RC Beam
Published: 28/05/26, Updated:
Version: 1.0.0
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Reinforced concrete section form performs design calculations of rectangular, T-beam and L-beam cross-sections currently to BS8110 (EC2 and ACI318 to be added). Calculation checks bending, shear, deflection and detailing requirements against selected code.
Assumptions
The following assumptions are considered in analysis:
Constant elasticity of steel modulus E = 200GPa and rectangular cross-section.
Constant cover around the perimeter.
Limitations
The calculation has the following limitations:
Section width and height limited to 1000mm.
Concrete compressive strength and resultant properties are code dependent.
Lateral torsional buckling (LTB) of the beam is not checked when axial force is applied.
| Input Variable | Description | Limits |
|---|---|---|
| Concrete strength | C15/20, C20/25, C25/30, C32/40, C40/50 | |
| fcu | Characteristic concrete strength | 0 < fcu < 99 |
| t | Concrete age | 0 < t < 99 |
| bf | Beam flange width | 0 < bf < 1000 |
| bartype | Reinforcement type | High Yield, Mild Steel |
| Tsec | Section type | Rectangular |
| Tsupp | Beam support conditions | Simply-supported, Fully-fixed, Cantilever |
| fy | Steel yield strength | 0 < fy < 999 |
| fyv | Shear steel yield strength | 0 < fyv < 999 |
| hagg | Aggregate size | 0 < hagg < 99 |
| Lclear | Clear span | 0 < Lclear < 10000 |
| h | Beam depth | 0 < h < 2000 |
| b | Beam width | 0 < b < 1000 |
| bwall | Width of supporting wall | 0 < bwall < 500 |
| tf | Fire resistance duration | 0 < tf < 200 |
| ctop | Top cover | 0 < ctop < 99 |
| cbot | Bottom cover | 0 < cbot < 99 |
| cside | Side cover | 0 < cside < 99 |
| φlink | Link diameter | 6, 8, 10, 12, 16, 20, 25 |
| nlink | Link legs number | 0 < nlink < 10 |
| slink | Link spacing | 0 < slink < 999 |
| φside | Side rebar diameter | 6, 8, 10, 12, 16, 20, 25 |
| sside,prov | Side rebar spacing | 0 < sside < h - (ctop + cbot) |
| ?Shear Cracking Limited? | Is shear cracking limited | True, False |
| MU,+ | Design positive moment | 0 < MU,+ < 9999 |
| MU,- | Design negative moment | 0 < MU,- < 9999 |
| VU | Design shear force | 0 < VU < 9999 |
| NU | Design axial force | 0 < NU < 9999 |
| TU | Design torsion | 0 < TU < 9999 |
| MS,+ | Service positive moment | 0 < MS,+ < MU,+ |
| MU,serv,- | Service negative moment | 0 < MS,- < MU,- |
| VS | Service shear force | 0 < VS < VU |
| ?Redistribution over 10%? | Redistribution over 10% | True, False |
| RU | Redistribution percentage | 10% < RU < 30% |
| Flexural Variable | Description |
|---|---|
| Leff | Effective Span Length |
| beff | Effective Width |
| λ | Slenderness Ratio |
| βb+ | Beta B ratio for positive moment |
| βb- | Beta B ratio for negative moment |
| MEd,+ | Design Positive Moment |
| MEd,+ | Design positive moment - adjusted for axial |
| K+ | K value for positive moment |
| K'+ | K' value for positive moment |
| z+ | Lever arm for positive moment |
| x+ | Neutral axis depth for positive moment |
| As+,req,top | Required top reinforcement for positive moment |
| As+,req,bot | Required bottom reinforcement for positive moment |
| MEd,- | Design Negative Moment |
| MEd,- | Design negative moment - adjusted for axial |
| K- | K value for negative moment |
| K'- | K' value for negative moment |
| z- | Lever arm for negative moment |
| x- | Neutral axis depth for negative moment |
| As-,req,bot | Required bottom reinforcement for negative moment |
| As-,req,top | Required top reinforcement for negative moment |
| As,req,top | Required top reinforcement |
| As,req,bot | Required bottom reinforcement |
| As,min,tension | Minimum reinforcement - tension |
| As,min,compression | Minimum reinforcement - compression |
| As,max | Maximum reinforcement |
| δ | Deflection |
| Flexural Design Variable | Description |
|---|---|
| As,top,prov | Required vs Provided Top Flexural Reinforcement |
| As,bot,req vs As,bot,prov | Required vs Provided Bottom Flexural Reinforcement |
| Nmax,allowable | Axial force vs Maximum Allowed Axial |
| As,top+,min,comp vs As,min,comp+ | Top reinforcement area to compressive minimum reinforcement - Positive moment |
| As,bottom+,min,tens vs As,min,tens+ | Bottom reinforcement area to tensile minimum reinforcement - Positive moment |
| As,top-,min,tens vs As,min,tens- | Top reinforcement area to tensile minimum reinforcement - Negative moment |
| As,bottom+,min,comp vs As,min,comp- | Bottom reinforcement area to compressive minimum reinforcement - Negative moment |
| As,top+,max vs As,max | Top reinforcement area to maximum reinforcement - Positive moment |
