Coursework – Structural Design of a Reinforced Concrete Beam to AS 3600

Introduction

This coursework designs a simply supported reinforced concrete floor beam for a two-storey commercial building in Geelong, Victoria: a Class 5 office development typical of the low-rise non-residential work reported each quarter in the building approvals series of the Australian Bureau of Statistics (2025). The member, Beam B1, spans 6.0 m between masonry piers and carries a one-way suspended slab.

Design follows AS 3600:2018 Concrete structures (Standards Australia 2018), with actions from AS/NZS 1170.0 (Standards Australia 2002a) and AS/NZS 1170.1 (Standards Australia 2002b), both called up by the National Construction Code (Australian Building Codes Board 2022). The scope covers the load take-down, design action effects, flexural and shear design, deflection, detailing and fire resistance; torsion and foundations fall outside the brief. Each calculation is set out as formula, substitution and result so it can be checked independently (Engineers Australia 2022).

Design Basis and Assumptions

Arrangement and materials

The floor comprises a 150 mm one-way slab spanning between parallel beams at 4.0 m centres, so the tributary width for Beam B1 is 4.0 m. The beam bears on 300 mm masonry piers, giving a clear span of 5.70 m. Under Clause 8.8 the effective span is the lesser of the centre-to-centre distance and the clear span plus overall depth, that is, of 6.00 m and 6.35 m, so Lef = 6.00 m. A trial section of 300 mm by 650 mm was adopted, deeper than the usual Lef/12 to Lef/15 rule (Loo & Chowdhury 2018) because deflection was expected to govern.

Normal-class concrete with f’c = 32 MPa and 20 mm nominal aggregate is specified. Table 3.1.2 gives Ec = 30,100 MPa, and f’ct.f = 0.6 x sqrt(32) = 3.39 MPa. Reinforcement is Class N deformed bar to AS/NZS 4671, fsy = 500 MPa (Standards Australia 2019). The enclosed interior is exposure classification A1, requiring 20 mm cover; 30 mm to the fitments is adopted for tolerance and fire, following Australian durability guidance (Cement Concrete & Aggregates Australia 2021).

Assumptions

• The beam is simply supported with no continuity steel over the piers, so no moment redistribution is available.
• The slab is designed separately and delivers a uniformly distributed line load; no composite action is claimed.
• Partitions are lightweight, so the non-brittle deflection limit applies.
• Shrinkage-induced tensile stress is taken as 1.0 MPa, suiting a lightly restrained interior member, and the design is for certification by an engineer registered under the Professional Engineers Registration Act 2019 (Vic).

Load Take-Down

Permanent actions were built up from the densities and allowances of AS/NZS 1170.1, using a concrete density of 24 kN/m^3; the imposed action for offices for general use is 3.0 kPa from Table 3.1. Area actions become line loads via the 4.0 m tributary width, as Table 1 shows.

Table 1: Load take-down for Beam B1, tributary width 4.0 m, to AS/NZS 1170.1.

The web contribution uses only the depth below the slab, so slab weight is not counted twice: 0.30 x 0.50 x 24 = 3.60 kN/m. Self-weight is therefore only 13 per cent of G, and the partition allowance contributes more than the beam itself: superimposed allowances, not structural mass, drive such floors.

Design Action Effects

The strength combination in AS/NZS 1170.0 is 1.2G + 1.5Q. Substituting the Table 1 subtotals:

w* = 1.2G + 1.5Q = 1.2 x 27.20 + 1.5 x 12.00 = 32.64 + 18.00 = 50.64 kN/m

The permanent-only case, 1.35G = 36.72 kN/m, is not critical. For a uniformly loaded simply supported member:

M* = w* x Lef^2 / 8 = 50.64 x 6.00^2 / 8 = 227.9 kNm

V* = w* x Lef / 2 = 50.64 x 6.00 / 2 = 151.9 kN

Clause 8.2.1.6 permits the design shear to be taken a distance d from the support face. With a 150 mm half-bearing and the effective depth of 598 mm derived below, that section lies 0.748 m from the centreline, giving V* = 50.64 x (3.000 – 0.748) = 114.0 kN. Table 2 collects the action effects; Figure 1 shows the loading and moment diagram.

Table 2: Design action effects for Beam B1 under the governing combinations.

