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]
How can the stability of the bridge be analyzed?
[ms]X_tilde_dd + [[cs]+[RA]]x_tilde_d + [[ks] + [Ka]]x = 0 Homogeneous solution
What tests are required to identify the aerodynamic forces?
- For Fi(xi0,xi0_d,si0) static/quasi static tests can be done
- For dxi_d terms forced motion tests can be done
- For buffetign term active turbulence generation can be done
What is reduced velocity?
Reduced velocity is equal to the time to pass a characteristic length to the time for structure cycle = (1/f)/(b/U) = U*
If U* «_space;then comparable to aero time
If U*»_space; then static coefficients can be used
What is reduced velocity?
Reduced velocity is equal to the time to pass a characteristic length to the time for structure cycle = (1/f)/(b/U) = U*
If U* «_space;then comparable to aero time
If U*»_space; then static coefficients can be used
Discuss forced motion test
Forced motion test allows for measuring static coefficients and flutter derivatives. Torsional, Vertical, Horizontal and Vertical&Horizontal forced motion tests can be done.
For each input a transfer function Hi(Ω) is computed for output. Hiθ is defined at each circular frequency or reduced velocity. Hi has the same Ω as the input, but a different phase.
What are flutter derivatives?
Aerodynamic transfer functions are usually presented through “Flutter derivatives” coefficients. They are functions of Reduced Velocity and Mean AoA
For V*» flutter derivatives should asymptotically match TQS theory.
How can the aerodynamic admittance function be calculated?
With the active turbulence generator. It consists of a dynamometric section and moving wings and generate periodic turbulence. Admttance functons are used for the buffeting matrix and also consist of real and imaginary part. They also depend on the frequency (or reduced velocity)
