Important Answers: Thin Cylinders, Spheres and Thick Cylinders

THIN CYLINDERS, SPHERES AND THICK CYLINDERS

1. List out the modes of failure in thin cylindrical shell due to an internal pressure.

i)Circumferential or hoop stress and

ii)Longitudinal stress

2. What do you mean by principal plane?

The planes which have no shear stress are known as principal planes.

3. What are assumptions involved in the analysis of thin cylindrical shells?

The material of the cylinder is homogeneous, isotr i)The hoop stress distribution in thin cylinder is uniform over the cross section from inner to outer

surface since the thickness of the cylinder is thin and

ii)Weight of fluid and material of the cylinder is not taken into account.

4.What are principal planes and principal stress one end is fixed and other end is free?

Principal stress: The magnitudes of normal stress, acting on a principal plane are known as principal stresses. The plane which have no shear stress are known as principal planes.

5. Define Circumferential and Hoop stress.

A thin cylinder shell is subjected to an internal pressure, as a result of internal pressure, the cylinder has tendency to split up into two troughs is called circumferential stress. The same cylinder shell, subjected to the same internal pressure, the cylinder also has a tendency to split in to two ieces is known as Hoop stress.

6.      What   is   the  ?use   of   Mohr’s

It is used to find out the normal, tangential, resultant and principal stresses and their

planes.

7.What are the planes along which the greatest shear stresses occurs?

Greatest shear stress occurs at the planes which is inclined at 45Ëšto its normal.

8.What   is   the   radius   of   Mohr’s ?

Radius of Mohr’s circle is equal to the maximum shear stress.

9. In case of equal like principal stresses what is the diameter of the Mohr’s circle?

In case of equal like principal stresses what is the diameter of the Mohr’s circle is zero.

10. What is mean by position of principal planes?

The planes on which shear stress is zero are known as principal planes. The position of principal planes are obtained by equating the tangential stress to zero.

11. What is solid length?

The length of a spring under the maximum compression is called its solid length. It is the product of total number of coils and the diameter of wire.

Ls = nt x d

Where, nt = total number of coils.

12. Define spring rate (stiffness).

The spring stiffness or spring constant is defined as the load required per unit deflection of the spring.

K= W/y Where , W - load

y-  Deflection

13. Define pitch.

Pitch of the spring is defined as the axial distance between the adjacent coils in uncompressed state. Mathematically

Pitch=free length n-1

14. Define helical springs.

The helical springs are made up of a wire coiled in the form of a helix and are primarily intended for compressive or tensile load.

15. What are the differences between closed coil & open coil helical springs? Closed coil spring

The spring wires are coiled very closely, each turn is nearly at right angles to the axis of helix . Helix angle is less (7⁰ to 10^o)

Open coil spring

The wires are coiled such that there is a gap between the two consecutive turns. Helix angle is large (>10o)

16.                      Write the assumptions in the theory of pure torsion.

1. The material is homogenous and isotropic.

2. The stresses are within elastic limit

3.                 C/S which are plane before applying twisting moment remain plane even after the application of twisting moment.

4. Radial lines remain radial even after applying torsional moment.

5. The twist along the shaft is uniform

17.                      Define : Polar Modulus

Polar modulus is defined as the ratio of polar moment of inertia to extreme radial distance of the fibre from the centre.

18. Write the equation for the polar modulus for solid circular section