Steel Beam Design (Eurocode 3)
Calculate your steel beam its design resistance and deformation with this EN1993 compliant tool. Chose easily the best beam for the job with the optimized selection.
Parameters explained
| Parameter name | Symbol | Unit | Info text |
|---|---|---|---|
| Length | L | mm | The total distance between the two supports of the beam. If the beam is resting on a support area then it is often good practice to add also half the support area its length (e.g. half the thickness of a brick wall). |
| Yield strength | fy | N/mm² | The characteristic yield strength of the structural steel (e.g., 235 MPa for S235). This is the stress limit where the material begins to deform plastically. |
| Lateral end supports | Describes the lateral restraint conditions at the beam's end supports. | ||
| Intermediate lateral restraints | Describes the lateral restraint conditions along the beam's length. For this calculation only restraints applied to the compresive side of the beam do count. The warping length is set equal to the longest unconstrained beam length. | ||
| Load application | Defines if the load is applied on the Top, Center, or Bottom of the beam. Loads on the top flange are destabilizing (lower Mcr), while loads on the bottom are stabilizing. | ||
| Free standing load | A free standing load on top of the beam is a destabilizing load. Practically meaning that if the beam moves sideways then the load can move freely with it. This is only the case if the applied load offers no resistance to lateral movement, for example a free standing brick wall. It is 'No' in case the brick wall rests on a floor, because in this case the floor resists the sideway movement. | ||
| Moment factors | C1, C2 | - | Coefficients depending on the bending moment diagram shape and loading conditions. Used to calculate Mcr. C1 accounts for the moment distribution, C2 accounts for load application height. C1 its default value is 1, which is a safe value and it can be manually increased. C2 its default value is 0.63, which is a safe value only for loads applied to the top. For loads applied to the bottom the conservative value is C2 = 0. |
Eurocode factors
| Parameter name | Symbol | Unit | Info text |
|---|---|---|---|
| Consequence class | CC | - | Defines the reliability level based on the consequences of failure. CC1 = Low, CC2 = Medium (Residential/Office), CC3 = High. Higher classes require higher safety factors. |
| Permanent load factor | γG | - | Partial safety factor applied to permanent loads in the Ultimate Limit State (ULS). |
| Variable load factor | γQ | - | Partial safety factor applied to variable loads (live load, snow, wind) in the Ultimate Limit State (ULS). |
| Combination factor (ULS) | Ψ0 | - | Additional factor for combinding variable actions. Used in ULS when multiple variable loads act together (e.g., wind + snow). The leading load uses 1.0, accompanying loads are reduced by Ψ0. |
| Frequent factor (SLS) | Ψ1 | - | Additional factor for combining variable actions. Used in Serviceability Limit State (frequent combination) to check reversible limits (e.g., comfort, cracking). |
| Quasi-permanent factor (SLS) | Ψ2 | - | Additional factor for combining variable actions. Used for long-term effects (creep/deflection). |
| Deflection limit (Characteristic) | wmax,char | 1/L | Allowable deflection under the characteristic load combination (unfactored). Controls irreversible deformation. |
| Deflection limit (Frequent) | wmax,freq | 1/L | Allowable deflection under the frequent load combination. Often used for comfort criteria or reversible limits. |
| Deflection limit (Quasi-permanent) | wmax,qper | 1/L | Allowable deflection under long-term loading (creep). Critical for timber or long-term appearance. |
| Cross-section class | Classification of the cross-section (Class 1, 2, 3, or 4). | ||
| Material factor | γM0 | - | Partial safety factor for resistance of cross-sections to yielding. Standard value is 1.00. |
| Material factor | γM1 | - | Partial factor for stability. Standard value is 1.00. |
| Material factor | γM2 | - | Partial safety factor for resistance of cross-sections in tension to fracture. Standard value is 1.25. |
| Shear area factor | η | - | Factor defined in EN 1993-1-5. Usually 1.0, but may be 1.2 for steel grades up to S460 to account for strain hardening during shear buckling. Standard value is 1.0 |
| Shear strength factor | ηV | - | Factor influencing the plastic shear resistance. Typically 0.5 unless a National Annex specifies otherwise. |
Results explained
| Parameter name | Symbol | Unit | Info text |
|---|---|---|---|
| Max design shear | Vz,Ed | kN | The maximum vertical shear force acting on the beam under the factored Ultimate Limit State (ULS) loads. |
| Max design moment | My,Ed | kNm | The maximum bending moment acting about the strong axis (y-y) under the factored Ultimate Limit State (ULS) loads. |
| Shear resistance | Vz,Rd | kN | The design shear capacity of the cross-section. If Vz,Ed > 50% of Vz,Rd, the moment resistance needs to be reduced. |
| Moment resistance | Mc,Rd | kNm | The design bending resistance of the cross-section. Depends on the section class (Plastic for Class 1/2, Elastic for Class 3). |
| Buckling resistance | Mb,Rd | kNm | The design resistance against Lateral Torsional Buckling (LTB). This is usually lower than Mc,Rd due to the beam's tendency to twist sideways. |
| Moment-shear interaction | Eurocode 3 check required when high shear forces are present. If shear force exceeds 50% of capacity, the yield strength is reduced for the bending check. | ||
| Max w (char) | wchar | mm | Deflection under the characteristic load combination. |
| Allowable w (char) | wlim,char | mm | The deflection limit set for the Characteristic combination. |
| Max w (freq) | wfreq | mm | Deflection under the frequent load combination. |
| Allowable w (freq) | wlim,freq | mm | The deflection limit set for the frequent combination. |
| Max w (qper) | wqper | mm | Deflection under the quasi-permanent load combination |
| Allowable w (qper) | wlim,qper | mm | The deflection limit set for the quasi-permanent combination. |
| Unity check | UC | - | The utilization ratio (demand / capacity). A value ≤ 1.00 indicates a PASS. A value > 1.00 indicates a FAIL. |