Once the slab is designed, the beams that collect its edge reactions are next in the load path. Beam design in reinforced concrete follows the same logic as slab design but adds shear: the section must resist the bending moment at mid span and the shear force at the supports, and the stirrups must hold diagonal tension cracks closed. This article works through slab beam design step by step, from the depth and breadth that satisfy the limiting moment of resistance, to the longitudinal steel area, to the vertical stirrup spacing that closes out the shear check. The beam grid also responds to the architectural design and building envelope design process, because wall positions and floor zones decide where beams can run without breaking the layout.
Loads That Reach the Beam
A beam supports the tributary slab area around it. For a square panel the slab load is distributed around the four edges, and each beam carries the share assigned to its span plus its own self weight. The same panel that was designed as a two way slab in the previous step now becomes the load source for the beams.
Tributary Load from the Slab
In the worked example, a 3.0 m by 3.0 m panel delivers a total factored load of about 89.44 kN to the beam grid. The perimeter of the panel is 12 m, so each beam receives roughly 7.45 kN per metre of length from the slab. Over a 3.0 m span that is 22.36 kN per beam.
Beam Self Weight
Self weight uses the beam cross section: (b x d x l) x 25 for a length l of beam. A 230 x 460 mm beam, 3.0 m long, weighs 0.230 x 0.460 x 3.0 x 25 = 7.94 kN. Adding the slab contribution of 22.36 kN gives a total of 30.3 kN acting on each beam, which is about 10.1 kN per metre along the span. The self weight term is small compared with the slab contribution, but it still flows into the shear calculation at the support.
The Load Path through the Frame
- Slab carries the floor load to its four edges.
- Beams collect the edge reactions along their spans.
- Beam end reactions pass to the columns below.
- Columns carry the accumulated load to the foundation.
The same tributary logic shows up in structural steel design principles, where floor beams pick up slab loads and deliver them to girders and columns through sized connections.
Beam Depth and Breadth from Moment Capacity
The Limiting Moment Equation
For a singly reinforced rectangular section, the limiting moment of resistance is Mu lim = 0.138 fck b d², given in SP 16 Table C for Fe 415 steel. The beam is sized so that its moment capacity equals or exceeds the applied moment at mid span, which for a simply supported beam carrying a uniform load is w l² / 8.
Depth to Breadth Ratio
Designers commonly take d = 2b, which gives a stiff and practical section. Substituting d = 2b into the moment equation gives Mu = 0.138 x fck x b x (2b)² = 0.552 x fck x b³, so the breadth can be solved directly from the moment.
Worked Sizing
With an applied moment of 22.36 kN.m, fck = 20 N/mm²: 22.36 x 10⁶ = 0.138 x 20 x b x (2b)². Solving gives b = 138.9 mm, which is rounded up to a practical 230 mm. The depth is then d = 2 x 230 = 460 mm, so the beam is 230 mm wide by 460 mm deep. The 230 mm width matches the common wall thickness, which simplifies the formwork and the masonry above. The same section works for both directions of the grid in the example, which keeps the formwork and the bar schedule identical on all four sides.
Engineers routinely verify these hand sizes in 3D structural analysis and design software, which checks the beam against the actual envelope of moments from the frame analysis rather than a single mid span value.
Longitudinal Steel for the Beam
Steel Percentage from the Moment
The tension steel percentage for a singly reinforced section is Pt = 50 (fck/fy) x (1 – sqrt(1 – 4.6 Mu / (fck b d²))). For the worked beam with fck = 20 N/mm² and fy = 415 N/mm²: Pt = 50 x (20/415) x (1 – sqrt(1 – 4.6 x 22.36 x 10⁶ / (20 x 230 x 460²))) = 0.131%.
Area and Bar Selection
The required steel area is Ast = (Pt/100) x b x d = 0.00131 x 230 x 460 = 138.6 mm². A 12 mm bar has an area of 113.04 mm², so 138.6/113.04 = 1.22, rounded up to 2 bars. Provide 2 Nos. 12 mm diameter bars at the bottom of the beam.