Flexural Design

With N24 bars in a single layer inside N10 fitments, d = 650 – 30 – 10 – 12 = 598 mm. A first estimate assumes a lever arm of 0.85d, a reliable start for lightly reinforced rectangular sections (Foster, Kilpatrick & Warner 2021), with phi = 0.85 from Table 2.2.2:

Ast = M* / (phi x fsy x 0.85d) = 227.9 x 10^6 / (0.85 x 500 x 0.85 x 598) = 1,055 mm^2

Three N24 bars provide 1,350 mm^2, a 28 per cent over-provision reflecting the discrete sizes available. Capacity is verified with the rectangular stress block of Clause 8.1.3, for which alpha2 = 1.0 – 0.003 x 32 = 0.904 capped at 0.85, and gamma = 1.05 – 0.007 x 32 = 0.826:

T = Ast x fsy = 1,350 x 500 = 675 kN, so gamma x dn = T / (alpha2 x f’c x b) = 675,000 / (0.85 x 32 x 300) = 82.7 mm, dn = 100.1 mm and ku = 100.1 / 598 = 0.17

Since ku is well below the 0.36 limit of Clause 8.1.5 the section is under-reinforced and phi = 0.85 applies. Capacity follows from the internal couple:

Mu = T x (d – gamma x dn / 2) = 675,000 x (598 – 41.4) = 375.7 kNm, so phi x Mu = 319.4 kNm > M* = 227.9 kNm

Flexural utilisation is therefore 0.71. Clause 8.1.6.1 guards against sudden failure at first cracking, requiring Ast.min = 0.20 x (D/d)^2 x (f’ct.f / fsy) x b x d = 0.20 x (650/598)^2 x (3.39/500) x 300 x 598 = 288 mm^2, exceeded 4.7 times over. Clear spacing between bars is (300 – 60 – 20 – 72) / 2 = 74 mm, above the greater of 25 mm, 1.5 times the aggregate size and the bar diameter, and the 98 mm centre-to-centre spacing is inside the 300 mm crack control maximum of Clause 8.6.1. Two N16 hangers add 400 mm^2 in the top.

Shear Design

Shear uses the simplified method of Clause 8.2.4.3, permitted where the member carries at least minimum shear reinforcement. The effective shear depth is dv = the greater of 0.72D and 0.9d, so dv = 538.2 mm. With minimum fitments, kv = 0.15 and the compression field angle theta = 36 degrees:

Vuc = kv x bv x dv x sqrt(f’c) = 0.15 x 300 x 538.2 x 5.657 = 137.0 kN

With phi = 0.75, phi x Vuc = 102.8 kN, less than the 114.0 kN at the critical section, so the fitments must supply Vus = V*/phi – Vuc = 152.0 – 137.0 = 15.0 kN. Two-leg N10 fitments give Asv = 157 mm^2, and cot 36 degrees = 1.376:

s = Asv x fsy.f x dv x cot(theta) / Vus = 157 x 500 x 538.2 x 1.376 / 15,000 = 3,877 mm

Strength is plainly not controlling; detailing is. Clause 8.2.1.7 requires Asv.min / s = 0.08 x sqrt(f’c) x bv / fsy.f = 0.272 mm^2/mm, permitting 578 mm for a 157 mm^2 fitment, while maximum spacing is the lesser of 0.5D = 325 mm and 300 mm. N10 two-leg fitments at 250 mm centres meet all three criteria and let one schedule serve the whole span. There Vus = 232.6 kN, so phi x (Vuc + Vus) = 277.2 kN and the shear utilisation is only 0.41. Web crushing under Clause 8.2.3.3 gives Vu.max = 0.55 x f’c x bv x dv x cot(theta) / (1 + cot^2(theta)) = 1,351 kN, so phi x Vu.max = 1,013 kN leaves the diagonal compression field far from its limit.

Serviceability and Deflection

Serviceability uses the combinations of AS/NZS 1170.0, with psi.s = 0.7 and psi.l = 0.4 for offices. The short-term service load is G + 0.7Q = 35.60 kN/m, giving Ms = 160.2 kNm, and the cracking moment allows for shrinkage-induced tension with Z = 300 x 650^2 / 6 = 21.13 x 10^6 mm^3:

Mcr = (f’ct.f – sigma.cs) x Z = (3.39 – 1.0) x 21.13 x 10^6 = 50.6 kNm

Because Ms greatly exceeds Mcr the beam is cracked at service load, so the effective second moment of area applies. With n = Es/Ec = 6.65, n x Ast = 8,971 mm^2, and equating first moments about the cracked neutral axis, 150x^2 = 8,971 x (598 – x), gives x = 161.6 mm:

Icr = b x^3 / 3 + n x Ast x (d – x)^2 = 300 x 161.6^3 / 3 + 8,971 x 436.4^2 = 422 x 10^6 + 1,709 x 10^6 = 2,131 x 10^6 mm^4

With I = 6,866 x 10^6 mm^4 and Mcr/Ms = 0.316, Clause 8.5.3.1 gives Ief = Icr + (I – Icr) x (Mcr/Ms)^3 = 2,131 x 10^6 + 4,735 x 10^6 x 0.0315 = 2,280 x 10^6 mm^4. Effective stiffness is thus only 33 per cent of gross, which is why gross-section calculations badly underestimate deflection (Gilbert 2017). Long-term effects are captured by kcs = 2 – 1.2 x (Asc/Ast) = 2 – 1.2 x (400/1,350) = 1.64, giving Fd.ef = 88.08 kN/m:

