Check immediate and long-term deflection of reinforced concrete beams against code limits. Use after flexural design to verify serviceability (L/360, L/480, L/180). Compliant with ACI 318-19 §24.2. Free to use. SI and Imperial units supported. No signup required.
Deflection Check
Immediate + long-term deflection vs L/Δ limit
Material PropertiesInput
✓Cracked Moment of Inertia
✓Immediate DeflectionACI 318-19 §24.2
✓Long-Term DeflectionACI 318-19 §24.2
✓Total vs LimitACI 318-19 §24.2
✓ PASS| Step | Formula | Substitution | Result | |
|---|
| Gross Inertia | I_g = bh^3/12 | 300×500³/12 | 3125×10⁶ mm⁴ | |
| Cracked Inertia | I_{cr} | transformed section | 1654×10⁶ mm⁴ | |
| Cracking Moment | M_{cr} = f_r I_g / y_t | 3.4×3125/250 | 42.45 kN·m | |
| Step | Formula | Substitution | Result | |
|---|
| Service Moment | M_a = wL²/8 | (26.5)×(6.0)²/8 | 119.25 kN·m | |
| Effective Ie | I_e = (M_{cr}/M_a)³I_g + [1-(M_{cr}/M_a)³]I_{cr} | 1720.4×10⁶ | 1720.4×10⁶ mm⁴ | |
| Δ immediate | Δ_i = 5wL⁴/(384EcIe) | 10.1 | 10.1 mm | |
| Δ long-term | Δ_{LT} = λΔ_i | 1.737×10.1 | 9.74 mm | |
| Δ total | Δ_{total} = Δ_i + Δ_{LT} | 10.1+9.74 | 14.23 mm | |
| Checked Δ | vs limit | | 4.49 mm | ✓ |
[1]
Deflection Check
ACI 318-19 §24.2
Project: N/A · Engineer: N/A · Date: 10/10/2026 · Rev: 0
[2]
Design reference: ACI 318-19 §24.2
[3]
Given:
L = 6000 mm (Span)
b = 300 mm (Width)
h = 500 mm (Height)
f'c = 30 MPa (f'c)
[4]
Material Properties:
Concrete
f'c = 30 MPa
Ec = 25743 MPa
Steel
fy = 400 MPa
As = 2000 mm²
[5]
Section Properties
ACI 318-19 §24.2
Gross Inertia
Ig = bh^3/12
= 300× 500³/12
= 3125× 10⁶ mm⁴
Cracked Inertia
Icr
= transformed section
= 1654× 10⁶ mm⁴
Cracking Moment
Mcr = fr Ig / yt
= 3.4× 3125/250
= 42.45 kN· m
[6]
Deflection
ACI 318-19 §24.2
Service Moment
Ma = wL²/8
= (26.5)× (6.0)²/8
= 119.25 kN· m
Effective Ie
Ie = (Mcr/Ma)³Ig + [1-(Mcr/Ma)³]Icr
= 1720.4× 10⁶
= 1720.4× 10⁶ mm⁴
Δ immediate
Δi = 5wL⁴/(384EcIe)
= 10.1
= 10.1 mm
Δ long-term
ΔLT = λΔi
= 1.737× 10.1
= 9.74 mm
Δ total
Δtotal = Δi + ΔLT
= 10.1+9.74
= 14.23 mm
[7]
Deflection Check
PASS
✓; PASS