OpenSees Cloud

OpenSees AMI

DuRe-Trans Webinar

TITLE

December 10, 2024

Michael H. Scott and Mark D. Denavit

Project Objectives

Overview of OpenSees

Analytical Model

Long-Term Load Effects

Jenkins and Frosch

Validation

Jenkins and Frosch

Jenkins and Frosch

Short term

Long term

Caltrans Bridge Columns

Look in ~/Caltrans-Slender-Columns/long_term_interaction.py

Hello, and welcome to part 2 of today’s webinar on Second Order Effects on the Design of Slender Reinforced Concrete Bridge Columns. My name is Michael Scott and I am a professor of structural engineering at Oregon State University.

In part 1 of the webinar, Prof. Mark Denavit discussed the evaluation of current design methods for slender RC bridge columns, quantified errors due to the simplifications made in current design methods, and made recommendations to reduce these errors. The outcomes summarized in part 1 allow engineers to make more accurate desicions when designing slender RC columns.

In part 2 of the webinar, I will discuss further details and validations of the second order analysis methods that formed the basis for the recommendations summarized in part 1.


This project was funded by Caltrans and managed by PEER, the Pacific Earthquake Engineering Research Center. As discussed in part 1 of the webinar, the project objective was to devleop guidelines for the efficient design of RC bridge columns. The project was analysis-based, i.e., no physical experiments were conducted, and was comprised of the six tasks shown on screen.

My objective in this part of the webinar is to give details on task 3, the development and validation of the refined second order analysis methods used in developing the design guidelines for slender RC bridge columns.


Second-order material nonlinear analysis is our “best guess” of the true behavior of slender RC bridge columns, against which current and trial design methods can be benchmarked.

For second-order analysis, we used pre-defined “off the shelf” modeling components, such as frame elements and fiber sections, along with analysis methods such as proportional loading and displacement control.

We examined short term loading using fiber sections comprised of concrete fibers using the Mander stress-strain relationship and steel fibers with EPP stress-strain response.

For long term loading, we developed a generalized wrapper material based on the TDConcrete material models implemented in OpenSees by Knaack, Tosic, and Kurama.


Some of you attending this webinar may be familiar with OpenSees, while other will not have heard of this software framework.

OpenSees is the Open System for Earthquake Engineering Simulation developed at UC Berkeley in the late 1990s for simulating the response of structural and geotechnical systems to earthquakes and other loadings. OpenSees continues to grow with thousands of users from the engineering research and professional communities.

OpenSees has a wide range of element formulations and material models, and users build and analyze models via Python scripts, making OpenSees suited to parametric studies.


For single non-sway columns, we performed geometric and material nonlinear analysis using a corotational mesh of frame elements. As shown on the left, a column was subdivided into multiple elements (each black square is a node and between each node is an element).

Within each element we used fiber sections to simulate material nonlinearity. Using a mesh of elements with the large displacement corotational transformation allowed us to simulate “P little delta” geometric nonlinearity without having to use stability functions or high order shape functions within the basic system of each element.

In addition to material and geometric nonlinearity of the elements, the nodes were defined with a slight out of straightness to trigger geometric instability.


Although short term loading has been previously validated using the aforementioned modeling approach in OpenSees, we performed additional validations against experiments conducted by Jenkins and Frosch. These researchers also performed long term loading experiments on columns identical to those used for short term loading, giving a good basis of comparison for our analysis approach.

The column shown below is 6-1/8 inch square with an eccentric axial load, P. In OpenSees, we discretized the cross-section into fibers using the Concrete04 material model, one of the more widely used conrete models in OpenSees, and the standard EPP stress-strain model for the lontiudinal reinforcing steel.

The column was loaded to failure by increasing the eccentric axial load. In the OpenSees simulation, loading to failure was accomplished via displacement-controlled analysis.


Here is R3-70-10-ST, one of the eight specimen configurations test by Jenkins and Frosch. This column has 4 #3 reinforcing bars, slenderness L/r = 70, or L/h of about 20, and normalized load eccentricity e/h = 0.1.

The comparison of results on the right shows the simulation captures the relationship between applied axial load and bending moment at mid-height of the column very well. This column loses stability as evidenced by the loss of load-carrying capacity (reducation in axial load and bending moment). In addition, the simulation captures the relationship between axial load and lateral deflection at column mid-height.


R5-70-25-ST is another case from Jenkins and Frosch. THis configuration has four #5 bars, slenderness L/r = 70 and normalized load eccentricity e/h = 0.25.

Although this column is subjected to a more eccentric axial load than the previous case, the column does not become unstable. Regardless, the numerical simulation is able to capture the peak axial load capacity and matches the experimental response quite well.

These validations for short term loading give us confidence that the simulation models are more than adequate and form the basis for exploring the long terms experiments conducted by Jenkins and Frosch.


