Did you know you can use Consteel to run second-order and buckling analyses on specific parts or elements of your model by defining a Custom Portion for the portion of interest?
The workflow starts in the Portions Manager, where you can manually group structural members, frames, columns, beams, bracings into Custom Portions. These are fully user-defined and, importantly, only these custom portions can be directly used for analysis. This allows you to isolate exactly the structural subsystem you want to investigate, without being constrained by the full model.
Once a portion is defined, it can be selected in the Analysis Settings, where you can choose whether second-order and buckling analyses should be performed on the entire model or only on the selected portion. The solver will then consider only that subset of elements when assembling the stiffness matrix and evaluating stability behavior.
Running these analyses on specific portions has clear engineering advantages. Second-order effects and buckling phenomena are often governed by local structural behavior, such as a critical frame, a bracing system, or a column group, rather than the entire structure. By isolating these regions, you can:
- reduce computational effort and analysis time, especially for large models
- focus on the most critical load paths and instability mechanisms
- perform faster iterations during design refinement
- avoid unnecessary influence from non-relevant parts of the structure
This targeted approach leads to more efficient and controlled stability analysis, particularly when investigating sensitive or highly utilized structural components.
Download the example model and try it!
Download modelIf you haven’t tried Consteel yet, request a trial for free!
Try Consteel for freeIntroduction
This article presents the calculation method for determining the buckling resistance of a pinned column with intermediate restraints in accordance with Eurocode standards. The procedure is based on an example from the Access Steel design examples collection and is compared with the calculation process implemented in Consteel’s steel member design functions, specifically within the Member Checks module.
In the following sections, a step-by-step guide is provided to demonstrate how the member check functionality can be applied to simple cases, highlighting both methodology and practical usage.
Input Data for the Example
The example considers a pinned column in a multi-storey building, subjected to a design axial force of $N_{Ed}$ = 1000 kN. The column has a total length of 10.50 m and is laterally restrained about the y–y axis at intervals of 3.50 m.
The member is a rolled HEA 260 section made of S235 steel. The cross-section is classified as Class 1. The geometric properties of the section are: height h = 250 mm, width b = 260 mm, web thickness $t_w$ = 7.5 mm, flange thickness $t_f$ = 12.5 mm, and fillet radius r = 24 mm. The cross-sectional area is A = 86.8 cm², with moments of inertia $I_y$ = 10450 cm⁴ and $I_z$ = 3668 cm⁴.
The material properties are defined according to EN 1993-1-1. Since the maximum thickness is less than 40 mm, the yield strength is taken as $I_y$ = 235 N/mm². The partial safety factors are γM0 = 1.0 and γM1 = 1.0.
Determining Design Buckling Resistance of a Compression Member
The design buckling resistance of the column $N_{b,Rd}$ is evaluated by determining the reduction factor χ for both principal buckling directions. This requires the calculation of the elastic critical forces $N_{cr}$, which form the basis for identifying the governing buckling mode.
Elastic critical force for the relevant buckling mode $N_{cr}$
The Young’s modulus is taken as $E=210000 \frac{N}{mm^2}$. The buckling lengths in the respective planes are $L_{cr,y} = 10.50m$ for buckling about the y–y axis and $L_{cr,z} = 3.50m$ for buckling about the z–z axis. Observe that the buckling lengths for the strong and weak axes differ according to the support conditions, which must be determined by the engineer in manual calculations.
$$N_{cr,y}=\frac{π^2*E*I_{y}}{L_{cr,y^2}}=1964.5 kN$$
$$N_{cr,z}=\frac{π^2*E*I_{z}}{L_{cr,z^2}}=6206.0 kN$$
In Consteel, the elastic critical force for the relevant buckling mode can be determined using the Individual Member Design approach. This is accessible in the Member Checks tab under the Steel module, where selected members can be added and evaluated.
Once a member is selected, the analysis results are automatically loaded, provided that first- or second-order analysis results are available. Ensure that the analysis has been run in the Analysis tab and the cross section check on the Global ckecks tab before proceeding to the Member Checks section.
For the pinned column with intermediate restraints, the relevant buckling cases, strong and weak axis, are selected, and the dominant load combination is automatically indicated with a *. Consteel identifies the intermediate restraints separately for each direction and divides the member into segments accordingly to help determine the correct buckling lengths.
