bridge - 0.61MB - Comsol

frizzflowerΠολεοδομικά Έργα

29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

98 εμφανίσεις

Example:

Bridge


Introduction


S
tatic and eigenfrequency analys
e
s are conducted for a bridge.


The bridge is model
ed

using 3D beams and shells elements
available in the Structural Mechanics Module.

Bridge

Geometry

Brid
g
e



Problem Definition


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

Brid
g
e



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).


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).






Brid
g
e


Problem Definition

Domain Settings

Domain Equations
-

Static

Bridge


Problem Definition






















M
L
U
U
N
N
K
T
0
0
Discretized static

problem


where

K
is the stiffness matrix

N
is the constraint matrix



楳⁴桥⁌杲g湧攠浵m瑩灬楥r

U
is the solution vector

L
is the load matrix

M
is the constraint residual

Domain Equations
-

Eigenfrequency

Bridge


Problem Definition

0
0
0
0
0






























U
N
N
K
U
D
T

Discretized eigenfrequency


problem


where

D
is the mass matrix

K
is the stiffness matrix

N
is the constraint matrix



楳⁴桥⁌杲g湧攠浵m瑩灬楥爠癥捴vr

U
is the eigenvector



is the eigenvalue

Bridge


Results

Roadway deformation and

axial forces in the frame structure

Bridge


Results


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.

Green: Members in tension

Blue: Members in compression

Compression and tension

Bridge


Results

First Eigenmode

First mode shape

Eigenfrequency: F
1

=1.8 Hz

Bridge


Results

Second mode shape

Eigenfrequency: F
1

=2.26 Hz

Second Eigenmode