STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

CE6306/CE8395 STRENGTH OF MATERIALS
PREPARED BY,
ARAVINDKUMAR B, ME
2 Marks
UNIT – 1 STRESS STRAIN AND DEFORMATION OF SOLIDS
1. Define stress
The force of resistance per unit area, offered by a body against deformation is
known as stress. Mathematically stress is written as,
Where σ = Stress
P= External force or load
A= Cross- Sectional area
2. Define strain
When a body is subjected to some external force, there is some change of
dimension of the body. The ratio of change dimension of the body to the
original dimension is known as strain.
Strain may be:
1. Tensile strain 2. Compressive strain
3. Volumetric strain, and 4. Shear strain.
3. Define elastic limit
The limiting value of force up to and with in which, the deformation
completely disappears on the removal of the force. The value of stress
corresponding to this limiting force is known as the elastic limit of the
material
4. State Hokes law
Hokes’s Law states that when a material is loaded within elastic limit; the
stress is proportional to the strain produced by stress.
5. Define shear stress and shear strain
The stress induced in a body, when subjected to two equal and opposite forces
which are acting tangentially across the resisting section, as a result of which
the body tends to shear off across the section, is known as shear stress. The
corresponding strain is known as shear strain. The shear stress acts tangential
to the area. It is represented by τ.
6. Define poison’s ratio
The ratio of lateral strain to the longitudinal strain is constant for a given
material, when the material is stressed within the elastic limit. This ratio is
called Poisson’s Ratio and it is generally denoted by μ

7. Define Young’s modulus
The ratio of tensile stress or compressive stress to the corresponding strain is a
constant. This ratio is known as Young’s Modulus.
8. Define Modulus of Rigidity.
The ratio of the shear stress to the corresponding shear strain within elastic
limit is known as Modulus of Rigidity or Shear Modulus. This is denoted by C
or G or N.
9. Define Factor of Safety
It is defined as the ratio of ultimate tensile stress to the working stress.
Mathematically it is written as
10. Define Strain energy
Whenever a body is strained, energy is absorbed in the body. The energy,
which is absorbed in the body due to strained effect, is known as strain energy.
11. Define bulk modulus
When a body is subjected to the mutually perpendicular like and equal direct
stresses, the ratio of direct stress to the corresponding volumetric strain is
found to be constant for a given material when the deformation is within a
certain limit. This ratio is known as bulk modulus.
12. What is compound bar?
A bar, made up of two or more bars of equal lengths but of different materials
rigidly fixed with each other and behaving as one unit for extension or
compression when subjected to axial tensile or compressive loads, is called a
composite bar.
13. Define lateral strain
The strain at right angle to the direction of applied load is known as lateral
strain.
14. Define Thermal stresses.
The Stresses induced in a body due to change in temperature are known as
thermal stresses.
15. Define thermal strain
If the ends of the body are fixed to rigid supports, so that its expansion is
prevented, then compressive stress and strain will be set up in the rod. This
strain is known as thermal strain.
16. What is the relation between three modules?
E = 2C (1+µ)
E = 3K (1-2µ)
Where, E= Young’s Modulus

C = Modulus of Rigidity
K = Bulk Modulus
µ = Poisson’s Ratio
17. Define Resilience.
The Total strain energy stored in a body is commonly known as resilience.
Whenever the straining force is removed from the strained body, the body is
capable of doing work. Hence the resilience is also defined as the capacity of
strained body for doing work on removal of straining body.
18. Define Proof Resilience
The Maximum strain energy stored in a body is known as proof resilience. The
strain energy stored in the body will be the maximum when the body is
stressed upto elastic limit. Hence the proof resilience is the quantity of strain
energy stored in ablody when strained up to elastic limit.
19. Define Modulus of Resilience.
It is defined as the proof resilience of a material per unit volume.
Mathematically,
20. What is the difference between suddenly applied load and Impact load?
If the load is constant throughout the process of deformation of the body, such
a type of loading is known as suddenly applied load.If the load is dropped
from certain height, before the load commences to stretch the bar that type of
loading is known as Impact load.
UNIT – II BEAMS-LOAD AND STRESSES
1. Define beam?
A beam is a structural member subjected to a system of external forces at right
angles to its axis.
2. What is mean by transverse loading on beam?
If the loads on the beam are perpendicular to the axis of the beam then it is
called transverse type of loading.
3. What is cantilever beam?
A beam which is fixed at one end and free at the other end is known as
cantilever beam.
4. What is simply supported beam?
A beam supported or resting freely on the supports at its both ends is
known as simply supported beam.
5. What meant by overhanging beam?
If the end portion of a beam is extended beyond the support, such beam is
known as overhanging beam.
6. What is mean by concentrated loads?
A concentrated load is one which is considered to act at a point, although in
practice it must really be distributed over a small area.
7. What is uniformly distributed load?