Design parameters for each segment are set with the three-dot icon:
At this step, users must verify the assigned values. By default, the first value is applied, and the correct buckling shape or effective length factor should be confirmed based on engineering judgment.
In order to use the critical load multiplier selection option, make sure to perform the calculation first:
In order to check whether the correct critical load multiplier was selected, you can examine the effective length factor, which is calculated based on it (in this case, it is 1 for both directions). In our example, the relevant buckling shapes for the y–y and z–z directions are as follows:
The elastic critical force $N_{cr}$ is calculated automatically, regardless of whether the effective length factor was entered manually or the critical load multiplier was selected.
| Access Steel – manual calculation | Consteel using the effective length factor | Consteel using the critical load multiplier | |
| $N_{cr,y}$ | 1964.5 kN | 1962.53 kN | 1973.76 kN |
| $N_{cr,z}$ | 6206.0 kN | 6189.01 kN | 6218.96 kN |
Once all parameters are defined, the design check is executed by clicking the Check button, and the results are displayed.
Results can be reviewed and filtered by member, load combination, and buckling case. Lateral-torsional buckling checks follow a similar procedure, with segment boundaries adjustable and critical moments calculated either analytically or using the critical load multiplier.
Non-dimensional slenderness
In order to determine the reduction factor, the non-dimensional slenderness λ must be calculated based on the elastic critical force corresponding to the relevant buckling mode.
$$\overline{\lambda_y} = \sqrt{\frac{A*f_y}{N_{cr,y}}}=\sqrt{\frac{86.8*23.5}{1965}}=1.016$$
$$\overline{\lambda_z} = \sqrt{\frac{A*f_z}{N_{cr,z}}}=\sqrt{\frac{86.8*23.5}{6206}}=0.573$$
In Consteel, the detailed calculations for strong and weak axis buckling can be reviewed separately on the Results tab:
Reduction factor
For axial compression, the value of χ corresponding to the relevant non-dimensional slenderness $\overline{\lambda}$ should be determined from the appropriate buckling curve in accordance with EN 1993-1-1 §6.3.1.2.
For $\frac{h}{b}= \frac{250mm}{260mm} = 0.96 < 1.2$ and $t_f = 12.5 mm< 100 mm$
- buckling about axis y-y, buckling curve b, imperfection factor $\alpha=0.34$
$$\varphi_y=0.5*[1+0.34(1.019-0.2)+1.019^2]=1.158$$
$$\chi_y=\frac{1}{1.158+\sqrt{1.158^2-1.019^2}}=0.585$$
- buckling about axis z-z, buckling curve c, imperfection factor $\alpha=0.49$
$$\varphi_y=0.5*[1+0.49(0.573-0.2)+0.573^2]=0.756$$
$$\chi_y=\frac{1}{0.756+\sqrt{0.756^2-0.573^2}}=0.801$$
$$\chi=min(\chi_y;\chi_z)$$
$$\chi=0.585<1.00$$
Design buckling resistance of a compression member
$$N_{b,Rd}=\chi*\frac{A*f_y}{\gamma_{M1}}=0.585*\frac{86.8*23.5}{1.0}=1193 kN$$
$$\frac{N_Ed}{N_{b,Rd}}=\frac{1000}{1193}=0.84<1.00$$
Conclusion
This example demonstrates the application of the isolated member approach for a simple compression member. For more complex cases or alternative stability verification methods, such as the imperfection approach or the general method, refer to the dedicated article on stability design methods, where their principles and applications are discussed in detail.
Download modelBevezetés
Amennyiben a síkban hajlított gerenda szabadon elmozdulhat és elcsavarodhat a két támaszpontja között, akkor a lehajlás mellett hirtelen merőleges elmozdulás és elcsavarodás jöhet létre: a gerenda kifordul a síkjából. Ezt a jelenséget szemlélteti az 1. ábra, amely egy kéttámaszú, az erős tengely körül hajlított I keresztmetszetű gerendát mutat: a függőleges síkban történő hajlítás során, amikor a nyomaték elér egy kritikus értéket, a gerenda hirtelen oldalirányban elmozdul és elfordul a két támasz között. Ez a jelenség a kifordulás, amely stabilitásvesztési mód a tökéletes gerendára és a valódi gerendára egyaránt vonatkozhat.
