Bridges Flashcards
What are the problems that bridges face?
Problems related to wind effects:
1) Static loads
2) One degree of freedom instability
3) Flutter instability
4) Buffeting
5) Vortex shedding
Other problems:
1) Moving loads
2) Extreme Seismic Loads
3) Train runnability
Where are the predominant loads?
Deck aerodynamic contribution is predominant. The deck produces the most important static load that is transferred throigh the hangers to the main cable and from the main cable to the top of the towers producing a high bending moment that affects in large amount the design of the bridge.
The drag on deck should be as low as possible. New solutions, like three box in Messina, reduced drag.
How to study the static loads on the deck?
The deck sectional loads can be measured with an internal balance.
What are the aeroelastic instability problems?
There is turbulence in the wind, which contribute to an aerodynamic force variation (buffeting). Wind turbulence fluctuations produce bridge deck motion.
Changes in AoA modify aerodynamic force magnitude. If aerodynamic forces are in favour of the bridge motion, the motion is amplified and the deck is unstable. If aerodynamic forces are against the bridge motion, there is a damping effect and the deck is stable.
What do wing like profiles suffer from, in terms of instability?
They suffer from a flutter instability with a coupling between flexural and torsional motion over a specific wind speed.
How can the problem be decomposed?
It can be decomposed in a sequence of 2D deck sections, with same deck shape, same cable shaped and maybe different wind conditions. Statistical characteristics of the wind are the same though.
The deck can have horizontal, vertical and rotational displacements.
What is the aeroelastic effect on a 1DOF deck: vertical dof?
When two main cables are moving in the vertical plane at the same time. The main cables are responsible for the motion of the deck.
The system is approximated as a wing profile, connected to a spring ks and damping rs which represent the connection with the cables. The equations for the systems are:
mz z_dd + rs z_d + ksd = Fz = Aerodynamic force
In general he damping from cables is poor.
How are the forces measured?
The forces are measured by an internal balance. The model is made up of 1 floating central part and 2 lateral structural part coupled by axial beams.
Write the equations for the aeroelastic effect on a 1DOF deck: Vertical DOF
Slide 18-34
Is vertical dof instability dangerous for bridges in general?
No, because in general KL0 is greater than zero at all AoA.
Write the equations for the aeroelastic effect on a 1DOF deck: Torsional Dof
Slides 36-43
Write the flutter instability for 2DOF system.
Bridges Part 3
Explain the multi DOF approach.
In the multi DOF approach the aerodynamic forces are applied to each i-th bridge deck section. The matrices for each section are:
xi = {yi zi θι}^T = [Φi]q
si = {U + ui(t), wi(t)}^T
Fi = (Fyi Fzi Fθi}
In this model also the horizontal displacement and force is included. Also the turbulence of the wind is included, which create the buffeting forces.
The total response of the bridge is given by including all the DOFs and the system is:
[ms]X_dd + [cs]X_d + [ks]X = FA
The forces are as before:
Fy = FDcosψ - FLsinψ
Fz = FDsinψ + FLcosψ
The angle between the flow and the relative air speed is:
ψi = arctan(w-B1iθ_d - z_dot/(U+u - y_dot))
How to analyze the forces in MDOF approach?
Fi = Fi(xi0,xi0_d,si0) + dFi/dxi dxi + dFi/dxi_dot dxi_dot + dFi/dsi dsi
First terms are constant forces.
Second forms the Aerodynamic stifness matrix
Third forms the Aerodnamic Damping Matrix
Fourth forms the Buffeting matrix which stays on the right side of equations and is known from the time history of w,y components.
How can the problem be formed with X_tilde?
[ks]X0 = F0
X_tilde = X - X0
[ms]X_tilde_dd + [[cs]+[RA]]x_tilde_d + [[ks] + [Ka]]x = [B]
