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With Superbeam feature, modelling of stiffeners is easy and effective. Multiple options and various shapes are available. Analysis is possible with beam and shell elements either.

Introduction

Are you wondering how a web opening would influence the lateral-torsional buckling resistance of your beam? Check it precisely with a Consteel Superbeam based analysis

It is often required to let services pass through the web of beams. In such cases the common solution is to provide the required number of opening in the webplate. Such an opening can have a circular or rectangular shape, depending on the amount, size and shape of pipes or ventilation or cable trays.

Beams must be designed to have the required against lateral-torsional buckling. The design procedure defined in Eurocode 3 is based on the evaluation of the critical bending moment value which provides the slenderness value, needed to calculate the reduction factor used for the design verification.

There is no analytical formula provided in the code for beams with web openings. Would the neglection of such cutouts cause a miscalculated and unsafe estimation of the critical moment value?

The following demonstration will be made with a 6 meters long simple supported floor beam with a welded section.

6 meters long simple supported floor beam with a welded section

Exposed to a linear load of 10 kN/m, the critical bending moment value of the solid web beam can be obtained by performing a Linear Buckling Analysis (LBA) with Consteel.

(LBA) with Consteel
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The obtained critical multiplier for the first buckling mode is 3.00 which means that the actually applied load intensity can be multiplied by 3.00 to reach the critical load level. The corresponding critical moment will have the value of Mcr = 3.0 * 47.18 = 141.54 kNm yielding a slenderness of 1.286 (Mpl,Rd = 234.20 kNm) and a lateral-torsional buckling resistance of 0.394 * 234.20 = 92.27 kNm. With this value the actual utilization ratio is at 51%.

How would this value change if a rectangular opening needs to be cut into the web of this beam?

Analytical formula for critical bending moment

By looking to the analytical formula (ENV 1993-1-1 F.4) to calculate the critical moment of double symmetric sections loaded at eccentric load application point it becomes obvious that the section properties having effect on the moment value are Iz, Iw and It.

ENV 1993-1-1 F.4 analytical formula

An opening in the web has no effect on the first two values and has very little effect on the last one. As it has been already shown in previous article, the presence of such an opening can have effect on the vertical deflection, but as long as the lateral stiffness of a beam is much lower than it’s strong axis stiffness, the vertical deflections can be neglected when the lateral-torsional buckling resistance is calculated. The usual linear buckling analysis (LBA) performed also by Consteel neglects the pre-buckling deformations.

Therefore one can expect that in general web openings can be disregarded when the critical moment value is calculated.

Analysis with Consteel Superbeam

Beam finite elements cannot natively consider the presence of web openings. In order to obtain the precise analysis result, it is possible to use shell finite elements. The new Superbeam functionality comes as a solution in such cases. Instead of using beam finite elements, let’s use shell elements!

Opening can be positioned easily along the web, either as an individual opening or as a group of openings placed equidistantly. The opening can be rectangular, circular or even hexagonal. Circular openings can be completed with an additional circular ring stiffener.

The rectangular opening for this example can be easily defined with this tool. As there is no need to provide any additional opening on the remaining part of the beam, only the first part which includes the opening will be modelled with shell elements and the rest can still be modelled with beam finite elements. Using this technique, the total degrees of freedom of the model can be kept as low as possible. When using Superbeam, the designer has the choice whether to use beam or shell finite elements, as appropriate.

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As the result of the new analysis using Consteel Superbeam with a mixed model from shell and beam elements, the obtained value of the first critical multiplier is 2.99 which is virtually identical to the value obtained with the beam with solid web.

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This confirms the feeling that in general such a web opening may not significantly impact the lateral-torsional buckling resistance of a simple supported beam.

But this can change when for example the same beam would have fixed end conditions. In this case the region with the opening is close to the position of change of sign of bending moment, plus the weakened bottom T shape is subject to elevated compression combined with an unstiffened edge of the opening which may result in a distortion of the cross-section which causes a stiffness reduction and therefore lower critical load level.

