Question

show that the rigidity of hollow cylinder of the same material, same mass and same length is greater than that of a solid cylinder ​

Answer 1

Step-by-step explanation:

By stronger I assume you are referring to bending stiffness, S . That is, how much a structure or beam bends for a certain applied force. S is proportional to EI , where E is the Young’s modulus of the material (a material property) and I is the second moment of area (a shape property).

S∝EIL3

If you look up these properties you will find many textbooks that give you a mathematic derivation of the second moment of area for many shapes, such as cylinders, squares, i-beams etc..

For a circular section:

I=π4r4

For a hollow circular section:

I=π4(r4o−r4i)

where r is the radius of a cylinder, ro is the outer radius of a hollow cylinder and ri is the inner radius of a hollow cylinder. From this you could easily prove that a beam of one shape (certain value of I ) has a greater bending stiffness than another since everything else in the formula would be the same, i.e. same Young’s modulus and same length.

I can recommend Materials Selection in Mechanical Design by Michael F. Ashby as a great textbook for this kind of work.

Answer 2

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