structural ANALYSIS Rigid and Non-Rigid Base Plate Assumptions Use of CBFEM for Validation By Arif Shahdin
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ave you ever stopped for a second and The purpose of this article is to further the thought, “do we ever validate our rigid understanding of non-rigid base plate design by: plate assumption when designing anchorage 1) Developing a non-rigid base plate to concrete?” The answer is simple. There is no criterion analytical method for validation and, because 2) Linking the (above) criterion with prethe design codes mandate it, the design viously explained CBFEM parameters engineer abides by it as it is a Building and 3) Using the criterion to define a “NonSafety (Plan check) requirement. This article Rigid base plate Close-To-Rigid” demonstrates how Component Based Finite 4) Understanding the power of CBFEM Element Modeling (CBFEM) can validate methodology for validating rigid or any base plate behavior, rigid or non-rigid. non-rigid base plate assumptions So, regardless of what base plate assumption you make as a design professional, now you Non-Rigid Base Plate Design can get validation. Design of anchorage per the American Figure 1. Bi-linear stress-strain curve. A criterion for Non-Rigid Base plate assumpConcrete Institute’s Building Code tion must first be developed. When a design Requirements for Structural Concrete (ACI 318) is mandatory for engineer thinks about a non-rigid base plate, what comes to mind structural engineers and design professionals in general. When dis- first? For instance, some say “a thin plate,” so thickness can be the first cussing anchorage to concrete, a non-rigid plate assumption is a assumption. But then, very quickly, it is concluded that “thickness of rarity, predominantly because the anchorage design codes mandate the plate” itself does not entirely paint the picture until plate loadthat the anchor forces be determined based on a rigid plate assump- ing is examined. Furthermore, since Finite Element Analysis (FEA) tion. In a previous article (Morgan and Shahdin, Structural Analysis, is the common computational approach, the stiffness and material STRUCTURE, January 2020), this and other consequences of non- type of the profile/fixture is also a key ingredient to obtain a realistic rigid plate assumptions such as increased anchor forces were discussed. load transfer. Finally, do not forget the anchors. In reality, the anchor CBFEM as a methodology to analyze the non-rigid plate behavior was types, sizes, and positions can also influence the load transfer and be also discussed, and the Bi-Linear Stress-Strain curve was introduced considered input to a criterion. to depict the behavior of the two-dimensional (2-D) shell elements To recap from the previous article, CBFEM methodology helps the of the plate. The article closed by highlighting some key CBFEM design professional make an engineered decision on whether or not parameters that would help a structural engineer make an engineer- to accept the resultant anchor forces from a non-rigid plate assumping judgment as to whether it is ok to go ahead with the non-rigid tion and proceed with an ACI anchorage design. This premise was plate-based anchor forces for anchorage design. developed on the three parameters.
Plastic Strain Limit
Figure 2. Defining Close-to-Rigid base plate behavior.
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The plastic strain limit depicts the behavior of the plate beyond the yield point. To understand this further, look at the defined material behavior curve. A material behavior curve is typically a stress-strain curve that determines the behavior of the steel elements. In this case, the elements of choice for the plate are 2-D shell elements, and a bi-linear stress-strain curve is the material behavior curve of choice. A bi-linear stress-strain curve eases the understanding of material behavior. The behavior remains linear after yield, with a slight slope associated with it, as shown in Figure 1. Until yield strength is reached, the plastic strain remains zero. This shows classic linear elastic behavior as defined by the American Institute of Steel Construction (AISC). Once the yield point is reached, the plastic strain counter starts. Now connect this parameter to the non-rigid plate criterion that was established above. In conjunction with the bi-linear stress-strain curve, the plastic strain limit percentage helps to understand the force level on the structure by relating it to the von Mises stress. The von Mises stress criterion is used to depict whether a given material will yield or fracture.
