Question

. A hollow cylinder 2 m long has an outside diameter of 50 mm and inside diameter of 30 mm. If the cylinder is carrying a load of 25 KN, find the stress in the cylinder. Also find the deformation of the cylinder, if the value of modulus of elasticity for the cylinder material is 100 GPa.

Answer 1

Answer:

(i) Stress in the cylinder, σ = 19.9 MPa

(ii) Deformation of the cylinder, ΔL = 0.4mm

Explanation:

Given

      L = 2 m = 2 000 mm

      D = 50 mm

      d = 30 mm

      P = 25 kN = 25 000 N

      E = 100 GPa = 100 000 MPa

Solution

  To find

          (i) Stress in the cylinder, σ

           (ii) Deformation of the cylinder, ΔL

(i) Stress in the cylinder, σ =$\frac{P}{A}$

       $A=\frac{\pi }{4} ((D)^{2} -(d)^{2} )$

      $A=\frac{\pi }{4} ((50)^{2} -(30)^{2} )$

     $A=1256.63 mm^{2}$

     σ   $=\frac{25000}{1256.63} =19.9 MPa$

     ∴  σ  $=19.9 MPa$

(ii) Deformation of the cylinder, ΔL =$\frac{P l}{AE}$

         =$\frac{25000*2000}{1256.63*100000} =0.398mm$

       ∴  ΔL=0.4mm

To learn more about stresses in the cylinder, visit

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To learn more about the deformation of the cylinder, visit

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