| As,bottom+,max vs As,max | Bottom reinforcement area to maximum reinforcement - Positive moment |
| As,top-,max vs As,max | Top reinforcement area to maximum reinforcement - Negative moment |
| As,bottom-,max vs As,max | Bottom reinforcement area to maximum reinforcement - Negative moment |
| Shear Variable | Description |
|---|---|
| vmax | Limit shear stress |
| v | Design shear stress |
| vc | Design concrete shear stress |
| vc',axial | Design axial shear stress |
| vs | Required design steel shear resistance |
| Asv,req | Required area of shear reinforcement |
| Shear Design Variable | Description |
|---|---|
| vmax vs v | Allowable Shear Stress vs Design Shear Stress |
| Asv,req vs Asv,prov | Required vs Provided Shear Reinforcement |
| Deflection Variable | Description |
|---|---|
| L/d | Basic Span to Depth Ratio |
| fs,bot | Service Stress in Bottom Reinforcement |
| Modbottom | Modification Factor for Bottom Reinforcement |
| L/dmod,bot | Modified Span to Depth Ratio - Positive Moment |
| fs,top | Service Stress in Top Reinforcement |
| Modtop | Modification Factor for Top Reinforcement |
| L/dmod,top | Modified Span to Depth Ratio - Negative Moment |
| Deflection Design Variable | Description |
|---|---|
| lbot,e/d | Modified Span to Depth Ratio vs Basic Span to Depth Ratio - Positive Moment |
| ltop,e/d | Modified Span to Depth Ratio vs Basic Span to Depth Ratio - Negative Moment |
| Detailing Variable | Description |
|---|---|
| φside,req | Minimum Side Bar Diameter to Control Cracking |
| smax | Maximum Spacing of Flexural Reinforcement |
| sh,min | Minimum Horizontal Spacing of Flexural Reinforcement |
| sv,min | Minimum Vertical Spacing of Flexural Reinforcement |
| dlinks,min | Minimum Diameter of Links |
| slinks,max | Maximum Spacing of Links |
| smax,link,top | Maximum distance between top compression bars and the nearest link |
| smax,link,bot | Maximum distance between bottom compression bars and the nearest link |
| Detailing Design Variable | Description |
|---|---|
| barmin,side vs barside | Minimum Side Reinforcement vs Provided Side Reinforcement |
| sside,max | Max Side Reinforcement Spacing vs Provided Side Reinforcement Spacing |
| smin,h vs sh | Minimum Tension Horizontal Reinforcement Spacing vs Actual Horizontal Bar Spacing |
| smin,v vs sv | Minimum Tension Vertical Reinforcement Spacing vs Actual Vertical Bar Spacing |
| smax,h | Maximum Tension Horizontal Reinforcement Spacing vs Actual Horizontal Bar Spacing |
| slink,max | Maximum Distance from Compression Bar to Link |
| Fire Variable | Description |
|---|---|
| bmin | Minimum Beam Width for Fire Resistance |
| cavg,min | Minimum Average Cover to Main Reinforcement for Fire Resistance |
| cavg,prov,bot | Provided Average Cover to Bottom Face Main Reinforcement |
| cavg,prov,top | Provided Average Cover to Top Face Main Reinforcement |
| cave,adj | Adjusted Minimum Average Cover (Table 4.1) |
| Fire Design Variable | Description |
|---|---|
| bchk | Beam Width Provided vs Required (Fire) |
| Cave,bot,chk | Bottom Cover Provided vs Required (Fire) |
| Cave,side,chk | Side Cover Provided vs Required (Fire) |
| Cave,top,chk | Top Cover Provided vs Required (Fire) |
| cspall,chk | Nominal Cover Provided vs Spalling Limit (Fire) |
| Torsion Variable | Description |
|---|---|
| β | Torsional rigidity coefficient |
| C | St. Venant torsional constant |
| vt | Torsional shear stress |
| v | Applied shear stress for torsion |
| vcomb | Combined shear + torsion stress |
| vt,min | Minimum torsional shear stress |
| vtu | Maximum combined shear stress |
| vt,lim,small | Torsion stress limit for small sections |
| x1 | Smaller centre-to-centre dimension of closed torsion link |
| y1 | Larger centre-to-centre dimension of closed torsion link |
| Asv,tors,req | Required closed link area per unit length |
| As,tors,req | Required longitudinal torsion bar area |
| sv,tors,max | Maximum permissible link spacing |
| Asv,tors,prov | Provided closed link area per unit length |
| As,tors,prov | Provided longitudinal torsion bar area (top + bottom reinforcement) |
| Torsion Design Variable | Description |
|---|---|
| v+vt ≤ vtu | Combined Torsion/Shear Stress Provided vs Crushing Limit |
| vt ≤ vtu·y₁/550 | Torsional Stress Provided vs Small Section Limit |
| Asv/sv,prov ≥ req | Torsion Link Area Provided vs Required |
| As,tors,prov ≥ req | Torsion Longitudinal Bars Provided vs Required |
| sv ≤ sv,tors,max | Link Spacing Provided vs Maximum Allowed |
Standards
BS8110-1
References
- BS 8110-1 1997
| Release Date | Version | Description |
|---|---|---|
| April 2025 | 1.0.0 | Initial release. |