Total deflection = 5 x Fd.ef x Lef^4 / (384 x Ec x Ief) = 5 x 88.08 x 6,000^4 / (384 x 30,100 x 2,280 x 10^6) = 21.7 mm

Because the partitions are lightweight and non-brittle, the total deflection limit from Table 2.3.2 is Lef/250 = 24.0 mm. The calculated 21.7 mm satisfies this at a utilisation of 0.90, the highest of any check performed. That result is the analytical centre of the design: serviceability rather than strength sets the depth, so the flexural utilisation of 0.71 is a consequence rather than a sign of inefficiency. A 600 mm depth would still satisfy bending and shear but would breach the deflection limit, so the section cannot be trimmed without compression steel, a higher grade or a precamber.

Detailing, Fire Resistance and Compliance

Development length for the N24 bottom bars follows Clause 13.1.2.2, with k1 = 1.0 for bottom-cast bars, k2 = (132 – 24)/100 = 1.08 and k3 = 1.0 – 0.15 x (37 – 24)/24 = 0.92, taking cd = 37 mm as the smallest of side cover, bottom cover and half the clear spacing:

Lsy.t = 0.5 x k1 x k3 x fsy x db / (k2 x sqrt(f’c)) = 0.5 x 1.0 x 0.92 x 500 x 24 / (1.08 x 5.657) = 903 mm

This exceeds the lower bound of 0.058 x fsy x k1 x db = 696 mm and therefore governs. At a simply supported end the bottom bars must extend at least 12db = 288 mm past the support face or be anchored for the force present; a standard 90 degree cog within the 300 mm bearing provides that anchorage, and all three bars are carried through rather than curtailed. The building is Type B construction, requiring a 90 minute fire resistance period for the floor (Australian Building Codes Board 2022). Section 5 of AS 3600 then requires a 40 mm axis distance at a 300 mm web width; the provided 52 mm satisfies that and the side axis distance. Table 3 consolidates every verification.

Table 3: Design summary for Beam B1, 300 x 650 mm with 3 N24 bottom bars and N10 fitments at 250 mm centres.

Conclusion

A 300 mm by 650 mm beam in 32 MPa concrete with three N24 bottom bars, two N16 top bars and N10 fitments at 250 mm centres satisfies every strength and serviceability requirement of AS 3600:2018 for a 6.0 m span carrying an office floor loaded to AS/NZS 1170.1. The design load of 50.64 kN/m gives a midspan moment of 227.9 kNm against 319.4 kNm capacity, and a shear of 114.0 kN against 277.2 kN.

The most instructive outcome is the ranking of utilisation ratios in Table 3. Deflection controls at 0.90 while bending sits at 0.71 and shear at 0.41, so this is a serviceability-governed design in which depth cannot be reduced despite ample reserve strength. Compression reinforcement would lower kcs and the long-term deflection, potentially allowing a 600 mm section and a saving in floor-to-floor height, while a higher grade would raise Ec and Mcr and stiffen the cracked section. Both must be weighed against buildability and cost, the trade-off that separates a compliant design from a well-judged one.

References

Australian Building Codes Board 2022, National Construction Code 2022, Volume One: Building Code of Australia, ABCB, Canberra.

Australian Bureau of Statistics 2025, Building approvals, Australia, ABS, Canberra.

Cement Concrete & Aggregates Australia 2021, Guide to concrete construction, CCAA, Sydney.

Engineers Australia 2022, Code of ethics and guidelines on professional conduct, Engineers Australia, Barton.

Foster, SJ, Kilpatrick, AE & Warner, RF 2021, Reinforced concrete basics, 3rd edn, Pearson Australia, Melbourne.

Gilbert, RI 2017, ‘Deflection of reinforced concrete beams and slabs at service loads’, Australian Journal of Structural Engineering, vol. 18, no. 2, pp. 76-88.

Loo, YC & Chowdhury, SH 2018, Reinforced and prestressed concrete, 3rd edn, Cambridge University Press, Melbourne.

Standards Australia 2002a, AS/NZS 1170.0:2002 Structural design actions, Part 0: General principles, Standards Australia, Sydney.

Standards Australia 2002b, AS/NZS 1170.1:2002 Structural design actions, Part 1: Permanent, imposed and other actions, Standards Australia, Sydney.

Standards Australia 2018, AS 3600:2018 Concrete structures, Standards Australia, Sydney.

Standards Australia 2019, AS/NZS 4671:2019 Steel for the reinforcement of concrete, Standards Australia, Sydney.