Loading and design action
- Simply supported span
- Permanent (dead) line load
- Imposed (live) line load
- Factored load, 1.2G + 1.5Q (AS/NZS 1170.0)
- Design bending moment at midspan
Structural · worked example · 4 pages
Reinforced concrete beam design to AS3600
Ultimate-limit-state bending design of a singly reinforced rectangular beam using the rectangular stress block of AS 3600:2018. Scope: bending strength, ductility and minimum reinforcement only — shear, deflection, crack control and durability are separate checks outside this example.
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What this calculation covers
Materials
- Concrete strength (28 day)
- Reinforcement yield strength
- Flexural tensile strength (cl 3.1.1.3)
Section and reinforcement
- Overall depth
- Beam width
- Concrete cover
- Stirrup diameter
- Longitudinal bar diameter (4N28)
- Number of bars
- Capacity reduction factor, bending
- Effective depth to the bar centroid
- Reinforcement area provided
Reinforcement required
- Approximate area required (0.9d lever arm)
- Enough reinforcement for the moment
- Minimum reinforcement (cl 8.1.6.1)
- Minimum reinforcement satisfied
Bending capacity
Rectangular stress block (cl 8.1.3): the reinforcement is assumed to yield, then ductility is confirmed with the neutral-axis check.
- Stress block intensity (cl 8.1.3)
- Stress block depth factor (cl 8.1.3)
- Yield force in the reinforcement
- Depth to the neutral axis
- Neutral axis parameter
- Ductility (cl 8.1.5)
- Ultimate moment capacity
- Design moment capacity
- Bending strength adequate
- Bending utilisation
Results summary
- The factored midspan moment of the 7.5 m beam is about 380 kN·m. With 4N28 bars at 534 mm effective depth the design capacity is about 482 kN·m — 79% utilised. Minimum reinforcement passes easily; the neutral-axis check gives k_u = 0.31 against the 0.36 ductility limit, a real but modest margin worth watching if bars are added.
Try changing…
- Drop to 3 bars — capacity falls to about 376 kN·m, below the demand: two checks turn red.
- Raise f'c to 50 MPa — capacity grows only ~5% (steel governs) while k_u eases to 0.23.
- Stretch the span to 9 m — the demand grows with L² to about 547 kN·m and overtakes capacity.