Mechanics - a branch of physical science that deals with energy and forces and their effect on bodies
1) What is flexural rigidity and its significance?
Ans. The flexural rigidity is the product of the modulus of elasticity (E) and moment of inertia (I) of the
beam about the neutral axis. (Also, it is moment of resistance M required to produce bending with
unit radius of curvature).
The significances of the flexural rigidity are as follows:-
a. The resistance of the beam for the bending depends on flexural rigidity. As we increase the
value of flexural rigidity, the strength of the beam to resist bending also increases.
b. The beam with a higher value of flexural rigidity has less value of deflection.
2) What is significance of I (moment of inertia)?
Ans. MOI is analogous to mass in rotational motion. It give considerations to mass, shape of body, and
position of axis of rotation.
a. As in case of linear motion, higher the mass, higher would be the force required to move the
body, similarly, higher the MOI higher would be torque required to give angular acceleration.
b. In beams, deflection is depend on bending resistance which is directly proportional to MOI.
Higher the MOI higher would be bending resistance and less would be deflection.
3) What is pure bending?
Ans. Pure bending (Theory of simple bending) is a condition of stress where a bending moment is
applied to a beam without the simultaneous presence of axial, shear, or torsional forces. Pure bending
occurs only under a constant bending moment (M) since the shear force (V), which is equal to
dM/dx=V, has to be equal to zero. In reality, a state of pure bending does not practically exist, because
such a state needs an absolutely weightless member. The state of pure bending is an approximation
made to derive formulas.
Kinematics of pure bending
a. In pure bending the axial lines bend to form circumferential lines and transverse lines remain
straight and become radial lines.
b. Axial lines that do not extend or contract form a neutral surface
Assumptions made in the theory of Pure Bending
a. The material of the beam is homogeneous1 and isotropic2.
b. The value of Young's Modulus of Elasticity is same in tension and compression.
c. The transverse sections which were plane before bending, remain plane after bending also.
d. The beam is initially straight and all longitudinal filaments bend into circular arcs with a
common centre of curvature.
e. The radius of curvature is large as compared to the dimensions of the cross-section.
f. Each layer of the beam is free to expand or contract, independently of the layer, above or
below it.
, 4) What shape will you prefer for storage of high pressure gas and why?
Ans. Sphere (best) and cylinder (good not best)
Circular shape: The pressure is distributed evenly and there is no concentration of force. Hence, there
is no weak or break down point in the body. (P = F/A and for constant pressure force may concentrate
at sharp edges if present)
Spherical – hard to form
Cylindrical – Easy to form
5) Describe toughness, rigidity, hardness, stiffness.
Ans. Toughness – Ability to absorb strain energy till fracture point. Toughness = strain energy at
fracture point
Modulus of toughness – Toughness/volume
Resilience – Strain energy up-to (at point of consideration) elastic limit.
Proof resilience – Strain energy at elastic limit.
Modulus of resilience – Proof resilience/volume
Stiffness – Load per unit deflection
Compliance – inverse of stiffness
Flexural rotation – slope of beam
Axial rigidity – Axia force required to produce unit strain in axial direction. = EA
Flexural rigidity – EI
Torsional rigidity – GJ (where J is polar MOI). It is measure of torque required to produce unit angle
twist in a unit length of bar (=TL/theta).
Torsional stiffness – GJ/L. Torque required to produce unit angle of twist. (=T/theta)
Flexibility – inverse of stiffness
6) What is signify by area of stress-strain diagram and force-deflection diagram?
Ans. Stress-strain diag. – strain energy absorbed per unit volume
Force-displacement diag. – total strain energy absorbed
7) What is section modulus. What is its significance.
1) What is flexural rigidity and its significance?
Ans. The flexural rigidity is the product of the modulus of elasticity (E) and moment of inertia (I) of the
beam about the neutral axis. (Also, it is moment of resistance M required to produce bending with
unit radius of curvature).
The significances of the flexural rigidity are as follows:-
a. The resistance of the beam for the bending depends on flexural rigidity. As we increase the
value of flexural rigidity, the strength of the beam to resist bending also increases.
b. The beam with a higher value of flexural rigidity has less value of deflection.
2) What is significance of I (moment of inertia)?
Ans. MOI is analogous to mass in rotational motion. It give considerations to mass, shape of body, and
position of axis of rotation.
a. As in case of linear motion, higher the mass, higher would be the force required to move the
body, similarly, higher the MOI higher would be torque required to give angular acceleration.
b. In beams, deflection is depend on bending resistance which is directly proportional to MOI.
Higher the MOI higher would be bending resistance and less would be deflection.
3) What is pure bending?
Ans. Pure bending (Theory of simple bending) is a condition of stress where a bending moment is
applied to a beam without the simultaneous presence of axial, shear, or torsional forces. Pure bending
occurs only under a constant bending moment (M) since the shear force (V), which is equal to
dM/dx=V, has to be equal to zero. In reality, a state of pure bending does not practically exist, because
such a state needs an absolutely weightless member. The state of pure bending is an approximation
made to derive formulas.
Kinematics of pure bending
a. In pure bending the axial lines bend to form circumferential lines and transverse lines remain
straight and become radial lines.
b. Axial lines that do not extend or contract form a neutral surface
Assumptions made in the theory of Pure Bending
a. The material of the beam is homogeneous1 and isotropic2.
b. The value of Young's Modulus of Elasticity is same in tension and compression.
c. The transverse sections which were plane before bending, remain plane after bending also.
d. The beam is initially straight and all longitudinal filaments bend into circular arcs with a
common centre of curvature.
e. The radius of curvature is large as compared to the dimensions of the cross-section.
f. Each layer of the beam is free to expand or contract, independently of the layer, above or
below it.
, 4) What shape will you prefer for storage of high pressure gas and why?
Ans. Sphere (best) and cylinder (good not best)
Circular shape: The pressure is distributed evenly and there is no concentration of force. Hence, there
is no weak or break down point in the body. (P = F/A and for constant pressure force may concentrate
at sharp edges if present)
Spherical – hard to form
Cylindrical – Easy to form
5) Describe toughness, rigidity, hardness, stiffness.
Ans. Toughness – Ability to absorb strain energy till fracture point. Toughness = strain energy at
fracture point
Modulus of toughness – Toughness/volume
Resilience – Strain energy up-to (at point of consideration) elastic limit.
Proof resilience – Strain energy at elastic limit.
Modulus of resilience – Proof resilience/volume
Stiffness – Load per unit deflection
Compliance – inverse of stiffness
Flexural rotation – slope of beam
Axial rigidity – Axia force required to produce unit strain in axial direction. = EA
Flexural rigidity – EI
Torsional rigidity – GJ (where J is polar MOI). It is measure of torque required to produce unit angle
twist in a unit length of bar (=TL/theta).
Torsional stiffness – GJ/L. Torque required to produce unit angle of twist. (=T/theta)
Flexibility – inverse of stiffness
6) What is signify by area of stress-strain diagram and force-deflection diagram?
Ans. Stress-strain diag. – strain energy absorbed per unit volume
Force-displacement diag. – total strain energy absorbed
7) What is section modulus. What is its significance.
