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
e.g. 25 kN (~2.55 metric tonnes)
Structural Steel ~200 GPa, Aluminium ~70 GPa, Structural Timber (F7/MGP10) ~10-12 GPa
e.g. 2140 cm⁴ for 200UB25 steel Universal Beam (1 cm⁴ = 10,000 mm⁴)
Distance between top and bottom outer fibers
Calculation Results
Formula & How Structural Beam Deflection & Bending Stress Calculator Works
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.
- Enter Beam Boundary / Support Type: Input your target parameter value.
- Enter Applied Load Configuration: Input your target parameter value.
- Enter Clear Span Length (meters) (m): Input your target parameter value.
- Enter Total Applied Load (kN) (kN): Input your target parameter value.
- Enter Material Modulus of Elasticity E (GPa) (GPa): Input your target parameter value.
- Enter Second Moment of Area / Inertia I (cm⁴) (cm⁴): Input your target parameter value.
- Enter Total Section Overall Depth (mm) (mm): Input your target parameter value.
- 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. - 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.
Authoritative Standards & Verified Reference Citations
Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:
Australian Standards including AS/NZS 3000 (Wiring Rules), AS 3600 (Concrete Structures), and AS 4100 (Steel Structures).
Accreditation and technical guidelines for civil, structural, mechanical, and electrical engineering.
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