RC Beam

Published: 28/05/26, Updated: 01/09/26

Version: 1.0.0

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Reinforced concrete section form performs design calculations of rectangular, T-beam and L-beam cross-sections to BS8110, EN1992-1-1 (Eurocode 2, UK National Annex), or ACI 318 (2014/2019 editions). Calculation checks bending, shear, deflection and detailing requirements against the selected code. For BS8110, flanged-beam flexure uses the effective flange width per cl 3.4.1.5 (T-beam: web width + lz/5; L-beam: web width + lz/10), with the cl 3.4.4.5 method when the neutral axis falls below the flange. For EN1992-1-1, the effective width follows cl 5.3.2.1, exp.5.7 (beff = Σbeff,i + bw). For ACI 318, the effective width follows Table 6.3.2.1 (T-beam: bw + 2×min(8hf, ln/8); L-beam: bw + min(6hf, ln/12)). For L-beam the flange overhangs the web on the left side of the section. ACI 318 inputs can be entered in metric or imperial units via the toggle at the top of the input form (f'c/fy/fyt and every ACI-specific geometry field convert; longitudinal reinforcement bar diameters switch to a true US bar catalog #3-#11 via a fixed metric/imperial pairing; stirrup/link diameter stays mm-labelled, shared with BS8110/EC2's reinforcement editor).

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Input example for RC beam

The limitations and assumptions below apply to every supported design standard. Limitations and assumptions specific to BS8110, EN1992-1-1, or ACI 318 are listed under each standard's own tab further down this page.

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.

Assumptions

Constant elasticity of steel modulus E = 200GPa.

Top, bottom and side cover are each independently configurable — cover is not assumed constant around the section perimeter.

No self-weight or load combination is performed — for each load case, the design (ULS) and service (SLS) moment, shear, axial force and torsion must be supplied already combined and factored, including self-weight if relevant.

Each load case is designed as a single, prismatic cross-section under its own M/V/N/T — there is no whole-beam envelope or multi-span moment model, so section geometry and material properties are assumed constant along the full length of the beam.

Positive and negative moment are designed independently within a load case, each producing its own top/bottom reinforcement requirement — there is no interaction check between a co-existing sagging and hogging effect in the same load case.

Every reinforcement layer within a face (top or bottom) must have the same total number of bars (main + additional) as that face's first layer — the bar-layout geometry engine reshapes a single flat bar list using one bar count for every layer, so a layer with a different bar count will misalign rather than draw correctly.

Limitations

Torsion design is not available for T-beams or L-beams — flanged sections require the component-rectangle method of BS8110-2:1985 cl 2.4.4.2, which is not implemented yet. The design torsion must be 0.

Crack width checks for T-beams and L-beams are calculated conservatively using the rectangular web section only — the tension-zone width (BS8110-2:1985 cl.3.8.2, bt) is always taken as the web width, never the flange. This is exact for the bottom face under sagging, where the tension steel sits in the web; for the top face under hogging (and for axial tension), the true bt is wider (flange width), so using the web width overstates the calculated crack width. For flanged sections the axial interaction limit is also evaluated on the web rectangle (conservative).

Shear vc formula caps fcu at 40 N/mm² regardless of the section's actual concrete strength, per the code's own limit on the 100As/(bvd) enhancement term.

Assumptions

Axial force is treated as a secondary/minor action, not a full column interaction analysis. The design moment is adjusted by a simplified Madj = M ± N×(0.5h−d) term, valid only while N ≤ 0.1×fcu×b×h — beyond that the calculation flags an error and the member should be designed as a column instead.

Compression reinforcement is assumed to yield at the full design stress (0.87fy) — there is no strain-compatibility check. The calculation warns (without correcting the result) when d′/x suggests the compression steel may not have reached yield.

Enhanced shear resistance for loads close to a support (cl.3.4.5.8) is not applied — shear is always checked conservatively at full strength regardless of where the load acts relative to the support.

Deflection's "Continuous" support condition does not distinguish an end span from an interior span — the more conservative interior-span factor is always used (Table 3.9).

Torsion reuses the section's existing shear links and top/bottom flexural bars as the torsion reinforcement (cl.2.4.9) rather than independently designing and detailing separate torsion links and longitudinal bars.

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 b < bf ≤ 5000
hf Beam flange depth 0 < hf < h
bartype Reinforcement type High Yield, Mild Steel
Tsec Section type Rectangular, T-Beam
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
fc Concrete design stress in the rectangular stress block (0.45fcu)
fs Steel design stress (0.87fy)
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
s+ Rectangular stress block depth for positive moment (0.9x)
Fc+ Concrete compression force for positive moment
Fst+ Tension steel force for positive moment
Fsc+ Compression (top) steel force for positive moment
0.9x Depth of rectangular stress block vs flange depth
βf Flanged section moment capacity factor
Mf Flanged section moment capacity limit
As,req,fl Required tension reinforcement (neutral axis below flange)
As,min,fl Minimum tension reinforcement (flange in tension)
As,min,fl,comp Minimum compression reinforcement (flange in compression)
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
s- Rectangular stress block depth for negative moment (0.9x)
Fc- Concrete compression force for negative moment
Fst- Tension steel force for negative moment
Fsc- Compression (bottom) steel force 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
Ast,min Minimum transverse reinforcement in flange (per metre of span)
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

EN1992-1-1

BS8110-1

ACI 318

References

- BS 8110-1 1997

Release Date Version Description
April 2025 1.0.0 Initial release.
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