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Composite beam design according to EN 1994 (esacbd.01.01)

esacbd.01.01

SCIA Engineer provides a comprehensive solution for the modelling, analysis and design of composite floors. The software automates the two principal tasks that engineers need to tackle with in order to achieve a safe and executable design:

- the structural analysis of the floor inside a 3D FEM environment: including construction stages, partial composite action between beams and slab, and the particular handling of loads that is typical for this structural system;
- the code-based design of the individual composite beams: checks for ultimate and serviceability limit states including an automatic design and shear connection arrangement.

What is more, the composite entities are integrated in advanced engineering design workflows: by modelling the slabs as well as the beams, it is now easy to represent rigid diaphragm behaviour, to capture nonlinearities. The engineer can employ stability, modal, seismic and second-order analysis with initial imperfections in order to understand the behaviour of the building as a whole.

Therefore, engineers can now use the same platform to create sophisticated models in a 3D CAE analysis environment and to run design checks and code-compliant optimisation on all or selected composite beams in these models.

## Main advantages of this composite floor solution

- A
**multi-model**approach allows for checking the**construction**and the**final**(composite)**stages**at the same time without having to make modifications to the model. - This staged analysis model also includes
**creep**deformation and a**partial shear connection**between the steel beams and concrete slab. As a result, the FEM results represent the real deformation of the floor. - Slabs can be represented by
**rigid**,**semi-rigid**, or**flexible**floor**diaphragms**, depending on their stiffness and on the user needs for a particular task or verification. - The distribution of surface loads based on the
**tributary area**method make the results easier to understand and comparable to hand calculations. This method best represents the actual structural response of this building system. - An automated handling of selfweight (i.e. increased
**weight of fresh concrete**and higher safety factors related to it during execution) and load combinations makes it easy for the user to correctly take construction stages into account during the design. - A comprehensive
**member verification**is performed according to**EN 1994-1-1**or**AISC 360**, including ULS and SLS checks for both the construction and the final stage. **Detailing requirements**ensure that the beams can be built on site and that the design methods remain applicable: the geometry of the steel beam and profile sheeting, the thickness of concrete topping, the position, diameter and spacing of shear connectors, and the reinforcement in the slab are checked.- Both code-based and
**user-defined spacing requirements**for the shear connectors are taken into account. This is important when the contractor sets special requirements for the execution on site. - The final stage ULS bending moment resistance is based on a
**plastic stress distribution**in the composite section, also taking into account**partial shear connection**. - In the case of
**openings in the web**of the steel beam, additional verifications are performed: according to*SCI P355*in the*EuroCode 4*context, and according to*AISC Design Guide #2*in the*AISC 360*context. - The
**automatic design**(AutoDesign) proposes a suitable cross-section, shear stud layout and camber (if needed) to cover all ULS, SLS and additional opening verifications for the construction and final phase, also taking into account detailing conditions. - The various levels of output and visualisation in the 3D scene let the engineer create
**informative**and**scalable reports**of the design. - Rigorous
**floor vibration checks**are available for composite beams designed according to*AISC 360*. - A simplified check of the predicted
**natural frequency**is performed in the case of*EuroCode 4*verifications. Rigorous**footfall**analysis based on SCIA Engineer results is available as an external third-party add-on. **Fire resistance checks**according to EN 1994-1-2 for both the construction and final stage are available in the EuroCode environment.

## Scope and limitations

- The composite beam functionalities described here pertain to the design of
**buildings**. - The steel beams must be
**prismatic**and have a**symmetrical I-section**: any I-profile (e.g., HE, UB, IPE, or sheet-welded) in the case of*EuroCode 4*verifications, or a W-shape in the case of*AISC 360*verifications. - The composite slabs must consist of a profiled steel sheeting and a concrete topping. Solid slabs can be designed using workarounds with some conservative margin, using engineering judgement.
- The connection between the steel beams and concrete slab is realised by headed studs.
- Only a single web opening per beam can be taken into account in the
*AISC 360*checks. - The fire-resistance checks according to EuroCode 4 do not take web openings into account.

## Modelling and analysis in 3D FEM context

The Composite Analysis Model (CAM) in SCIA Engineer analyses the entire structure during the stages of construction, service or maintenance. Stages are fully automated, which means that the user can work as usual and in a linear context: for load combinations, analysis, results, etc. Deformations and load effects obtained from the different stages are superimposed, also taking into account the actual shear connection between beams and slab and the creep in concrete.

There are no limitations on the structural system or on the arrangement of beams: the composite beams may be simply-supported, continuous, or cantilevers, parallel to each other or with arbitrary orientation. The CAM detects which beams are primary and which are secondary based on the steel sheeting orientation. This is taken into account in the checks and *AutoDesign* later on.

The CAM derives the exact orthotropic properties of the corrugated steel sheeting and the concrete topping and uses these in the FEM calculations. The stiffness of the composite beams is augmented based on the degree of shear connection between beams and slab.

The effective width of composite beams is calculated automatically as well. The design codes EN 1994-1-1 and AISC 360-10 stipulate the width of concrete slab that contributes to the strength and stiffness of a composite beam. The following is detected automatically:

- the span length,
- the boundary conditions in this and in neighbouring spans,
- the distance to neighbouring elements in the 3D model (i.e., other beams, walls, openings in the slab),
- the distance to slab edges.