Solid web – beam finite element, αcr=17.27
Web with opening – Superbeam, αcr=16.11
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In cases where such section distortion happens, another violation of the basic assumptions of Bernoulli-Navier Hypothesis used also by the 7DOF beam finite element happens.

In order to get the most precise analysis results, the use of shell elements is recommended at locations where the assumptions of a beam finite element are significantly violated. Consteel Superbeam provides to the designer a very efficient tool to analyse such critical parts locally with shell elements and continue to use the well established 7DOF beam elements elsewhere. This provides an optimum compromise between analysis result precision and size of finite elements model and solution time.

Defining cutouts is a useful additional function within the Superbeam feature. They are easy to modify, various shapes and multi-placing option are available. Watch our feature preview for more details.

Superbeam is a new function introduced with Consteel 15. It is developed for dual handling of members. Superbeam makes it possible to examine structural parts with the accuracy of shell elements but with the ease of using a beam element concerning definition, modification and model handling. We prepared a video to show how to convert a 7DOF beam into shell elements and how easy it is to work with it.

It is often required to let services pass through the web of beams. In such cases, the common solution is to provide the required number of openings in the web plate. Such an opening can have a circular or rectangular shape, depending on the amount, size and shape of pipes or ventilation or cable trays. 

If the structural engineer has the freedom to position these openings along the beam, where to place them? What would be its effect on the deflection of the beam? 

The effect of such openings on the deflection is more important when the length of the opening along the beam is increased. As circular openings are made with equal length and depth, they are usually less critical than rectangular openings. 

The following demonstration will be made with a 6 meters long simple supported floor beam with a welded section.

Exposed to a linear load of 10 kN/m, the deflection at mid-span of the solid web beam is 4.6 mm.

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Let’s assume that a 250 mm deep rectangular opening with a length of 400 mm needs to be provided on the web, at a distance of 300 mm from the left support.

Traditional analysis with beam finite elements

Consteel 7DOF beam finite elements are very powerful, but cannot consider natively such opening. The usual approach is to build a Vierendeel-type of model, by using additional beam elements with a T shape section „above” and „below” the opening. These additional beam elements are defined eccentrically to the reference line of the solid-web beam.

Eccentricities can be easily defined in Consteel using both smart and traditional link elements.

The deflection with this refined model will be equal to 4.8 mm.

Download model file

Analysis with Consteel Superbeam

In order to find a more precise analysis result, it is possible to use shell finite elements. The new Superbeam functionality comes as a solution in such cases. Instead of using beam finite elements, let’s use shell elements!

Opening can be positioned easily along the web, either as an individual opening or as a group of openings placed equidistantly. The opening can be rectangular, circular or even hexagonal. Circular openings can be completed with an additional circular ring stiffener.

The rectangular opening for this example can be easily defined with this tool. As there is no need to provide any additional opening on the remaining part of the beam, only the first part which includes the opening will be modelled with shell elements and the rest can still be modelled with beam finite elements. Using this technique, the total degrees of freedom of the model can be kept as low as possible. When using Superbeam, the designer has the choice of whether to use beam or shell finite elements, as appropriate.

As the result of the new analysis using Consteel Superbeam with a mixed model from shell and beam elements, the precise deflection of 5.2 mm can be obtained.

Download model file

This deflection is higher than the value obtained with the solution using the Vierendeel-type of structure using beam finite elements.

In order to get the most precise analysis results, the use of shell elements is recommended at locations where the assumptions of a beam finite element are significantly violated. Consteel Superbeam provides to the designer a very efficient tool to analyse such critical parts locally with shell elements and continue to use the well established 7DOF beam elements elsewhere. This provides an optimum compromise between analysis result precision and size of finite elements model and solution time.

