Technical Background on the Advanced Baseplate Feature of our Anchor Software PROFIS Engineering- Part 1

Every structure needs to be connected to the ground via a foundation. These foundations are in most cases made from concrete. To transfer the loads acting on the structure a connection of the structural steel components (beams, columns, …) to concrete foundations is required. One of the most popular solutions is fastening the structural steel component welded to a base plate with anchors to the foundation. All relevant elements of this connection need to be designed for the acting loads.

Bar members are preferred by engineers when designing steel structures. However, there are many locations on the structure where the theory of members is not valid, e.g., base plate, anchors connections, welded joints. The structural analysis in such locations requires special attention. The behavior is non-linear and the nonlinearities must be respected, e.g., yielding of the material of plates or profiles, base plate and concrete block, one-sided actions of anchors, welds.

The base plate and anchors needs to be designed at the intersection between steel design, anchor design and concrete design guidelines. The design assumptions for the full connection must not contradict each other. Main example for steel to concrete connection is the assumed behavior of the base plate. Design codes, e.g. EN 1993-1-8 [1], and technical literature offer engineering solution methods. Their general feature is derivation for typical structural shapes and simple loadings. The approach is based on the component method.

Over the last years finite element (FEM) based design revolutionized structural engineering. Nowadays most engineers have access to powerful FEM software packages. Since the term “rigid base plate” can mean everything and nothing there are a lot of design engineers modeling their base plates, concrete and anchors in FEM solutions (sometimes even with a non-linear FEM software utilizing the plastic design according to Eurocode 3). Most likely they are not aware that the anchor design guidelines are based on a rigid base plate assumption.

This document is meant to give guidance and additional details on the Advanced Base Plate solution in Hilti’s PROFIS Engineering software.

 Component-based Finite Element Method

Reality behavior of steel to concrete connections cannot be solved by simple beam equations. Component Method (CM) solves the connection as a system of interconnected items – components. The corresponding model is built per each connection type to be able to determine forces and stresses in each component. (Figure 1)

Figure 1: Anchors modeled by springs in steel-to-concrete connection

Concrete is modelled with compression spring, anchor is modelled with tension spring, and steel is defined with shell elements. The mechanical properties of the individual components are defined by EN 1992 for concrete, EN 1993 for steel, and Hilti Technical Data based on laboratory tests for anchors.
Each component’s resistance is checked separately using corresponding equations from the code (more information given later in this document).
The method used by PROFIS Engineering to simulate reality behavior of base plate is the Component-based Finite Element Method (CBFEM) which is:

• General enough to be usable for most of connections in engineering practice
• Simple and fast enough in daily practice to provide results in a time comparable to current methods and tools
• Comprehensive enough to provide structural engineer clear information about connections behavior, stress, strain and reserves of individual components and about overall safety and reliability.

The CBFEM is based on the idea that most of the verified and very useful parts of CM should be kept. The weak point of CM – its generality when analyzing stresses of individual components – was replaced by modeling and analysis using Finite Element Method (FEM). The connection is divided into main components: profile, stiffeners, welds, plate, concrete and anchors.
This method has been proved by a verification and validation process of benchmark cases, both numerical and experimental, source [2].

Rigid base plates: problems when designing base plates today

Rigid base plate assumptions from ETAG/EN/ACI guidelines are usually not top of mind for engineers – however anchor guidelines are explicitly valid for rigid base plates only. There is no clear definition available when a base plate can be considered rigid. The current design software gives a solution to the load distribution on the anchors, but the assumptions behind these calculations are not transparent at all, giving a black box feeling. The main influencing effects of non-rigid base plate:

• Reduction of inner lever arm

In case the base plate cannot be considered rigid the inner lever arm between resulting tension and resulting compression decreases. Limiting case to consider is a very thin plate where the center of compression will be underneath the compressed flange of the I-profile. A reduction in inner lever arm will lead to an increase in anchor forces. (Figure 2)

Figure 2: Reduction of inner lever arm for non- rigid base plates

• Prying effects

For non-rigid base plates with certain geometries prying forces can be observed. These forces will increase the anchor forces coming from the acting loading (tension or bending moments). (Figure 3)

Figure 3: Increase of anchor forces due to prying effects

• Different load distribution in anchors groups

In case of different distances of fasteners to the profile and non-rigid base plates the load distribution between the single anchors will be different, e.g. in a 3x3 anchor arrangement the center anchor will get much more load than the outer ones in case the base plate is non-rigid. (Figure 4)

Figure 4: Increase of anchor forces due to different load distribution for non-rigid base plates

• Different concrete stress distribution

In case of non-rigid base plate, the compression stress will be concentrated underneath the profile. This will lead to higher concrete stresses. (Figure 5)

Figure 5: Different concrete stress distribution

• SLS considerations

For cantilever beams a non-rigid base plate will create more displacement because there is more rotation in the base plate. (Figure 6).

