Extraction of Strut and Tie Model From 3D Solid Element...

Extraction of Strut and Tie Model

From 3D Solid Element Mesh Analysis

ICSBE 201012-14 December 2010

International Conference on Sustainable Built Environment

Dammika Abeykoon, Naveed Anwar, Jason C. Rigon

• The conventional “Beam” or “Plate” theory does not predict the response of structural members with large proportions and in areas of concentrated loads and discontinuities

• Design based on conventional approaches is not appropriate

• The “Truss Analogy” or the Strut and Tie Models are more appropriate

• Members can be divided in “B” Regions where Bernoulli’s theory holds, and “D” regions which are “Disturbed” by stress fields

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D-Regions and Discontinuities (ACI 318R-02 Appendix A)

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Ritter’s Truss Model (Ritter 1899)

Stress FieldIdealized Force

Paths

• Strut and Tie Model (STM) approach originated from truss analogy concept has become more rational to use as a tool for designing of D-regions of concrete structures

• The structural member is idealized as a truss by introducing uniaxial compressive struts and tension ties

• The truss action is produced by diagonally cracked web concrete struts while longitudinal and transverse reinforcement are act as horizontal and vertical ties

• The locations where struts and ties intersect called as nodes

• Manual selection and analysis of Strut and Tie Model (STM) is arbitrary and time consuming

• Available tools to find STM are iterative and more time consuming

• Difficulties in imagination of STM for a particular structural members as their complexities in stress distribution

• Difficulties in confirming the adequacy of identified STMs and selection of better model from available many options

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Previous Research, using Shape Optimization and Form Finding

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Present approach: Direct extraction from Finite element Models

• Create a Finite Element Model using Shell or Brick Elements

• Apply the primary loads and assign boundary conditions

• Run the analysis and obtain results

• Transfer results to text files

• Read results, compute principle stress directions and values

• Group using appropriate techniques

• Find resultant vector and value of the group

• Try and complete strut and tie model from the groups

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12

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Modified space truss model by Kanok-Nukulchai, Anwar.(1996)

• All the structural members considered are analyzed using Solid element model in SAP 2000 V12

• Solid element is an eight node element consisting six quadrilateral faces with a joint located at each corners

Solid Element & Stresses(CSI Analysis Reference Manual SAP2000)

• Required output results from FEA– Solid element corner joints and centroid coordinates

– Solid element joint connectivity

– Solid element principal stresses at corner joints

– Principal stress direction cosines at solid element corner joints

– Solid element properties

• Principal Stresses Averaging– Principle Stresses averaging within the element

– Principle Stresses averaging of each node

– Averaged Principal Stresses which has maximum absolute magnitude in each node & centroid is taken as significant stress component for strut & tie extraction

Averaged Principal stresses

(Maximum absolute values)

Sorting based on Direction cosines

Principal

stresses with

same directions

stored in

separate cells

-1 1

1

-1

1

-1

Direction cosines in X direction

Dire

ctio

n c

osin

es in

Z d

ire

ctio

n

Direction

cosines in Y

direction

…::

::…:.

Principal

stresses with

same

direction

Sorting based on magnitude

Principal

stresses with

same

direction &

magnitude

Rotate back to original position

Principal stresses with same

direction & magnitude

Rotating of Principal stress vectors to align with

vertical (Z) axis & bring it to the origin

Extracted strut or tie through stress tubes

Divide the xy plane

in to grid based on

strut or tie size &

identify the stress

tubes

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

• Rerun the program by changing following parameters to get better strut and tie layout – Stress limit considered

– Number of divisions in direction cosines

– Number of divisions in stress range

– Strut or tie size

• Program output of strut & tie layout is coming out from two formats– Graphical interface

– Text format data file

• Because of the complexity of three dimensional stress states, finding of connectivity between extracted struts and ties is not implemented

• As an alternative method, extracted struts & ties are modeled in SAP 2000 to generate final truss model

Solid Element Model of Two

Piles-Pile Cap

Principal

Compressive

Stress Contours

Principal Tensile

Stress Contours

Stress Trajectories from Program Output Strut & Tie Layout from Program Output

Although many strut and tie members present in the layout, the basic

expectation of triangular shaped strut and tie layout is achieved

Simple 3D Struts and Tie Model for a Four Piles-Pile Cap

(Adebar, Kuchma, & Collin, 1990)

Four pile cap configurations having span/depth vary from 1 to 4 are modeled

with solid element and FEA results are used to extract possible strut and tie layout

Pyramid shaped strut and tie model is expected according to reviewed literature

Principal

Compressive

Stress

Contours

Principal

Tensile Stress

Contours

Solid element model (Frame

element for piles & column)

Strut and Tie Layout from Program Output

Four inclined strut layout is clearly shown in program output

Results of Four Piles Pile Cap - Span/Depth = 1

Stress Trajectories from Program Output

Principal

Compressive

Stress Contours

Principal Tensile

Stress Contours

Solid element model (Frame

element for piles & column)

• Four horizontal ties clearly appeared in between piles at the bottom of pile cap

• Two inclined struts are appeared in each corner of the pile cap

• Although the inclinations of struts are not sufficient to intersect within the body of the pile

cap, it can be idealized as a shape of pyramid when each corner struts are represented

by a single strut

Strut and Tie Layout from Program OutputStress Trajectories from Program Output

Principal

Compressive

Stress Contours

Principal Tensile

Stress Contours

Solid element model (Frame

element for piles & column)

Solid element

model

Principal Compressive Stress Contours Strut & Tie Layout from Program Output

The program output Shows the strut & ties layout clearly showing four

inclined struts at pier head region and four vertical struts in vertical shaft

Solid element

model

Principal Compressive

Stress Contours

Principal Tensile

Stress ContoursStrut & Tie Layout from

Program Output

Although the truss configuration is not cleared well, the horizontal ties at top of

the pier head, inclined struts at bottom of the pier head and vertical strut at shaft of

the pier is cleared which is match with principal stress contours

Extraction of Strut and Tie Model from 3D Solid

Mesh Analysis

Solid element

model

Principal Compressive

Stress ContoursPrincipal Tensile

Stress Contours

Strut & Tie Layout from

Program Output

Results Output from Program

Tension ties on top of the pier head and vertical compressive struts at pier shaft

can be seen from the extracted strut and tie layout which is match with principal

stress contours of the pier

Compressive struts cannot be clearly seen at the bottom of the pier head

• Extracting models from Shell Element in planer problem is much easier than in solid mesh

• Solid element mesh analysis can display the internal stress flow of three dimensional structural members & initial strut & tie layout can be visualized through it

• Proposed method can extract the possible strut and tie member layout that match with internal stress flow of three dimensional disturbed region members

• Pile caps with piles & column modeled from frame element give better results

• Further modifications are required to improve the quality of the results