How do I calculate tilt stiffness as a function of linear stiffness?

[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 rit the expression as a function of the angle?

Thanks

Note I have posted this in https://www.physicsforums.com/showthread.php?t=553883. which I believe is the correct place.

 

[eljose79]

Hello,

Thank you for sharing your attempt and asking for feedback. I am also not sure if the left-hand side attempt is correct. Let's discuss your queries one by one.

1) To calculate the actual force, you can use the equation F = kx, where F is the force, k is the linear stiffness, and x is the displacement. In this case, x would be the distance from the pivot point to the point where the force is applied, which is the moment arm. So, the force would be F = k * d, where d is the moment arm.

2) To write the expression as a function of the angle, you can use trigonometry. Let's say the angle is theta, then the moment arm would be d = L * sin(theta), where L is the length of the lever arm. Substituting this into the equation above, we get F = k * L * sin(theta). This shows that the force is directly proportional to the length of the lever arm and the sine of the angle.

I hope this helps. Let me know if you have any further questions or if you need clarification on anything. Also, it's great that you have posted this in a physics forum, as you can get feedback from other experts as well. Good luck with your calculations!