**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.

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.

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 M_{cr} = 3.0 * 47.18 = 141.54 kNm yielding a slenderness of 1.286 (M_{pl,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 I_{z}, I_{w} and I_{t}.

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.

gate## Defining cutouts with Superbeam feature in Consteel

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.

gate## Web openings and their deflection effect on beams

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.

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.