Force Required to Bend Hose

Without information on the material, I don't think it's possible. One could assume what material would be used (based on the pressure and physical information you provided) then use that to determine the forces.

I am sorry but I guess I didn't make it clear enough.

Let us assume synthetic rubber is used, and force is applied at the two extreme ends of the 50 cm hose (like using 2 hands). Additionally, the mid-point is assumed to remain fixed i.e. it doesn't move when force applied (if this makes it any simpler).

thanks.

Reinforced, or not? If yes, what's the reinforcement. Why not ask the supplier?

Not reinforced. I am doing this solely to understand the way how force is calculated in this case using given geometric and material properties. I am not looking for any engineering purposes. So please feel free to make assumptions and help me understand the process its calculated.

many thanks.

Take a look at this:

SF, BM, slope and deflection - John F Claydon. Civil ...

For any meaningful numbers, you will need to know the properties of the specific materials involved.

Hope this helps.

You refer to forces, this will work to some extent if the center is restrained from moving in the same direction. The problem arrives when the angle is large, at that point the moment arms start to shorten.

If you apply a bending moment at each end, as taking each end into your hands and rotating the hands in opposite directions, it will provide circular bending, the hose would bend in a circular arc....

At least, it would if it wasn't for another effect; because of the compression along the inside of the bend, and the tension on the outside of the bend, the hose will become oval, reducing it's resistance to bending.

This is a long-winded way of saying that it needs a very sophisticated analysis.

A simple approach to Beam Theory

Web search "Stress intensification in pipe elbows".

i will look into both of the links you guys provided and let you know.

thanks.

I have narrowed it to the above derivation, after looking both the links and reading about simplified beam theory.
My question now would be: can I use the above derivation for a hollow hose (the above is done for a solid metal bar for small deflections). I can find moment of inertia for a hollow cylinder (hose) and look up the material's Young's modulus. Then can I use it to approximate forces at the edges if deflection at the middle is given ?
Additionally, can you guys suggest me readings for full derivation for large angles for materials like that of a hose ? you pointed out yesterday it will be an arc and so on....i am okay to deal with further complexities but would like to know where i can find that in literature.
many thanks

I cannot lead you on large angles, that is outside my expertise. The hose may collapse because of the deformation of the cross-section when bent to extreme; you see that starting in the second link I provided.

I suggest you get some pieces of various sized hoses and experiment for yourself.

All the complex formula in the world won't keep it from kinking with that length to diameter ratio if it's unsupported hose.