A gerenda kifordulással szembeni méretezése teljes mértékben analóg a nyomott oszlop kihajlási elleni méretezésével. Az analógiát az 1. táblázat szemlélteti, ahol feltüntettük a kihajlási és a kifordulási ellenállást befolyásoló, egymásnak megfelelő paramétereket.
| Kihajlás | Kifordulás |
|---|---|
| tervezési nyomóerő ($N_{Ed}$) | tervezési nyomaték ($M_{Ed}$) |
| kritikus erő ($N_{cr}$) | kritikus nyomaték ($M_{cr}$) |
| kihajlási karcsúság ($\frac{}{\lambda}$) | kifordulási karcsúság ($\frac{}{\lambda}_{LT}$) |
| kihajlási csökkentő tényező ($\chi$) | kifordulási csökkentő tényező ($\chi_{LT}$) |
| kihajlási ellenállás ($N_{b,Rd}$) | kifordulási ellenállás ($M_{b,Rd}$) |
A tökéletes gerenda kritikus nyomatékát a My,Edtervezési hajlítónyomaték-diagram maximális értékének helyén kell meghatározni. Kétszeresen szimmetrikus I keresztmetszet esetén:
$$M_{cr}=C_1\frac{\pi^2EI_z}{(k_z⋅L)^2}\left[\frac{I_\omega }{I_z}+ \frac{(k_zL)^2GI_t}{\pi^2EI_z}\right] ^{0.5} $$
ahol kz a keresztmetszet gyenge tengelye körüli befogási tényező, G a nyírási modulus, It és Iω pedig a keresztmetszet tiszta (St. Venant) és gátolt csavarási tehetetlenségi nyomatéka. A C1 tényező értéke a hajlító nyomatéki diagram alakjától függ, az értéke megfelelő táblázatokban és kézikönyvekben megtalálható. Konstans nyomatéki ábra esetén C1=1.0. A többi tervezési paraméter, különösen a $\chi_{LT}$ kifordulási csökkentő tényező képlete a figyelembe vett tervezési szabványtól függ.
Kifordulási ellenállás az EN1993-1-1 szerint
A hajlított gerenda kifordulás elleni méretezését (teherbírás-ellenőrzést) az EC3-1-1 szerint a következő lépésekben kell elvégezni:
gateA nyomott rúd méretezésének fejlődése
A rudakból épített acélszerkezetek (pl. rácsos tartók) egyik jellegzetes alkotó eleme a nyomott rúd. Nyomott rúdról akkor beszélünk, ha a rendszerint egyenes tengelyű szerkezeti elem központos P nyomóerővel terhelt (1. ábra).
A 2. ábra a nyomott rúd méretezésének fejlődését illusztrálja. Kezdetben (a régi időkben) az építőmesterek az évszázadok során felhalmozódott tapasztalati ismeretek alapján, amelyek mesterről tanítványra szálltak, állapították meg a különböző anyagú és méretű nyomott oszlopok teherbírását. Jelentős változást a klasszikus matematikai differenciálanalízis mérnöki alkalmazása hozott. Euler (1707-1783) svájci matematikus és fizikus megoldotta a nyomott rugalmas vonal kihajlásának problémáját, amely megoldás alkalmazható volt a rugalmas nyomott rúd megoldására (Euler erő). A mérnökök a következő évszázadokban felismerték, hogy az Euler erő csak bizonyos esetekben (elsősorban nagy karcsúságoknál) ad elfogadható közelítést a nyomott rúd valós teherbírására. Számos, az Euler képletnél fejlettebb megoldás született a nyomott rúd teherbírására, de jelentős változást csak a II. világháborút követő hatalmas szerkezetépítési konjunktúra hozott. A világ minden számottevő szerkezeti laboratóriumában sorra végezték a nyomott rúd kísérleteket, majd az eredményekből összeállítottak egy több mint kétezer kísérletből álló adatbázist. A nyomott rúd teherbírását az adatbázis alapján, a matematikai statisztika módszerével meghatározott képlettel adták meg.
Ez a módszertan a mai napig meghatározó: „a nyomott rúd méretezése az acélszerkezeti szakma politikai kérdése lett…”. Ezért a nyomott rúd méretezési elvének megértése a szerkezet-építőmérnök számára alapvető fontosságú.
