Calculating Deflection at first crack for wall panels (eccentric loading)

[Gousey]

Hi,

I am trying to determine the deflection of a thin precast concrete panel (used as a wall) at the point of first crack based on a vertical load on the panel.

I have obtained the cracking moment of the panel and therefore just need to calculate the deflection the panel will experience based on the vertical load.

The vertical load acting on the panel is also known - this is a UDL that can be converted as a point load over the full panel width.

It seems to me that the deflection to cause first crack would be based on the lever arm of the eccentric load and the stiffness of the panel. Is there a standard formula for this?

I have attached a sketch.

Any help is much appreciated.

 

[BAretired]

If there is no lateral load on the wall panel, then:
P.e = M[sub]cr[/sub];
so e = M[sub]cr[/sub]/P
where M[sub]cr[/sub] = cracking moment
e = eccentricity

Unless there is an initial eccentricity, there should be no deflection prior to buckling. If P > P[sub]critical[/sub], the panel will buckle and deflection at first crack is academic.

If the wall is subjected to a lateral load in addition to P, then deflection due to lateral load, augmented by axial load must be included. This would involve panel stiffness.

BA