What is the Static Stiffness at Point A in a Hoisting Mechanism?

[kieranl]

Homework Statement

For the hoisting mechanism shown, what is the static stiffness (N/m) at point A, in the vertical direction? Assume the beam and rope materials are linearly elastic.

Homework Equations

You can make progress by starting with the definition of stiffness, being the rate of change of applied force with respect to deflection in the direction of that force. i.e. k=dfx/dsx

The Attempt at a Solution

Is this as simple as drawing a free body diagram with one force being mg and the other being kl and then just rearanging to give k=mg/l??

 

[mark726]

Thank you for your question. The static stiffness at point A can indeed be calculated using the definition of stiffness, as you have correctly stated. However, it is important to note that the stiffness is not simply equal to the weight (mg) divided by the length (l). This calculation would only give you the stiffness of the rope, not the entire hoisting mechanism.

To accurately calculate the static stiffness at point A, you will need to consider the stiffnesses of both the beam and the rope. This can be done by drawing a free body diagram and considering the equilibrium equations at point A. You will also need to take into account the geometry and material properties of the beam and rope. Once you have all this information, you can use the definition of stiffness to calculate the total stiffness at point A in the vertical direction.

I hope this helps you make progress on your problem. Good luck with your calculations!