Az ábra jobb oldala a jövőre is tartalmaz utalást. A tudományos kutatás szintjén már jelen, hogy a valós nyomott rúd teherbírását matematikai-mechanikai szimulációval is meg lehet határozni. Sőt, a közeljövőben minden eddigi ismeretet meghaladó adatbázisok hozhatók létre a szuperszámítógépek bevetésével. Egy ilyen gigantikus adatbázis alapján a mesterséges intelligencia felülírhatja az eddigi mérnöki tudást és módszertant, legalábbis elvben. A valóság viszont az, hogy a szerkezet-éptőmérnökség nem tartozik a húzóágazatok közé (mint például a hadipar vagy az autóipar), ezért ez az új méretezéselméleti váltás még egy jó ideig bizonyosan várat magára.
A továbbiakban a ma acélszerkezeti mérnöksége számra kiemelten fontos Euler erőt és a kísérleti alapú szabványos méretezési formulát tárgyaljuk részletesen.
Az ideális nyomott rúd teherbírása: az Euler erő
Tételezzük fel, hogy az alábbi ábrán látható csuklósan megtámasztott nyomott rúd rendelkezik az alábbi tulajdonságokkal:
- tökéletesen egyenes,
- az anyaga tökéletesen lineárisan rugalmas,
- központosan nyomott.
A fenti feltételekkel végezzük el a nyomott rúd kísérletet a Consteel szoftver segítségével: futtassuk a lineáris kihajlási analízis (Linear Buckling Analysis, LBA) számítást. Az eredményt a 3. ábra szemlélteti.
gateDid you know that you could use Consteel to Consider the shear stiffness of a steel deck as stabilization for steel members?
In many practical steel structures, trapezoidal decking is treated only as a load-bearing surface. In reality, when properly connected to the supporting members, it behaves as a shear diaphragm and contributes to the overall stability of the structure. This effect can be directly taken into account in Consteel by applying shear field stiffness to beam elements.
The stabilizing effect comes from the in-plane shear stiffness of the deck. Under horizontal loading, the sheeting deforms and transfers forces between structural members. This behavior can be described by a single parameter, the shear stiffness (S), which represents the resistance of the diaphragm against deformation.
The overall stiffness is influenced by several components, including the shear deformation of the sheet, profile geometry, fastener slip, and connection flexibility. These contributions together define how effectively the deck can restrain phenomena such as lateral-torsional buckling.
A key requirement for this behavior is proper fastening. Typically, the sheeting must be connected along its edges and fixed to supporting members at each rib to ensure reliable diaphragm action.
In engineering practice, shear stiffness is determined using standardized or manufacturer-based methods rather than detailed analytical models. Consteel supports several established approaches:
- Schardt/Strehl method (DIN 18807), based on parameters describing shear and warping deformation
- Improved Schardt/Strehl method, including the effect of fastener spacing
- Bryan/Davies method, considering additional structural parameters
- Eurocode-based method, using general geometric properties of the sheeting
These methods differ in complexity and required input data, but all aim to provide a realistic stiffness value for use in global analysis. If the sheeting is not fixed at every rib, the calculated stiffness must be reduced accordingly.
The shear field object in Consteel allows engineers to include the diaphragm effect without detailed shell modeling. The calculated shear stiffness can be assigned directly to beam elements, providing additional lateral restraint.
The process involves selecting a trapezoidal sheet profile, choosing the appropriate calculation method, and defining the relevant geometric and connection parameters. The software then determines the stiffness and incorporates it into the structural model.
Including shear stiffness in the analysis can lead to higher critical load factors and reduced displacements, resulting in more efficient structural designs. However, it also means that the decking becomes part of the stabilizing system.
Any later modifications to the sheeting, such as openings or changes in fastening, may reduce this effect and should therefore be carefully assessed.
The shear stiffness of trapezoidal steel decking provides a measurable and often significant contribution to structural stability. By incorporating this effect in Consteel, engineers can achieve more realistic analysis results and optimize their designs while maintaining structural safety.
Download the example model and try it!
Download modelIf you haven’t tried Consteel yet, request a trial for free!
Try Consteel for freeIntroduction
This verification example studies a simple fork supported beam member with welded section (flanges: 200-12 and 100-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment distribution from concentrated transverse force is examined for both orientations of the I-section. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.
