [EC2 §7.4]▼
Deflection Check
EC2 §7.4.2(2)Reference reinforcement ratio
ρ₀ = 10⁻³√fck
ρ₀ = 10⁻³ × √30
ρ₀ = 0.00548, ρ = 0.00231
EC2 Table 7.4NStructural system factor
K per support type
Support: simply supported
K = 1
EC2 Eq. 7.16aBasic l/d ratio (ρ ≤ ρ₀)
l/d = K·[11 + 1.5·√fck·ρ₀/ρ + 3.2·√fck·(ρ₀/ρ−1)^1.5]
ρ=0.00231, ρ₀=0.00548
l/d basic = 58.6
EC2 §7.4.2(2)Steel provision modification
mod = min(As,prov/As,req, 1.5)
mod = min(393/591, 1.5)
mod = 0.66
EC2 §7.4.2Final span/depth check
l/d actual ≤ l/d allowable
l/d allow = 39.0, l/d actual = 29.4 ✓
Crack Width [EC2 §7.3]▼
Crack Control
EC2 §7.3.2(3)Effective tension area
hc,eff = min(2.5(h−d), (h−x)/3, h/2)
hc,eff = min(75.0, 28.9, 100.0)
hc,eff = 28.9 mm, ρp,eff = 0.0136
EC2 §7.3.4(2)Steel stress under service load
σs ≈ Ms/(As·0.87d)
σs = 25000000 / (393 × 147.9)
σs = 430.4 MPa
EC2 Eq. 7.11Maximum crack spacing
sr,max = 3.4·c + 0.425·k₁·k₂·φ/ρp,eff
sr,max = 3.4×25 + 0.425×0.8×0.5×10/0.0136
sr,max = 210.1 mm
EC2 Eq. 7.9Mean 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) = 1.4595 × 10⁻³
EC2 Eq. 7.8Calculated crack width
wk = sr,max · (εsm − εcm)
wk = 210.1 × 0.001459
wk = 0.307 mm ✓ (limit: 0.4 mm)
Suggested Bar Arrangements▼
X-direction (main) (As,req = 591 mm²/m)
T10@125
628 mm²/m✓
T12@175
646 mm²/m✓
T16@300
670 mm²/m✓
T12@150
754 mm²/m✓
T10@100
785 mm²/m✓
T16@250
804 mm²/m✓
Y-direction (secondary) (As,req = 221 mm²/m)
T8@225
223 mm²/m✓
T8@200
251 mm²/m✓
T10@300
262 mm²/m✓
T8@175
287 mm²/m✓
T10@250
314 mm²/m✓
T8@150
335 mm²/m✓