Reinforced Concrete Beam Design Calculator to AS 3600: Moment Capacity, ku, Minimum Steel and Steel Required

How this calculator works

Enter the beam width and depth, the cover, the stirrup and bar diameters, the number of bars, the concrete strength f'c and the steel yield strength.

The calculator follows AS 3600 clause 8.1: it finds the effective depth d, the stress block parameters alpha2 and gamma, the neutral axis ratio ku, the ultimate moment Mu = Ast fsy d (1 - gamma ku / 2) and the capacity reduction factor phi from Table 2.2.2.

It checks the ductility limit ku not over 0.36 and the minimum steel of clause 8.1.6.1, and with a design moment M* it finds the steel needed and the number of bars.

Formulas used

• \alpha_2 = 1.0 - 0.003 f'_c,\quad \gamma = 1.05 - 0.007 f'_c
• k_u = \frac{A_{st} f_{sy}}{\alpha_2\gamma f'_c b d}
• M_u = A_{st} f_{sy} d\left(1 - \frac{\gamma k_u}{2}\right)
• \phi = 1.19 - \frac{13k_{uo}}{12}\ (0.6 \le \phi \le 0.85)
• A_{st,min} = \alpha_b\left(\frac{D}{d}\right)^2\frac{f'_{ct.f}}{f_{sy}}bd

Worked example

With the default numbers in the calculator above:

1. Effective depth to the centre of the tension bars: 450.00 mm
2. Area of tension steel: 942.48 mm2 (3 bars of 20 mm)
3. Stress block parameters (AS 3600 cl 8.1.3): alpha2 = 0.85 (0.67 to 0.85), gamma = 0.83 (0.67 to 0.85)
4. Neutral axis depth ratio (AS 3600 cl 8.1.5): 0.16
5. Ultimate strength in bending (AS 3600 cl 8.1.5): 198.45 kN m
6. Capacity reduction factor for bending, Class N reinforcement (AS 3600 Table 2.2.2): 0.85
7. Design strength in bending: 168.68 kN m
8. Minimum tension steel (AS 3600 cl 8.1.6.1, rectangular section, alpha_b = 0.20): 226.27 mm2
9. Clear spacing between the bars: 80.00 mm (check AS 3600 cl 17.1.3 for the minimum spacing and the size of the aggregate)
10. Tension steel needed for the design moment (and not less than the minimum): 831.37 mm2, which is 3 bars of 20 mm (942.48 mm2)

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

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Further reading: AS 3600:2018 Concrete structures (Sections 2, 4, 8 and 13); AS/NZS 1170.0 Structural design actions: General principles; AS/NZS 4671 Steel for the reinforcement of concrete.

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