Introductory example

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Introductory example
Example:
Bridge
Bridge
Introduction
• Static and eigenfrequency analyses are conducted for a bridge.
• The bridge is modeled using 3D beams and shells elements
available in the Structural Mechanics Module.
Bridge – Problem Definition
Geometry
•
•
•
•
The bridge is 40 m long and
5 m wide.
The bridge geometry is
composed of surfaces
representing the roadway
and edges representing the
bridge frame structure.
The bridge structure is
inspired by the common
Pratt truss bridge
A Pratt truss is identified by
its diagonal members which,
except for the very end ones,
all slant down and in toward
the center of the span
Bridge – Problem Definition
Boundary Conditions
•
•
•
Displacement constraints in
x, y, and z are assigned to
the leftmost and rightmost
edges (red arrows).
Gravity load on both the
frame and the roadway (blue
arrows).
An additional load
representing a truck is
applied at the bridge center
(blue, denser arrows).
Bridge – Problem Definition
Domain Settings
• The concrete roadway is modeled using the shell application mode
in the Structural Mechanics Module.
• The steel frame structure is modeled using the 3D beams with cross
sectional data for a HEA100 beam (a H-beam).
Bridge – Problem Definition
Domain Equations - Static
K

N
N T  U  U 0   L 
 


0     M 
where
K is the stiffness matrix
N is the constraint matrix
 is the Lagrange multiplier
U is the solution vector
L is the load matrix
M is the constraint residual
Discretized static
problem
Bridge – Problem Definition
Domain Equations - Eigenfrequency
 D 0 U   K





 0 0     N
N T  U 
   0
0   
where
D is the mass matrix
K is the stiffness matrix
N is the constraint matrix
 is the Lagrange multiplier vector
U is the eigenvector
 is the eigenvalue
Discretized eigenfrequency
problem
Bridge – Results
Roadway deformation and
axial forces in the frame structure
Bridge – Results
Compression and tension
•
•
Green: Members in tension
Blue: Members in compression
The upper horizontal
members are in
compression and the
lower in tension.
All the diagonal members
are subject to tension
forces only while the
shorter vertical members
handle the compressive
forces. This allows for
thinner diagonal
members resulting in a
more economic design.
Bridge – Results
First Eigenmode
First mode shape
Eigenfrequency: F1 =1.8 Hz
Bridge – Results
Second Eigenmode
Second mode shape
Eigenfrequency: F1 =2.26 Hz

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