Figure 6: Displacement of cantilever beam incase of rigid and non-rigid base plate

Depending on the loading and the geometry, one or more of these effects will apply and will change the anchor forces in the connection. See the next example which compares rigid and flexible base plate.
In this example the reduction of the lever arm and prying forces lead to higher anchor forces. This is not a theoretical approach – also in physical tests this behavior is being observed.

Figure 7: Example compering rigid vs flexible

Advanced base plate design in PROFIS Engineering

After observing the lack of detail in the steel-to-concrete connections, alternative methods have been developed with more accurate results and closer to reality. In the next figure, it is shown the different methods to calculate. (Figure 8)

Figure 8: Base plate design options for determination of the load distribution to the anchors

Rigid

PROFIS Anchor and PROFIS Engineering with selection of rigid derive the anchor forces acting on individual fasteners from an applied load. The assumptions for the rigid design options based on the current anchor design guidelines ( [3], [4], [5], [6],
[7] and [8]) are:
•   No deformation of the plate (plane surfaces remain plane).
•   Strains are distributed linearly through the cross-section of the baseplate (corresponding to the “Bernoulli Hypothesis” in reinforced concrete).
•   Relevant mechanical properties for design are fastener cross-section (As) and fastener modulus of elasticity (Es).
•   Stiffness of the concrete is characterized by its modulus of elasticity.

Figure 9: Rigid base plate behavior

In the first step (1 in Figure 10 below), the rigid base plate method calculates the resultant anchor forces and concrete stresses, based on the rigid assumptions. Then (step 2 in Figure 10 below), it turns them into loading vectors and apply these to the base plate, to determine the plate moments. From the plate moments the thickness is being calculated using the yield strength of the base plate (step 3 in Figure 10 below) At the end, the user is responsible to check if the assumption of a rigid base plate was met (step 4 in Figure 10 below).
Unfortunately, this step is not done properly all the time.

Figure 10: Steps taken in the rigid design

Flexible
The real behavior of base plates may be rigid or non-rigid. Although, the anchor codes require the base plate to be rigid. Illustrated below are two limit examples of a plate with no deformations (rigid), and a case with deformations (non-rigid).
However, there is currently no clear definition of a rigid base plate

Figure 11: Two examples comparing non- rigid base plate

In a real behavior of a base plate, all the components geometry and mechanical properties influence the load distribution (profile, welds, stiffeners, plate, anchors and concrete).
Then Flexible design based in component method, according to component method considers the full connection design is explained in the flowing chapters. PROFIS helps users solve the rigid base plate, by checking how close to a rigid situation their design is.

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References
[1] Technical Commitee CEN/TC 250, Eurocode 3: Design of steel structures - Part1-8: Design of joints, 2009.
[2] Wald F.m Sabatka L., Bajer M., Barnat J., Gödrich L., Holomek J., Kabelac J.,Kocha M., Kolaja D., Kral P., Kurejkova M., Vild M., Benchmark cases for advanced design of structural steel connections, Prague, September, 2016.
[3] Technical Commitee CEN/TC 250, FprEN 1992-4 Design of concrete structures- Part 4: Design of Anchorage for use in concrete, 2015.
[4] European Organisation for Technical Approvals (EOTA), ETAG 001, Annex C:Design methods for anchorages (3rd amendment), Brussels, 2010.
[5] European Organisation for Technical Approvals (EOTA), TR 029, Brussels:EOTA, 2010.
[6] American Concrete Institute Comitee, ACI 318-11: Building code requirements for structural concrete, 2011.
[7] American Concrete Institute Comitee, ACI 318-14: Building code requirements for structural concrete.
[8] American Concrete Intitute Comitee, ACI 318-08: Building code requirements for structural concrete, 2008.