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Structural Beam Deflection & Bending Stress Calculator

Calculate maximum beam deflection (δ_max), bending moment (M_max), and extreme fiber bending stress (σ_max) under point and uniform loads.

Input Parameters

m
kN

e.g. 25 kN (~2.55 metric tonnes)

GPa

Structural Steel ~200 GPa, Aluminium ~70 GPa, Structural Timber (F7/MGP10) ~10-12 GPa

cm⁴

e.g. 2140 cm⁴ for 200UB25 steel Universal Beam (1 cm⁴ = 10,000 mm⁴)

mm

Distance between top and bottom outer fibers

Calculation Results

Maximum Beam Deflection (δ_max)
26.29 mm (Span Ratio L / 228)mm
Maximum Bending Moment (M_max)
37.5 kN·m (27,658 lb-ft)
Extreme Fiber Bending Stress (σ_max)
177.9 MPa (25,797 psi)MPa
Serviceability Assessment (AS 4100 / AS 1170.0)
Passes standard live load L/250 limit
Beam Rigidity (E·I Product)
4280 kN·m²
Summary: A 6m simply supported beam under 25 kN of point load deflects by 26.29 mm (L/228). Peak bending moment is 37.5 kN·m and extreme fiber stress is 177.9 MPa.
Step-by-Step Calculation Solution
1.M_max = (P × L) ÷ 4 = (25 kN × 6 m) ÷ 4 = 37.5 kN·m
2.δ_max = (P × L³) ÷ (48 × E × I) = 26.29 mm
3.Bending Stress σ_max = (M × y) ÷ I = (37500000 N·mm × 101.5 mm) ÷ 21400000 mm⁴ = 177.86 MPa
4.Deflection Span Ratio = 6000 mm ÷ 26.29 mm = L / 228

Formula & How Structural Beam Deflection & Bending Stress Calculator Works

Mathematical Formula
Simply Supported Point Load: δ_max = (P·L³) ÷ (48·E·I), M_max = (P·L) ÷ 4 | Bending Stress σ = (M·y) ÷ I

Beam deflection analysis evaluates whether a structural member meets serviceability limit states (deflection and vibration criteria) under applied gravitational and live loads. Under Australian Standard AS 4100 and AS/NZS 1170.0, total deflection is generally restricted to span/250 for general floors and span/360 for brittle plasterboard ceilings to prevent plaster cracking.

How to Calculate Structural Beam Deflection & Bending Stress Calculator (Step-by-Step)
  1. Enter Beam Boundary / Support Type: Input your target parameter value.
  2. Enter Applied Load Configuration: Input your target parameter value.
  3. Enter Clear Span Length (meters) (m): Input your target parameter value.
  4. Enter Total Applied Load (kN) (kN): Input your target parameter value.
  5. Enter Material Modulus of Elasticity E (GPa) (GPa): Input your target parameter value.
  6. Enter Second Moment of Area / Inertia I (cm⁴) (cm⁴): Input your target parameter value.
  7. Enter Total Section Overall Depth (mm) (mm): Input your target parameter value.
  8. Apply Formula: Calculate using Simply Supported Point Load: δ_max = (P·L³) ÷ (48·E·I), M_max = (P·L) ÷ 4 | Bending Stress σ = (M·y) ÷ I.
  9. Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)

What is the acceptable beam deflection limit in building construction?

Under Australian standards (AS 1170.0 / AS 4100), typical serviceability limits are L/250 for general floor beams (e.g. a 6m beam can deflect up to 24mm under full live load) and L/360 for beams supporting brittle finishes like plaster ceilings (max 16.7mm).

How do you calculate the maximum bending stress in a beam section?

Flexural stress is given by the bending formula $\sigma = \frac{M \cdot y}{I}$, where $M$ is the maximum bending moment, $y$ is the distance from the neutral axis to the extreme fiber (half the beam depth for symmetric sections), and $I$ is the second moment of area.

Official Regulatory & Government Data Sources

Authoritative Standards & Verified Reference Citations

Independent & Verified

Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:

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