Bar Area Reference
| Bar diameter (mm) | Area per bar (mm²) | Bars for 138.6 mm² |
|---|---|---|
| 10 | 78.54 | 2 |
| 12 | 113.04 | 2 |
| 16 | 201.06 | 1 |
Bar selection is a balance between area and practicality. Two 12 mm bars give 226 mm², which exceeds the required 138.6 mm² and leaves room for the small variations that occur in site bending. Larger bars reduce congestion but can make anchorage harder in short spans.
Reinforcement design follows the same strain compatibility logic used in flexible and rigid pavement design, where steel or the concrete itself is positioned to carry the tension that the surface cannot.
Shear Design and Stirrup Spacing
Shear Force at the Support
The design shear force for a uniformly loaded simply supported beam is Vu = w l / 2. With a total load of 30.3 kN over the 3.0 m span, the support shear works out to about 45 kN. Shear is maximum at the support and drops toward mid span, which is why the stirrup spacing can increase away from the ends.
Concrete Shear Contribution
Part of the shear is carried by the concrete. The design shear strength τc comes from IS 456 Table 19 for the given steel percentage. For 0.131% steel, τc = 0.28 N/mm², and the concrete contribution is τc b d = 0.28 x 230 x 460 = 29.6 kN. The balance to be carried by the stirrups is Vus = Vu – τc b d = 45 – 29.6 = 15.4 kN.
Stirrup Spacing from Shear
For 2 legged 8 mm vertical stirrups of Fe 415 steel, the stirrup area is Asv = 2 x (π/4) x 8² = 100.51 mm². The spacing required for shear is Sv = 0.87 x fy x Asv x d / Vus = 0.87 x 415 x 100.51 x 460 / 15400, which comes to about 1084 mm. Shear alone would allow a very wide spacing, so the code spacing limits govern.
Spacing Limits
| Limit | Value (mm) |
|---|---|
| Spacing from shear Sv | 1084 |
| 0.75 x d | 345 |
| Absolute maximum | 300 |
| Minimum shear reinforcement rule | 238 |
The minimum shear reinforcement rule, Sv = 0.87 x fy x Asv / (0.4 x b), gives 238 mm, and the governing spacing is the smallest of all the limits. The beam is detailed with 2 legged 8 mm stirrups at 230 mm centre to centre.
Shear design is one of the fundamental principles of structural analysis that keeps a beam from failing along a diagonal plane before its flexural capacity is reached.
Serviceability and Detailing Checks
Deflection and Crack Control
The depth chosen from the moment check is also checked against span to depth limits for deflection. Stirrup spacing already controls shear cracks, and flexural crack control follows from bar spacing rules similar to the ones used for slabs.
Cover and Fire Resistance
Clear cover to the stirrups protects the steel from corrosion and from fire. Structural fire protection rules set minimum covers based on the required fire rating period, and a deeper beam with more cover reaches a higher fire resistance without any change to the reinforcement.
Placing and Tying the Cage
The longitudinal bars sit inside the stirrup cage. The bottom bars carry the positive moment, the stirrups wrap them at the spacing just calculated, and the assembly is lifted into the formwork with spacers holding the cover. Top bars are added before concreting when the beam is continuous over a support.
- Confirm the moment capacity exceeds the applied moment.
- Confirm the steel area provided exceeds the required area.
- Confirm the stirrup spacing is the smallest of the four limits.
- Confirm the cover matches the fire rating and exposure conditions.
The beam design closes with a 230 x 460 mm section, 2 Nos. 12 mm bars at the bottom, and 8 mm two legged stirrups at 230 mm spacing. The procedure is a template for any rectangular beam carrying a slab, and the same load, moment and shear logic underpins the structural design methods for flexible and rigid pavements used in highway engineering, where the member is simply laid flat and called a slab. Sizing from the moment equation, rounding dimensions to practical values, and capping stirrup spacing at the smallest limit produces a beam that is safe and straightforward to build.