flexural stiffness

[Shz713]

I have seen in literature some researchers modified the bridge deck a uniform beam and obtained the corresponding fundamental frequencies from the well-known Euler beam vibration theory.
My query is that in some instances the moment of area about Ix axis is used, while in some circumstances is about Iy. In wikipedia, explanation is given is "I must be calculated with respect to the axis which passes through the centroid of the cross-section and which is perpendicular to the applied loading. Explicitly, for a beam whose axis is oriented along x with a loading along z, the beam's cross-section is in the yz plane".

As an example, for rectangular cross section of (200mm*400*); Ix=b*h^3/12 and Iy=b^3*h/12 which gives 2.667e-4 m4 and 1.067e-3 m4 respectively. When for free vibration of bridge (hereafter beam), natural frequencies are:

f = lambda^2/2*pi*length^2 sqrt (EI/mass density) where lambda is function of boundary condition.

After performing routine eigenvalue analysis, I realized that in fact 2nd moment of area does significantly affect the global frequency.

So, for free vibration, which one is the right moment of area? Assuming that X is along the bridge centerline, Y is perpendicular to bridge centerline and Z is orthogonal in XY plane (in direction of gravity.

Thanks to bridge experts

Shoot for the Moon, even if U miss, U still land among Stars!

 

[yakpol]

If you are interested in vertical vibrations use stiffness about horizontal axis normal to the bridge centerline (Y), for sway vibrations use stiffness about vertical axis (Z). Typical roadway or railway bridges are much stiffer about vertical axis than about transverse axis. Slender pedestrian bridges need to be checked for both direction.

 

[Shz713]

Considering zero moment of inertia is mass, and 1st moment of inertia is center of gravity and 2nd moment of inertia is moment of plain area; I agree that vertical vibration are more predominant in highway bridges.
For torsion or sway, I reckon it must be with respect to X (bridge centerline), back into definition of inertia, Z is considered as cross product of xy. Would you elaborate more why Z axis needs to be considered?

Cheers

Shoot for the Moon, even if U miss, U still land among Stars!