BSI Newsletter - Issue #3, Spring 2005

Welcome to the Spring issue of the BSI Newsletter!

We are pleased to announce that the release of FB-MultiPier has arrived. This new program is the next stage of development for the FB-Pier program, adding new features while retaining the strengths of the old. Please read below or visit our website for FB-MultiPier details and pricing information.

In this issue's Technical Corner, we explain the new FB-MultiPier's Interaction Diagrams. Christopher Mills, from DRMP Inc., explains how to simplify the soil data entry process in Discussions.

We would like to thank all the users whose feedback and comments helped make the completion of this program possible. Important issues were raised by users and lead to major corrections and improvements in the program. We hope that with continued feedback we can keep improving the program to better serve the engineering needs of our clients.

The articles "Technical Corner" and "Discussions" are open for input from all readers. Do you have a topic that you think should be discussed? Did you create a model that you feel contains notable information that you want to share? Everyone is welcome to submit articles for possible inclusion in subsequent issues. Please contact BSI at BSI@ce.ufl.edu with your ideas.

FB-MultiPier is available for purchase!

The FB-MultiPier analysis program is a nonlinear finite element analysis program capable of analyzing multiple bridge pier structures interconnected by bridge spans. The soil behavior is modeled with a series of uncoupled springs along the depth of the pile. The full structure can be subjected to a full array of AASHTO load types in a static analysis, or time varying load functions in a dynamic analysis. Combined with the full bridge option, dynamic analysis modes have been added that will allow the user to have a more complete picture of the overall structure.

FB-MultiPier Screenshot The most notable features include:

Updated Graphical Interface
Multiple (99) Pier Modeling
- Distinct Properties Per Pier
- Pier Rotation
- Bridge Span Superstructure
- Two Rows of Bearings
- Plot Displacement vs. Time
Dynamics Analysis
- Modal Analysis
- Time Step Integration
- Animated Results

The FB-MultiPier program is available as an upgrade for all current FB-Pier v3 license holders to update to the equivalent license of FB-MultiPier. FB-MultiPier has several levels of licensing that will allow for different levels of use and pricing. Different levels can be included in a single license to allow for maximum flexibility. This allows one enginner to work with a single pier model and another to incorporate that single model into a full bridge, using a single licnese with both Single Pier and Full Bridge capabilities.
Find out more about the FB-MultiPier features and pricing here.

FB-MultiPier Pricing
1) Single Pier $1200

FB-Pier v3 Equivilant - Upgrade Option

2) Single Pier Modeling w/ Dynamic Anaylsis $2000

3) Three Pier Modeling w/ Dynamic Anaylsis $3000

4) Full Bridge Modeling w/ Dynamic Anaylsis $5000

99 Pier Limit

FB-MultiPier Pricing
1) Single Pier	$1200
FB-Pier v3 Equivilant - Upgrade Option
2) Single Pier Modeling w/ Dynamic Anaylsis	$2000
3) Three Pier Modeling w/ Dynamic Anaylsis	$3000
4) Full Bridge Modeling w/ Dynamic Anaylsis	$5000
99 Pier Limit

The analysis of members under biaxial loading is reduced to numerically calculating the failure surface of a section. The interaction failure surface (interaction diagram) is a three dimensional plot representing the ultimate capacity of a column subjected to biaxial bending (Mx, My) and axial load, P (Figure 1). This is an extension to the single axis bending moment interaction diagram which is a plot of axial load versus bending moment in one direction. The failure surface is a function of the amount and distribution of reinforcing steel, concrete cross section and the stress-strain properties of the concrete and reinforcement.

FB-MultiPier Screenshot In practice the concrete may be confined by transverse reinforcement commonly in the form of closely spaced steel spirals, hoops, steel shells etc. At low levels of stress in the concrete, the transverse reinforcement is hardly stressed; hence the concrete behaves as it is unconfined. As the stresses become higher the concrete bears out against the transverse reinforcement, which then applies a confining reaction to the concrete. In such case the confinement can considerably increase the stress-strain characteristics of the concrete.