Before showing long term simulation results, I would like to discuss a new contribution to OpenSees. While the TDConcrete material models developed in OpenSees by Knaack, Tosic, and Kurama are technically sound, from a software design point of view, the models are limited due to tight coupling of the concrete stress-strain response with creep and shrinkage evoluation equation within the TDConcrete class.

To apply creep and shrinkage to Concrete04 or other widely used uniaxial concrete models within OpenSees would require significant code dupclication, e.g., by creating a new “TDConcrete04” class. The same code dupcliation would be required for creep with Concrete23 or any other of your favorite material models.

By separating the creep and shrinkage evoluation equations, e.g., those prescribed in ACI 209, from the mechanical stress-strain response, we were able to develop the CreepMaterial wrapper class. Now every uniaxial material model in OpenSees is creep and shrinkage enabled.


Returning to the experiements of Jenkins and Frosch, identical column configurations were tested for long term loads. For the OpenSees models, we simply wrapped the Concrete04 model with the CreepMaterial wrapper, then passed the wrapped material to the fiber sections. In their experimentis, Jenkins and Frosch help the axial load for approximately 100 days, then loaded the column to failure. After the hold phase, displacement-controlled analysis was used in OpenSees to reach failure.


Here is the long term version of the R3-70-10 specimen (four #3 bars, L/r = 70, and e/h = 0.1). The simulations using short term and long term material models in OpenSees are compared to the experiment on the right. As expected, the short term material model (unwrapped Concrete04) does not undergo increasing deflection during the hold phase.

On the other hand, the long term material model (Concrete04 with CreepMaterial wrapper) gives increasing deflection with respect to time during the hold phase. The magnitude and rate of increasing deflection, as well as the peak axial load, match the experiment well, giving confidence that the modeling approach is valid.


The long term version of the R5-70-25 specimen (four #5 bars, L/r = 70, e/h = 0.25). Similar to the previous slide, the simulated long term results match the experiment, both in terms of the magnitude and the rate of increase in deflection during the hold phase, as well as the peak axial load.


For the design of slender RC bridge columns, the reduction in maximum axial load for short term vs. long term loading is important to quantify.

The bar chart on this slide compares the reduction in axial load capacity observed in all eight configurations test by Jenkins and Frosch, compared to the simulated reduction obtained from our OpenSees models. The simulation models do a good job of capturing the general trends, though perhaps not the exact percent loss in capacity, which is difficult to realize.

It is important to note that the specimens with lower reinforcing ratios (the R3 cases) experience much greater losses in axial load capacity compared to the columns with higher reinforcing ratios (the R5 cases).


With validated numerical models, we can turn our attention to the types of columns and range of column parameters typically found in Caltrans bridges. With the scripting capabilities of Python and the modeling strengths of OpenSees, we can perform long term load analysis for all 3168 cases summarized in this slide.

Two cases are shown in the following slides.


On this slide is the axial-moment capacity curve for case C06-L15-NS01, a 48 inch diameter circular, non-sway column with L/D = 15 and 2% reinforcing steel.

Here M1 is the applied moment (for every fixed axial load), and M2 is the second order moment (including P-little-delta effects).

As shown in the plot, long term load effects cause a decrease in flexural capacity (M1) for every level of axial load. However, the second order moment is not affected by long term load effects. This column is not very slender and the reinforcing ratio is not small.


The second column we will examine is Ox01-L20-NS01, a 48 inch diameter obround column bent about is minor axis. The column span to depth ratio is L/D = 20 and there is only 1\% reinforcing steel.

As shown in the plot, long term load effects cause a decrease in flexural capacity (M1) for every level of axial load. And for high axial loads, long term loading affects the second order moment (M2). Compared to the previous case, this column is more slender and has a lower reinforcing ratio.


In this project, we we able to validate OpenSees models for the strength of slender RC bridge columns. The models included material and geometric nonlinearity and both short and long term loading.

The new CreepMaterial wrapper will facilitate the analysis of long term loads on all uniaxial material models available in OpenSees. The wrapper we implemented used ACI 209 evoluation equations for creep and shrinkage and a separate wrapper can be defined for Model Code (Eurocode) evolution equations.

From these second-order analysis models, we were able to justify practical modleing guidelines for determining the available strength of slender RC bridge columns, giving bridge engineers additional tools and rationale for effective designs.


This concludes part 2 of the webinar. I would like to thank our research team–Prof. Mark Denavit and Mr. Javad Esmaeelpour from the University of Tennessee and Dr. Minjie Zhu from Oregon State University. I would also like to thank the advisory committee from Caltrans, particularly Sharon Yen, who guided the research team throughout the project. And an extra special thank you to Prof. Nikola Tosic from UPC in Barcelona for insights on the TDConcrete model implementations in OpenSees.

Thank you for your time and I hope you enjoy the rest of your day.



© 2019-2026 by Michael H. Scott. All rights reserved.

I work on problems related to modeling and nonlinear structural analysis. If these problems are relevant to a current professional project, feel free to reach out.