Geometry
Normal orientation – wide flange in compression
Constant bending moment distribution
Triangular bending moment distribution – load on upper flange
Triangular bending moment distribution – load on bottom flange
Reverse orientation – narrow flange in compression
Constant bending moment distribution
Triangular bending moment distribution – load on upper flange
Triangular bending moment distribution – load on bottom flange
Calculation by hand
Factors to be used for analitical approximation formulae of elastic critical moment are taken from G. Sedlacek, J. Naumes: Excerpt from the Background Document to EN 1993-1-1 Flexural buckling and lateral buckling on a common basis: Stability assessments according to Eurocode 3 CEN / TC250 / SC3 / N1639E – rev2
Normal orientation – wide flange in compression
Constant bending moment distribution
Reverse orientation – narrow flange in compression
Computation by Consteel
Version nr: Consteel 15 build 1722
Normal orientation – wide flange in compression
Constant bending moment distribution
- 7 DOF beam element
First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=25). The eigenshape shows lateral torsional buckling.
Superbeam
First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).
Introduction
This verification example studies a simple fork supported beam member with welded section (flanges: 200-12; web: 400-8) subjected to bending about major axis. Constant bending moment due to concentrated end moments and triangular moment dsitribution from concentrated transverse force is examined. Critical moment and force of the member is calculated by hand and by the Consteel software using both 7 DOF beam finite element model and Superbeam function.
Geometry
Constant bending moment distribution
Triangular bending moment distribution – load on upper flange
Triangular bending moment distribution – load on bottom flange
Calculation by hand
Constant bending moment distribution
Triangular bending moment distribution
Computation by Consteel
Version nr: Consteel 15 build 1722
Constant bending moment distribution
7 DOF beam element
First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16). The eigenshape shows lateral torsional buckling.
Superbeam
First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).
Triangular bending moment distribution – load on upper flange
7 DOF beam element
First buckling eigenvalue of the member which was computed by the Consteel software using the 7 DOF beam finite element model (n=16).
Superbeam
First buckling eigenvalue of the member which was computed by the Consteel software using the Superbeam function (δ=25).
Triangular bending moment distribution – load on bottom flange
(tovább…)Perfect the understanding of your structure with advanced buckling sensitivity results illustrated on proper mode shape and colored internal force diagrams.
gateConsteel 14 is a powerful analysis and design software for structural engineers. Watch our video how to get started with Consteel.
Contents
- Set analysis parameters
- Perform first and second order analysis
- Perform buckling analysis
- Analysis results in graphics and in tables
- Results: deformation, internal forces, reactions
Part 2 – Imperfection factors
The Eurocode EN 1993-1-1 offers basically two methods for the buckling verification of members:
(1) based on buckling reduction factors (buckling curves) and
(2) based on equivalent geometrical imperfections.
In the first part of this article, we reviewed the utilization difference and showed the relationship between the two methods. It was concluded that the method of chapters 6.3.1 (reduction factor) and 5.3.2 (11) (buckling mode based equivalent imperfection) are consistent at the load level equal to the buckling resistance of the member, so when the member utilization is 100%. The basic result of the procedure in 5.3.2 (11) is the amplitude (largest deflection value) of the equivalent geometrical imperfection. However, the Eurocode gives another simpler alternative for the calculation of this amplitude for compressed members in section 5.3.2(3) b) in Table 5.1, where the amplitude of an initial bow is defined as a portion of the member length for each buckling curves (Fig. 1.). We use the first column (“elastic analysis”) including smaller amplitude values.
It is an obvious expectation that these two standard procedures should yield at least similar results for the same problem. However, this is by far not the case in general.
In order to show the significance of the imperfection amplitudes this part is dealing with these two calculation methods, the variation of their values and the effect on the buckling utilization.
Let’s see again the simple example of Part 1: a simply supported, compressed column with a Class 2 cross-section (plastic resistance calculation allowed). The column is 6 meters high and has an IPE300 cross-section made of S235 steel. The two methods are implemented into Consteel and on Figure 2. it can be seen, that the two values for the amplitude of the geometrical imperfection is very different – e0 = 24 mm by the 5.3.2(3) b) Table 5.1 (L/250) and e0 = 13,4 mm by the 5.3.2 (11) (same as in Part 1).
