1. Example: Bridge

2. 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.

3. Geometry Bridge – 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

4. Boundary Conditions Bridge – Problem Definition
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).

5. Domain Settings Bridge – Problem Definition
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).

6. Domain Equations - Static
Bridge – Problem Definition
Domain Equations - Static
Discretized static
problem
where
K is the stiffness matrix
N is the constraint matrix
L is the Lagrange multiplier
U is the solution vector
L is the load matrix
M is the constraint residual

7. Domain Equations - Eigenfrequency
Bridge – Problem Definition
Domain Equations - Eigenfrequency
Discretized eigenfrequency
problem
where
D is the mass matrix
K is the stiffness matrix
N is the constraint matrix
L is the Lagrange multiplier vector
U is the eigenvector
l is the eigenvalue

8. Roadway deformation and axial forces in the frame structure
Bridge – Results
Roadway deformation and axial forces in the frame structure

9. Compression and tension
Bridge – Results
Compression and tension
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

10. First Eigenmode Bridge – Results First mode shape
Eigenfrequency: F1 =1.8 Hz

11. Second Eigenmode Bridge – Results Second mode shape
Eigenfrequency: F1 =2.26 Hz