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.
| 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. |