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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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
