Deflection Check / Serviceability check in SDC Verifier

For civil engineering and many other industries, it is important to ensure that a structure meets the functional requirements – the Serviceability limit state (SLS). It does not involve collapse or strength of a building but impair it usefulness and stiffness.

What is a deflection check

The deflection of members is one of the checks that should be performed for serviceability limit state design. Deflection is the displacement within a structural member under influence of loads, ignoring the displacements of the rest of the structure.

The deflection limits

The deflection limits for beam members depend in general on the beam member span (member length). Since the requirements for different beam member types are different the responsibility of designer is to choose the appropriate limits.

How to check the member deflection in a FEM model

Performing a deflection check in a general CAE package (like Ansys, Femap, Simcenter3D, etc.) is a simple but time consuming task because:

  • Beam member deflection is not the same as the nodal displacement of the beam member nodes
  • Deflection limit depends on the type of beam member and the beam member span (member length)
  • The deflection needs to be checked for every load scenario

Difference between model displacement and beam member deflection

The first problem is that a finite element analysis does not provide you directly deflection results but only nodal displacements in the global coordinate system, which requires additional post-processing. The influence of the displacement of the support points of the beam member should be removed from the displacement of the nodes of the beam member.

displacement of the nodes of the beam member

What is the allowable beam member deflection

Deflection limits vary between standards and can be even different for different countries what share the same standard like the Eurocode series where each country can further specify limits in national annexes.

In general the deflection limits are based on beam members lengths (span) which results in different allowable deflections in every point or node of the construction. For example the serviceability limits suggested by the UK National Annex for the Eurocode 3 (BS EN 1993-1-1)  for allowable vertical and horizontal deflections are shown below:

Cantilevers Length/180
Beams carrying plaster of brittle finish Span/360
Other beams (except purlins and sheeting rails) Span/200
Purlins and sheeting rails To suit the characteristics of particular cladding

This needs to be transferred to all beam member nodes in the model:

beam model

Load combinations

Because standards prescribe to check large number of load scenarios (or load cases as we call them in SDC Verifier) the deflection check needs to be repeated also for all these load cases.

For simple analysis (e.g. 50 beam members and 20 load scenarios) an engineer should perform 50 x 20 = 1000 calculations.  Consider how much time you need for complex models with more than a hundred load cases and much more beam members.

SDC Verifier solution

How do we deal with the above difficulties in SDC Verifier?

Beam member recognition

With a help of Beam Member Finder tool SDC Verifier automatically recognizes beam member lengths:

Beam Member Finder

Recalculation of nodal calculation to beam member deflection

The deflection of all the nodes of the beam member is calculated automatically. For all individual loads and all load combinations the global deformation of the beam member nodes and the support nodes are transferred into beam member deflection results. The maximum deflection of the nodes of a member is compared by the specific deflection limit. The picture below shows for single load case both the total global displacements (left) and the beam member deflection (right)

displacement and deflection

For beam member 7 the deflection for  load combination one is shown below:

Load group results (envelope results)

To evaluate if the deflections are below the limits, it’s enough to display one table or plot for a group of load scenarios or Load Group in SDC Verifier.

The table below summarizes the results and indicates which load scenario is governing (the source of the absolute maximum deflection)  for each beam member:

Member Length Min Deflection Max Deflection Deflection  / Length Allowable Utilization  Factor Source Load
Member 1 3000 -1.11 1.11 0.000370 0.005 0.07 LC4
Member 2 3000 -1.11 1.11 0.000370 0.005 0.07 LC4
Member 3 3000 -0.55 0.55 0.000182 0.005 0.04 LC4
Member 4 3000 -0.55 0.55 0.000182 0.005 0.04 LC4
Member 5 4000 0.0 0.71 0.000178 0.005 0.04 LC2
Member 6 4000 0.0 0.71 0.000178 0.005 0.04 LC2
Member 7 4000 -4.82 0.0 0.001200 0.005 0.24 LC2
Member 8 4000 -4.82 0.0 0.001200 0.005 0.24 LC2
Submember 9.1 3000 0.0 0.8 0.000266 0.005 0.05 LC4
Submember 9.2 3000 0.0 1.66 0.000554 0.005 0.11 LC4
Submember 10.1 3000 0.0 1.66 0.000554 0.005 0.11 LC4
Submember 10.2 3000 0.0 0.8 0.000266 0.005 0.05 LC4
Submember 11.1 3000 0.0 1.66 0.000554 0.005 0.11 LC4
Submember 11.2 3000 0.0 0.8 0.000266 0.005 0.05 LC4
Submember 12.1 3000 0.0 0.8 0.000266 0.005 0.05 LC4
Submember 12.2 3000 0.0 1.66 0.000554 0.005 0.11 LC4
Member 13 (Y) 5000 0.0 0.0 0.000000 0.005 0.0 LC1
Member 14 (Y) 5000 0.0 0.0 0.000000 0.005 0.0 LC1
Member 15 (Y) 5000 0.0 0.0 0.000000 0.005 0.0 LC1
Member 16 (Y) 5000 0.0 0.0 0.000000 0.005 0.0 LC1

For each load group the extreme deflection results (min/max/absmax) for all load combination of the Load Group can be shown the picture below shows the maximum deflection results for the full model and all load scenarios:

full model and all load scenarios

Conclusion

SDC Verifier contains all the necessary tools to perform the deflection check quickly directly within your favorite FEA program. (Ansys, Femap and Simcenter 3D are currently supported).  The automatic beam member recognition, result transformation and the usage of the envelope results of a load group reduce the calculation and postprocessing time significantly. So if you are looking for a tool to check the results of your model directly within your FEA software, SDC Verifier offers you all the tools to quickly comply with Standards without tedious manual post-processing.