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.
Last reviewed by the myCalculator Editorial Team
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
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Formula & How Structural Beam Deflection & Bending Stress Calculator Works
For a simply supported beam with a single point load at midspan, the maximum deflection is δ = P·L³ ÷ (48·E·I) and the maximum bending moment is M = P·L ÷ 4. Bending stress at the extreme fibre is σ = M·y ÷ I, where y is half the section depth. For a 6 m span carrying 25 kN, with E = 200 GPa, I = 2,140 cm⁴ and a 203 mm deep section, deflection is about 26 mm (span ÷ 228), the maximum moment is 37.5 kN·m and the peak bending stress is about 178 MPa. Compare deflection with the limit for your use (span ÷ 250 to ÷ 360 is common) and stress with the material's design strength. This is a preliminary check, not a substitute for a design to AS 4100.
- 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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MyCalculator.com.au. (2026). Structural Beam Deflection & Bending Stress Calculator. Retrieved October 24, 2026, from https://www.mycalculator.com.au/calculators/engineering/beam-deflection-stress
MyCalculator.com.au. (2026) 'Structural Beam Deflection & Bending Stress Calculator'. Available at: https://www.mycalculator.com.au/calculators/engineering/beam-deflection-stress (Accessed: 24 October 2026).
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.
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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.
Dedicated Australian home loans, borrowing capacity, mortgage repayments & refinance modeling.