An exact mathematical formula to describe a failure surface is impractical because of the number of parameters affecting the surface shape. Therefore, different methods of failure surface approximations have been suggested such as

1) The Bressler reciprocal load method,
2) The Bressler load contour method,
3) The PCA load contour method,
4) The Weber design chart method etc.

FB-MultiPier

In addition to the approximate calculations for the shape of the failure surface a number of analytical models have been developed which are implemented and used in computer codes. FB-MultiPier uses a rational model which performs a series of calculations over a section that is discretized into fibers. The failure surface is then generated at various levels of axial loads (load contour curves). The load contour curves plot the moments Mx and My at a particular axial load.

For this method the nonlinear bending theory for flexural members is used which accounts for force equilibrium, strain compatibility over the section and the nonlinear stress-strain relationships for concrete and reinforcement. The stress-strain relationship for the concrete is characterized by the Hognestad parabola. The stress-strain for the steel is bilinear whereas the stress-strain relationship for the confined sections is characterized by the models presented by Mander et al[1].

FB-MultiPier Solution Process

The FB-MultiPier solution process is two fold. First the program calculates the strength criteria (interaction diagrams) of the given sections; the design engineer will use these as tools to perform the design. Then the program performs the analysis which is based on the geometry, the materials of the structure and the applied loading. It is important to note that the two stages of the solution process are performed independently and should not be confused. The two parts of the solution process are described below.

The first part of the solution process is to generate the strength criteria of the sections which the design engineer can use to prepare the design. In the case of FB-MultiPier these criteria are the interaction diagrams. The interaction diagrams for each section are generated based on the specified model. In FB-MultiPier there are three options available. The first option is the section without any confinement (NONE). In this case the interaction diagram will be generated based on the size, the shape of the cross section, the steel reinforcement and the assumption that the section is not cracked. The second option is the confinement with the spiral (SPIRAL ONLY). In order to generate the interaction diagram for this model FB-MultiPier follows the model that is presented by Mander et al [1]. In this model the concrete inside the spiral reinforcement is assumed to have an improved stress-strain behavior whereas the concrete outside the spiral is assumed to spall. The third option (SHELL AND SPIRAL) is similar to the second one. In this case the concrete inside the spiral core is assumed to be confined by the spiral and the shell so it is capable of reaching even higher strain levels whereas the concrete outside the spiral is assumed to be confined by the shell and therefore it does not spall. Note for option three, the shell can not be used for confinement and longitudinal reinforcement at the same time.

The other part of the solution process consists of the analysis of the structure. The program applies the loads to the structure and the structure displaces. Based on the displacement it develops strains. In order to calculate the response of the structure the program uses the specified stress-strain curves for the section. If it is a regular section then it uses the Hognestad parabola for the concrete and the bilinear curve for the steel. If it is a confined section it uses the graphs suggested by Mander et al [1]. In the case of a user specifying custom stress-strain curves then those will be used instead. The program performs an integration over the cross section to get the forces from the stresses. The program will then check for equilibrium and if it is not achieved it will iterate until it obtains a state when the applied loads are balanced by the internal stresses which are calculated based on the specified stress-strain graphs.

References

[1] "Theoretical stress strain model for concrete" J.B.Mander, M.J.N Priestley and R. Park (1988) published in the Journal of structural engineering vol 114 No8.

I recently worked on a project with two bridges, each having 20 intermediate bents. A total of 27 borings were sampled. The soil conditions were poor and highly variable from boring to boring. Due to this variability and the anticipated long length of piles, several different soil layers (up to 14) were encountered within each boring.

Inputting the FB Pier soil parameters for so many layers is very time-consuming, requiring the user to go through multiple input windows for the different soil models for each individual layer. To increase efficiency, I developed an Excel spreadsheet that converts the soil input from table format into FB Pier input (see Engine Input Users Guide in the FB-Pier help for more information).

This FB Pier input was then directly pasted into the text format of my files, saving considerable time. My spreadsheets used "concatenations" (linking text strings) and number format functions in Excel to create the FB Pier soil input. Care must be taken when editing the input file of FB Pier. Be sure to review the FB-Pier help file for proper formatting and spot check some of the soil information to make sure that it was incorporated correctly.