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Question answers increase the understanding and clarity of the subject. It helps to apply the fundamentals in the practical applications. It is really the ultimate objective in real life.

Q. What is the energy of distortion or shear strain energy?

ANS: Every object in universe is under a number of forces. Thus, it is under complex loading. From the complex loading, one can determine the three principal stresses σ1, σ2 and σ3 respectively. ASSUME

(i) these principal stresses as tensile and

(ii) σ1> σ2 > σ3

Then energy of distortion OR shear strain energy is

usse=(1/12G)[ (σ1–σ2)2 + (σ2—σ3)2 + (σ3—σ1)2]

NOTE: if any of the three principal stresses σ1, σ2 and σ3 is not tensile, then respective sign must be used in the above relation.

Q. Explain the necessity of the theories of failure.

ANS: When identical jobs (Same shape and same size) of different materials are tested in the lab under identical loading, it is found that failure of different materials take place differently. Therefore we need a way to explain these different types of failures under identical loading. Then only these theories of failure help us. Thus these are needed to explain different failures under identical testing.

Q. Define stiffness of a spring or define a spring constant.

ANS: Spring is a highly elastic body. Force required to cause unit deflection is called spring stiffness.

K = W/δ    N/mm

Where k is the stiffness

W is the load acting on the spring

δ  is the deflection under the load W

Q. For what purpose, cylindrical and spherical vessels are used?

ANS: Cylindrical vessel are used as process vessels as boilers for producing steam.

These vessels are used as storage vessels as LPG cylinders and Oxygen cylinders.

Spherical vessels are used only for storage vessels as these can store more volume in a given space.

Q. State Lame’s equations.

ANS: Lame’s equations are for stresses in a thick vessel. The three stresses are hoop stress

σh, radial stress, σr and longitudinal stress σl

Lame’s equations are

σh =α + β/r2

σr =α — β/r2

Where α and β are Lame’s constant. These are found from the boundary conditions like

use σr =pi at r = ri

and σr =po at r = r0

σl =α  and σl is negligible.

Q. List the types of stresses produced in a rotating disc of uniform thickness.

ANS. Variable hoop and radial stresses are produced in a rotating disc of uniform thickness.

Q What is a trapezoidal section and why is this used in initially curved beams as in a hook of a crane?

ANS: A trapezoidal section is a quadrilateral with two parallel and two non- parallel sides. This is used in a crane hook

because its area is variable which makes stress nearly uniform in the innermost and outermost fibers

Q. Where does the maximum shear stress occurs in an I section?

ANS: It occurs in the center of the web section of the I section.

Q. Explain the importance of the full length leaf in a leaf spring.

ANS: One full length leaf is necessary for mounting of the spring on the vehicle. Any extra full length leaf takes the transverse shear force which is maximum at the ends.

Q. For what purpose are compound cylinders used?

ANS: These are used to resist high pressures. As it is difficult to make a cylinder from a single thick plate, it is made with number of thin cylinders by hoop shrinking. Such a thick vessel made from thin vessels is called a compound cylinder.

Q. Distinguish between longitudinal and hop stresses in a thick cylinder.


Sr. No. Longitudinal stress Hoop stress
1. This stress is in the length direction. Hoop stress is in the tangential direction.
2. The magnitude of this stress is constant.  Magnitude of hoop stress is variable.
3.  Symbol of this stress is σl. Its symbol is σh.
4. Magnitude of this stress is quite small. Its  magnitude is quite large. It is greater than the fluid pressure
5. This stress is tensile. It is also tensile.


Q. For the crane hook, locate the plane which is severely stressed.

ANS: The innermost curve of the crane hook is severely stressed.

Q. Define strain energy.

ANS: When a body is under an external force, strain is produced in the body. Thus force moves through some distance. Hence the work is done on the body while at rest. This work is stored in the body as long as it is strained. This work is called strain energy. Its symbol is U. Its units are Joules. It is given by the formula

U =(1/2) F δl = σ2x volume/2E=( σ2/2E)x Volume