Concrete · Beams

Doubly reinforced RC beam calculator

Rectangular beam with compression steel: neutral axis by trial on compression-steel yield, capacity and ductility.

Standard: AS 3600 Cl 8.1 · strain compatibility for compression steel

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Result	Value	Unit
α2 = 0.85 − 0.0015 f′c (≥ 0.67)	0.802
γ = 0.97 − 0.0025 f′c (≥ 0.67)	0.890
Assume Asc yields: ku from (Ast − Asc) fsy = α2 f′c b γ ku d	0.324
Compression steel strain 0.003(1 − dc/(ku d))	0.002
Compression steel yields?	no: stress reduced
Compression steel stress (first estimate)	394.4	MPa
ku iteration 1	0.354
fsc iteration 2	411.5	MPa
ku iteration 2	0.349
fsc iteration 3	408.9	MPa
ku (converged)	0.350
Concrete force	1,509	kN
Mu = Cc(d − γkud/2) + Asc fsc (d − dc)	923.8	kNm
φ	0.850
φMu	785.2	kNm

Diagram for the worked example

α2 = 0.85 − 0.0015 f′c (≥ 0.67) = MAX(0.67,0.85-0.0015*32) = 0.802
γ = 0.97 − 0.0025 f′c (≥ 0.67) = MAX(0.67,0.97-0.0025*32) = 0.89
Assume Asc yields: ku from (Ast − Asc) fsy = α2 f′c b γ ku d = (4000-1200)*500/(0.802*32*350*0.89*540) = 0.3243
Compression steel strain 0.003(1 − dc/(ku d)) = 0.003*(1-60/(0.3243*540)) = 0.0019722
Compression steel yields? = IF(0.0019722*200000>=500,"yes","no: stress reduced") = no: stress reduced
Compression steel stress (first estimate) = MIN(500,MAX(0,0.0019722*200000)) = 394.43 MPa
ku iteration 1 = (4000*500-1200*394.43)/(0.802*32*350*0.89*540) = 0.35365
fsc iteration 2 = MIN(500,MAX(0,0.003*(1-60/(0.35365*540))*200000)) = 411.49 MPa
ku iteration 2 = (4000*500-1200*411.49)/(0.802*32*350*0.89*540) = 0.34891
fsc iteration 3 = MIN(500,MAX(0,0.003*(1-60/(0.34891*540))*200000)) = 408.93 MPa
ku (converged) = (4000*500-1200*408.93)/(0.802*32*350*0.89*540) = 0.34962
Concrete force = 0.802*32*350*0.89*0.34962*540/1000 = 1509.3 kN
Mu = Cc(d − γkud/2) + Asc fsc (d − dc) = (1509.3*(540-0.89*0.34962*540/2)+1200*408.93*(540-60)/1000)/1000 = 923.76 kNm
φ = MIN(0.85,MAX(0.65,1.24-13*0.34962/12)) = 0.85
φMu = 0.85*923.76 = 785.19 kNm

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.