For a more accurate stiffness estimation of e.g., cellular beams and other beams with openings, the CAM also takes into account all openings in the steel beams webs. Web openings modelled on the 1D members are later on considered in the design modules. Cellular beams can also be designed using the *Cellbeam* design tool by the British fabricator *Westok*. A bi-directonal link is available between SCIA Engineer and *Cellbeam* for the export and import of both steel and composite beams.

### Construction stages

Internally, the software manages three FEM submodels with different stiffness of the composite slabs – one for the construction stage and two for the final composite stage: with long-term and short-term stiffness. The stage-based model includes rheological effects (i.e. creep) by distinguishing between long and short-term load cases in the final (service) phase.

The engineer can let the software fully manage load cases or combinations between the different stages, or he/she may manage them manually. In addition, the software automatically takes into account that fresh concrete weighs more during the construction stage due to its higher water content. Fresh concrete is also considered as a variable load with suitable safety factors. This is due to the delivery methods and the fact that liquid concrete can heap in specific areas of the slab and on individual beams.

### Compatibility with design codes

Two mathematical formulations of the composite slab with steel beams are supported. The default one (*"standard composite action"*) allows us to avoid normal forces from the eccentricity between the slab and beams in the FEM model. This idealisation is suitable for the majority of design tasks, and is the only one compatible with the design methods described in AISC 360 and EuroCode 4. In this formulation, bending moments in the beams are increased and match simplified load descending methods usually used in hand calculations.

The second formulation ("advanced composite action") is based on the actual cross-section properties and alignment of the beams. As a result, normal forces are generated in both beam and deck as a result of the eccentric placement of the 1D member. The latter approach is useful for more advanced analysis of the whole composite structure.

### Load: diaphragms and tributary areas

Rigid in-plane diaphragms combined with tributary area distribution for gravity loads offer a good approximation of the actual behaviour of composite floors. These two modelling features let the user obtain clear and verifiable results while reducing computation time.

**Rigid diaphragms** simplify the analysis model based on reasonable assumptions that are verified by decades of engineering experience. Lateral loads are distributed to vertical load-bearing elements based on their stiffness, while gravity loads are distributed to the floor beams based on tributary areas.

Results obtained from such a numerical formulation of the composite slab are directly comparable to hand calculations and parasitic moments in various parts of the structure are avoided. One can even say that the actual structural behaviour is better represented in this way (compared to a pure FE-analysis) due to the geometry and physical properties of composite floors, e.g., the cracking in concrete, the location of the connections between floors beams.

**Flexible diaphragms** are useful for the modelling of steel decking roofs. Such roofs are often found in buildings where the floors are composite, but the pouring of a concrete slab for the roof is, in most cases, not financially justified.

**Semi-rigid diaphragms** are a good solution when the user wants to make use of the tributary area load distribution method for gravity loads, but would like to keep the FEM formulation for lateral loads. This is often needed in the case where openings in the slab compromise the lateral rigidity of the floor in certain parts of it.

### Libraries

The following libraries simplify the definition of a composite floor:

- a steel sheeting library with common decking from European, British and North American manufacturers;
- a shear stud library.

During modelling, the user is prompted to select products from the library or define decking or studs manually. The user can further extend the decking library with own sheets. Filtering based on various criteria (e.g., manufacturer or wildcard) is also available.

## Code-based design

The design of composite beams is performed according to *EN 1994-1-1* and relevant parts of EC2, EC3 and a number of *Steel Construction Institute* (SCI) publications on the topic. The following is included:

- Ultimate and serviceability limit states are checked for both the construction and the final composite stage.
- Primary and secondary beams are recognised and treated differently when, e.g., determining the stud arrangement.
- The concrete slab contribution to the resistance of steel beams in the final stage is taken into account via effective width that varies along the beam length.
- Section classification is based on the actual position of the neutral axis in the composite cross-section.
- Shear studs design is based on ULS considerations and detailing; the user may also input a stud spacing manually, and have it verified. Additional checks on the studs placement are performed when significant point forces are present on the beam.
- Camber can be designed or inputted (as an absolute value or as a value relative to the span length).
- EuroCode national annex parameters are supported.
- The headed stud resistance is modified according to the SCI publication
*“NCCI PN001a-GB: Resistance of headed stud shear connectors in transverse sheeting”*when the UK National annex is selected. This takes into account the geometry and behaviour of more modern steel sheeting and complies to both the EuroCode 4 and the engineering practice in that region. - The user may define multiple openings in the steel beam web; in this case, additional checks are performed according to
*SCI P355 “Design of composite beams with large web openings”*. Circular, rectangular, and elongated openings are supported, reinforced or not. - A more economic design may be achieved by reducing composite action below the limitations of EN 1994-1-1: the user can design studs according to
*SCI 405: Minimum degree of shear connection rules for UK construction to Eurocode 4.* - The check outcome can be plotted on the beams in the 3D scene and listed in
*Table Results*. Error, warning and note indicators and design summaries are plotted directly on the beams in the 3D scene. - The performed verifications are described in three levels of output, thus ensuring scalability of the final report: the user selects the right output based on the particular needs at hand: the
*Brief*output summarises the design in a single table row, the*Standard*output summarises the main milestones of the design, while the*Detailed*output provides a description of the calculation with rendered formulas, intermediate calculation steps, and images in scale.

More on the implemented SCI publications can be read here.

Cellular beams can also be designed using the *Cellbeam* design tool by the British fabricator *Westok*. A bi-directonal link is available between SCIA Engineer and Cellbeam for the export and import of both steel and composite beams.

07/01/2014