How Do You Calculate Tilt Stiffness as a Function of Linear Stiffness and Angle?

[bugatti79]

Folks,

See attached. I wish to calculate the tilt stiffness as a function of some linear stiffness.

My attempt is on the RHS of FBD and there is somebody elses attempt on the LHS. I am not sure if it is right.
I have 2 queries

1) My attempt on the RHS I wrote the expression of f in terms of linear stiffness (data of which I have let's say 100N/mm). How do I get the actual force? Ie, I am not sure with moment arm to multiply this stiffness value by?

2) How to write the expression as a function of the angle?

Thanks

NOte this has been posted in
https://www.physicsforums.com/showthread.php?t=553861 which I believe was the wrong place.

Regards

 

[Navin A S]

,The tilt stiffness of a system can be calculated using the following equation: Tilt stiffness = Moment arm * Linear stiffness where the Moment arm is the distance between the point of application of force and the point of rotation, and the Linear stiffness is the stiffness of the linear element in the system. For example, if you have a system with a spring attached to a beam, the Moment arm would be the distance between the spring and the center of rotation of the beam, and the Linear stiffness would be the stiffness of the spring. To calculate the Tilt stiffness, you would multiply the Moment arm by the Linear stiffness. To write the expression as a function of the angle, you would need to consider the Moment arm, which is a function of the angle. For example, if the Moment arm is a constant, then the Tilt stiffness would be a linear function of the angle.