How to assess if the baseplate can be considered ''Close to Rigid'' by engineering Judgement
This article explains how engineers can determine whether a baseplate can be considered“close to rigid” instead of perfectly rigid, which is a theoretical assumption used in anchor design. In reality, all baseplates deform under load, but if their behaviour closely matches that of a rigid plate, simplified design approaches can still be applied using engineering judgement
Introduction
Rigid base plate is a theoretical approach. In real-life no member is fully rigid - if you load it enough the base plate will deform. “Close to rigid” base plates behave similar than rigid base plates acknowledging the real behaviour. If the behaviour is very similar, the anchor design guidelines can be applied by engineering judgement.
Fig.1 Definition of ''Close to rigid'' base plates
Engineering judgement to define “Close to rigid” base plates behavior Whereas no check of the actual base plate rigidity was previously carried out, this is now performed at the end of the calculation process (Image below: Rigid and Flexible comparison window). The anchor loads calculated according to the elasticity theory are compared with the anchor loads taking account of equilibrium and compatibility conditions on the basis of realistic assumptions of the load-displacement behaviour and the stress-strain curves of the individual components, and assuming a rigid base plate. By comparing the anchor loads of both methods, the gap between theory (rigid base plate) and practice within a software can be determined.
Fig 2. Rigid and Flexible comparison window
The increase of anchor forces associated with a flexible baseplate, from [18], shows experimentally determined mean failure loads of anchor groups (N(u,test)) related to the calculated failure load taking into account the elasticity theory (N(u,Etheory)) as a function of highest loaded anchor of the group based on non-linear assumptions, related to the calculated value of the most loaded anchor, determined on the basis of the elasticity theory. These tests consider anchor groups with four and nine anchors under uniaxial and biaxial bending in non-cracked concrete. In the tests, cast-in headed studs and post-installed anchors were used.
The image below, was chosen in order to estimate to what extent a deviation of the most heavily loaded anchor of a group from the calculation according to the elasticity theory affects the overall group’s load capacity. Based on the available test values, with a deviation of the anchor loads of the most loaded anchor of a group of approx. 10% - 15% – between rigid and realistic baseplate assumptions – the mean failure load of the group fixture corresponds to the mean group failure load calculated according to the elasticity theory. This means that in the case of an approx. 10% - 15% deviation in the anchor loads between the rigid plate and the flexible plate, no negative influence on the load bearing capacity could be observed in the tests.
The comparison of the rigid and the realistic base plate in combination with the above investigations should help the planning engineer to make an assessment of the existing base plate thickness that does not contradict the applicable guidelines. If there are other engineering judgement considerations to go beyond the 10% value proposed here, please apply your own engineering judgement.
Looking at the influencing parameters of non-rigid base plates, the following parameters are important to define if a base plate can be considered “close to rigid”.
Fig 3. Increase of anchor forces associated with a flexible baseplate distribution
Anchor forces
The following three effects will lead to an increase in anchor forces:
Reduction of inner lever arm
Prying effects
Different load distribution in anchor groups
Fig. 4 Image showing movement on baseplates
If the anchor forces are similar to the rigid base plate results one can assume that the plate behaves in a very similar compared to a rigid plate – in this case the plate can be considered “close to rigid”. Some literature on this point to be able to take an engineering judgement are: Mallée/Burkhardt [1], Fichtner [2]. The anchor force results of a rigid vs non-rigid base plate will be accepted up to engineering judgement by the engineer who is designing.
Concrete stresses
EN 1993-1-8 [3] defines how concrete stresses should be evaluated based on the T-stub model, which is also valid for non-rigid base plates. Therefore, a check of the concrete stresses coming from our “close to rigid” FEM calculation is sufficient.
Deformation
It’s up to the engineer and/or the owner to decide which deformation in serviceability limit state will be acceptable.
Hilti recommendation for engineering judgement
Based on the information given above the engineer needs to decide if the base plate can be considered “close to rigid” on a case by case basis to ensure that the scope of the anchor design guidelines is at least met by engineering judgement. Due to the fact there is no general rule applicable for all cases, Hilti is not giving a recommendation how much deviation from the rigid base plate can be accepted. If you would like to start using PROFIS Engineering and start design as per EC2 visit our webpage clicking here You are also welcome to ask us for support: simply leave a comment or post your question in the community, or improve your knowledge and skills via our Webinars or training sessions.
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References
[1] R. Mallée and F. Burkhardt, Befestigung von Ankerplatten mit Dübeln, Beton- und Stahlbetonbau 94, Heft 12, S. 502-511, Ernst & Sohn Verlag, 1999.
[2] S. Fichtner, Untersuchungen zum Tragverhalten von Gruppenbefestigungen unter Berücksichtigung der Ankerplattendicke und einer Mörtelschicht, Dissertation Universität Stuttgart, 2011.
[3] Technical Commitee CEN/TC 250, Eurocode 3: Design of steel structures - Part 1-8: Design of joints, 2009.