A model with floor beams to learn more about the smart link feautre
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A model with floor beams to learn more about the smart link feautre
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The smart link is a different version of the already existing link element, that was introduced into Consteel with version 14. In case of the smart link, we developed a different definition method for easier application. The smart link is also capable of updating its geometry based on changes made to other elements that it connects. This way it provides a more versatile modelling tool.

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Geometry definition

Geometry in Pangolin can be described by lines or circular arcs and polygons made up of the former two. The relevant components are the simplest ones, acting as converters from the native Grasshopper geometry types, with the possibility of specifying a Consteel Layer.

Section definition

The geometry definition of the sections is more refined since Consteel uses detailed section models composed of solid representation for analysis and thin-walled representation for standard design checks. There are two options to create sections in Pangolin: use a predefined section from the section bank or create custom sections by predefined parametric macros.

Predefined sections from section bank

7000+ different profiles can be defined from the section bank (hot-rolled, cold-fromedetc.). This workflow contains two steps: 1. Getting the section preview from the bank. 2. Getting the actual section from the preview. (The reason for this is the performance, as in Pangolin sections are real objects, loading all the 7000+ sections from our bank would take minutes even on a powerful pc.) The section bank component provides various filtering options, to help select the section. After the desired section preview is selected, you can create a real section from it along with a material, and check the cross-section surface in Rhino.

Custom sections based on predefined macros

This workflow consists of placing a section macro component, selecting a base macro, and defining the macro parameters.

One of the most important unique features of Consteel is its advanced analysis and design calculations for members with cold-formed sections having various stiffeners. Correspondingly Pangolin makes it possible to create custom cold-formed sections, with custom stiffeners parametrically:

As you can see, the components help in building complex sections with available default values providing a wide range of parameters to be customized.

Structural member definition

Defining beams is as easy as pulling the reference edges and the beam section into the Beam component:

In the example above we also defined a haunch on the beam ends, another unique feature of Consteel, which will be taken accurately into account during analysis and design. 

To make modelling easier, Pangolin also provides several useful implicit data conversions, like in the picture above: at the start, we have the IPE 300 beams, and just connecting them into a Grasshopper Plane parameter, the beams get converted to their local coordinate systems. This plane can be directly connected with the Z purlins section direction parameter to correctly lay them upon the main beams.

Structural details

Let us stop at the purlins for a moment! Pangolin also provides a detailed linking of structural objects through Consteel’s link elements which can be rather important in order to consider accurately the lateral restraint effect on the beam provided by the purlins.

The definition of link elements includes setting the interface position, the direction, and the stiffness attributes of the connection. Defining supports for the model is also helped by automatic conversions, where you can directly ask a beam’s endpoint, and place the support there, instead of manipulating with indexes through a complex definition.

Pangolin also provides the possibility to define edge and plate supports.

Load definition

Pangolin’s load definition includes load cases, grouped into load groups with specific types like permanent, variable, snow, etc… and custom load combinations. Once the model is sent to Consteel, you can also use its automatic standard-based load combination generator with the groups and cases defined in Grasshopper.

As for the loads themselves, currently, you can define nodal loads, uniform and variable line loads, and uniform and variable plate loads. Additionally, to help place loads on bar members, Pangolin provides a load transfer surface component, which distributes the surface load on (optionally filtered) beams overlapping it.

Variable surface load definition with two points:

Using the model for calculations

The model can be calculated by Consteel or Steelspace. Communicating the model with either is done through Pangolin’s Connection component.

This component can accept all Consteel objects and will save a .smadsteel file, and/or send them to Consteel running in the meantime. You can automate either one by defining true for the corresponding parameters. Additionally, the component will make sure to send everything needed to make the objects valid. Meaning you only have to pull in the beam objects, loads, and supports. The underlying lines, sections, materials, haunches, load cases, support models, and others will be automatically collected by Pangolin for you.

Consteel 14 is a powerful analysis and design software for structural engineers. Watch our video how to get started with Consteel.

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