CEE 371
Notes on Structural Modeling, p. 1
STRUCTURAL MODELING [AC1:5-6, AC2:1-3]
What is structural modeling?
A process through which we:
Gain insight into the behavior of a structure --- deformation, stress,
strain, and energy fields, and possible damage in the structure --- so that
we can predict its performance before it is built, while it is being built,
after it is built but before it is loaded, or explain observations of behavior
after it is built and loaded.
Why do we need to know about deformation behavior?
•Serviceability
•Durability
•Safety
•Economics
Why do we need to know about stress, strain and energy behavior?
•Strength
•Safety
•Economics
Modeling is part of a larger process:
Problem
Definition
Structural
Design
Specifications
Conceptual
Designs
Downselect
Preliminary
Designs
The Design/
Analysis Cycle
Structural
Modeling:
Analysis
Construction/
Manufacture
Final
Design
Structural Modeling can be either physical or mathematical:
 Physical Model: A tangible representation of the structure, sometimes
at full length- and time-scale, more frequently at some reduced lengthand time-scale.
 Mathematical Model: An intangible representation of the structure,
sometimes in analytical form, more frequently in computational form.
CEE 371
Notes on Structural Modeling, p. 2
Modeling of
Structural Systems
CEE 371
Physical Modeling
Mathematical Modeling
Wind Tunnel Model of CN
Tower
Analytical Modeling
Computer Modeling
By:
By:
Equilibrium Methods,
e.g., Statics
Finite Element
Method, this course
Energy Methods,
e.g., Virtual Work
Other methods, later:
Finite differences
Boundary
elements
Meshless
methods
Solution of Diff. Eqs.
CEE 371
Notes on Structural Modeling, p. 3
Mathematical Structural Modeling
All mathematical structural models are the results of idealization.
Idealization --> approximation, averaging, homogenization, etc.
The idealizations result from selection of the length- and time-scales in
which we want to study behavior, and result in abstraction from reality = a
representation.
In CEE 371, we will refer to Mathematical Structural Modeling as simply
Structural Modeling (with the explicit understanding that we are excluding
significant discussion of Physical Structural Modeling).
Length and Time Scales
DEFINITION: The length-scale of a model is the smallest spatial
dimension over which we can effectively average all smaller scale effects.
Examples:
DEFINITION: The time-scale of a model is the smallest temporal
dimension over which we can effectively average all smaller scale effects.
Examples:
Structural Modeling Involves Leaps of Abstraction from Reality
A loop – does it close?
 Reality
 Tangible image
 Geometrical/physical model
 Mathematical/analytical model
 Mathematical/computational model
 Digital representation
 Calculated results
 Prediction of performance/explanation of behavior
 Assessment of how this ties back to reality
The length- and time-scale at which we build our structural model depends
on what we:
 Need to know
 Understand
 Can represent
 Can compute
CEE 371
Notes on Structural Modeling, p. 4
All Structural Models Involve Idealizations
We idealize 4 key things:
 Geometry
 The relationship between Stress and Strain (aka material or
constitutive behavior)
 The relationship between Strain and Displacement (aka kinematic
behavior)
 Boundary conditions (restraints and loads)
Let’s look at examples of idealizations of each type, declare the level of
idealization we will make in this course for each type, and study some
guidelines for making such idealizations:
Guidelines for Geometrical Idealization
Key Issues: Consistency, Level-of-detail (LOD), Accuracy, Probability
• LOD should be consistent with length-scale chosen
e.g.
• LOD should be consistent with types of behavior sought
e.g.
• Accuracy should be consistent with available measurements and/or
design information
e.g.
• Remember: even geometry is stochastic. Its variability must be
accounted for in modeling
e.g.
Guidelines for Constitutive Idealization
Key Issues: Consistency, Homogenization, Linearization, Accuracy, Probability
• Constitutive model should be consistent with length- time-scales chosen
e.g.
• Constitutive model should be consistent with modeling objective: is this
analysis or simulation?
e.g.
• Accuracy should be consistent with available measurements and/or
design specifications
e.g.
• Remember: material behavior is stochastic. Its variability must be
accounted for in modeling
e.g.
CEE 371
Notes on Structural Modeling, p. 5
Guidelines for Kinematic Idealization
Key Issues: Consistency, Linearization, Accuracy
•Kinematic model should be consistent with length- time-scales chosen
e.g.
• Kinematic model should be consistent with structural form and expected
boundary conditions
e.g.
• Accuracy should be consistent with modeling objectives: is inclusion of
geometric non-linearity justifiable?
e.g.
Guidelines for Boundary Condition (BC) Idealization
Key Issues: Consistency, Accuracy, Probability
•Idealizations should be consistent with length- time-scales chosen
e.g.
• Accuracy should be consistent with available measurements and/or
design information
e.g
• Remember: BC’s are stochastic. Their variability must be accounted for
in modeling
e.g.
Common Symbols Used for Boundary Conditions in Mathematical Models
CEE 371
Notes on Structural Modeling, p. 6
The above and those that follow are used for both analytical and computational models. Each
implies both static and kinematic information, something we know or don’t know about forces
and displacements.
1 static
2 kinematic
1 static
2 kinematic
1 static
2 kinematic
1 static
2 kinematic
2 static
1 kinematic
2 static
1 kinematic
3 static
0 kinematic
CEE 371
Notes on Structural Modeling, p. 7
Concept of Degree-of-Freedom (DOF)
What are the 3D analogues to these symbols?
What do you notice in the “Number of Unknowns” column in the above
tables?
DOF DEFINITION: Location and direction on model where static (force,
moment) or kinematic (displacement) information is required.
Location is result of discretization process in computational modeling.
Direction is result of definition of frame of reference, e.g., Global or local
coordinate system.
Analytical models have infinite # of DOF’s
Computational models have finite, user-defined # of DOF’s
Static (Force) Boundary Conditions
 Generic Classifications:
o With respect to source:
 Body: inertial, thermal, …
 Surface: pressure, point load, …
o With respect to time-dependence
 Static: anything not time-varying
 Dynamic: earthquake, …
o With respect to motion
 Stationary: self-weight,….
 Moving: traffic, ….
 Building Code Classifications:
o Dead Loads
 Self-weight and other stationary loads
o •Live Loads
 Occupancy load
 Traffic
 Snow
 Wind
 Water and Soil Pressure
 Earthquake
 Temperature Changes
 Blast Loads
Are there other classifications?