# Two Dimensional Linear Finite Element Analysis Of Post-tensioned Beams

## Keywords

finite elements, post-tensioned beams, MATLAB, CALFEM, concrete beams

## Abstract

The objective of this research project was to create a Finite Element Routine for the Linear Analysis of Post-Tensioned beams using the program CALFEM® [20] developed at the division of Structural Mechanics in Lund University, Sweden. The program CALFEM and our own made files were written in MATLAB, an easy to learn and user-friendly computer language. The approach used in this thesis for analyzing the composite beam consists in embedding the steel tendons at the exact location where they intersect the concrete parent elements, without moving the concrete parent element nodes. The steel tendons are represented as one dimensional bar elements inserted into the concrete parent elements, which at the same time are represented as 8 node Iso-parametric plane elements. The theory presented in Ref. [4] served as basis for the modeling of the post-tensioned beams; however it only explained the procedure for modeling simple reinforced concrete beams, due to this we needed to make the appropriate adjustments so we could model post-tensioned beams. Assembly of the tendon stiffness into the concrete elements will depend on the bond interface between the steel and concrete, this bonding effect will be modeled using link elements; the stiffness of this link element used in the concrete-tendon interface will be the change in cohesion (between the grout or duct and the steel tendon) at the interface due to the relative slip between the concrete and the steel elements nodes. Loads (Distributed, Concentrated or Post-Tensioning) are applied directly into the concrete parent elements, and then from their resultant displacement the displacements and forces of all the steel tendon elements are obtained, this is done consecutively for all the post-tensioned tendons at every load increment. Four examples from different references and software programs are solved and compared with our results: (1) A simply reinforced cantilever plate. (2) A reinforced concrete beam, under the effect of a vertical concentrated load at mid-span. For this problem the force distribution along the steel reinforcement is obtained for two conditions, perfectly bonded and perfectly un-bonded, our results are compared with the ones obtained with the program SEGNID. (3) Consists of a continuous un-bonded post-tensioned beam with two spans, without stress losses on the tendon. The reactions at the supports and the concrete stress distribution at the location of the mid-support are obtained after the post-tensioning force is applied at both ends. (4) Consist on a un-bonded post-tensioned beam with stress losses on the tendons due to friction, wobbling and anchorage loss, under gradual loading and consecutive post-tensioning of two tendons, the results are compared with the ones reported using the program BEFE [5] developed at the University of Technology Graz, Austria. The results obtained using our program are very similar to the ones obtained with the other programs, including the more powerful curved embedded approach used by BEFE [5].

2004

## Semester

Fall

Onyemelukwe, Okey

## Degree

Master of Science (M.S.)

## College

College of Engineering and Computer Science

## Department

Civil and Environmental Engineering

## Degree Program

Civil Engineering

application/pdf

CFE0000256

## URL

http://purl.fcla.edu/fcla/etd/CFE0000256

English

December 2004

None

## Access Status

Masters Thesis (Open Access)

COinS