A uniformly distributed load is one which is spread over a beam in such a
manner that rate of loading “w” uniform along the length. The rate of loading
is expressed as w N/m run. Uniformly distributed load is, represented by
U.D.L.
8. What are the different types of beams?
1. Cantilever beam 2. Simply supported beam 3. Over hanging beam
4. Fixed beam 5. Continuous beam.
9. Define point of contra flexure? In which beam it occurs?
At some point, the B.M. is zero after changing its sign from positive from
negative or vice-versa. That point is known as the point of contra flexure or
point of inflexion
10. What is meant by positive or sagging BM?
The bending moment at a section is considered positive if the bending
movement at that section is such that it tends to bend the beam to a curvature
having concavity at the top as often called sagging moment
11. What is meant by negative or hogging BM?
Similarly the bending movement(B.M.) at a section is considered negative if
the bending movement at that section is such that it tends to bend the beam to
a curvature having convexity at the . The positive B.M. is often called sagging
moment and negative B.M. as hogging moment.
12. Define shear force and bending moment?
The algebraic sum of vertical forces at any section of a beam to the right or
left of the section is known as shear force.
The algebraic sum of moments of all the forces to the right or left of the
section is known as bending moment.
13. When will bending moment is maximum?
The bending moment will be maximum at a point where the shear force is
minimum.
14. What is maximum bending moment in a simply supported beam of span
‘L’subjected to UDL of ‘w’ over entire span?
15. In a simply supported beam how will you locate point of maximum
bending moment?
The maximum bending moment in a simply supported beam will be at the
point where the shear force line crosses the base line.
16. What is shear force and bending moment diagram?
The shear force diagram is one which shows the variation of the shear force
along the length of the beam.
The bending moment diagram is one which shows the variation of bending
moment along the length of the beam.
17. What are the types of loads?
The different types of loads are
1. Concentrated load or point load
2. Uniformly Distributed load
3. Uniformly Varying load.

18. What is bending stress?
The stresses introduced by bending moment are known as bending stresses
19. Define pure bending.
If a length of beam is subjected to a constant bending moment and no shear
force(Zero shear force) then the stresses setup in that length of the beam due to
bending moment only and that length of the beam is said to be in pure bending
or simple bending.
20. Write the theory of simple bending equation?
21. State any three assumptions of Theory of simple bending.
1. The material of the beam is homogeneous and isotropic
2. The value of young’s modulus of elasticity is the same in tension and
Compression.
3. The transverse sections which were plane before bending remain plane after
Bending also.
22. What is neutral layer of a beam?
If a beam is subjected to simple bending the top layer of beam is subjected to
compression and the bottom layer is subjected to tension. At a level between
top and bottom, there will be a layer which is neither shortened nor elongated.
This layer is known as Neutral layer.
24. Define Moment of Resistance.
Due to pure bending, the layers above NA are subjected to compressive
stresses where as the layers below NA are subjected to tensile stresses. Due to
these stresses, the forces will be acting on the layers. These forces will have
moment about the NA. The total moment of these forces about the NA for a
section is known as Moment of Resistance of that section.
25. Define Section Modulus.
Section modulus is defined as the ratio of moment of inertia of a section about
the NA to the distance of the outer most layers from the NA. It is denoted by
the symbol Z. Mathematically,

UNIT – III TORSION
1. Define Torsion?
A shaft is said to be in torsion, when equal and opposite torques are applied at
the two ends of shaft. The shaft is subjected to a twisting moment. This causes
the shear stresses and shear strains in the material of the shaft.
2. What are the assumptions made in torsion equation.
Torsion is based on the following assumptions:
 The material of the shaft is uniform throughout.
 The twist along the shaft is uniform.
 The shaft is uniform circular section throughout.
 Cross-sections of the shaft, which are plane before twist, remain plain
after twist.
 All radii which are straight before twist remain straight after twist.

3. Define polar modulus
Polar modulus is defined as the ratio of the polar moment of inertia to the
radius of the shaft.
4. Write down the expression for power transmitted by a shaft.
2πNTmean
Power(Watts) = ----------------- Where,
60
N = Speed of the shaft, rpm
T = Mean Torque transmitted, Nm.
5. Write the polar modulus for solid shaft and hollow shaft.
π D3
Zp = ----------- where D = Diameter of solid shaft
16
π [D 4 - D 4]
o i
Zp = --------------------- where, Do = Outer Diameter of hollow shaft
16 Do Di = Inner diameter of Hollow shaft
6. Why hollow circular shafts are preferred when compared to solid
circular
shafts?
For the same power transmission and Material, the weight of hollow
shafts are less compared to solid shaft.
7 . Write torsional equation
T τ GӨ
------ = ------ = ------ where,
J r l
T = Torque Transmitted, Nm
J = Polar Moment of Inertia, m4
r = Radius of shaft, m
G = Modulus of rigidity, N/m2
Ө = Angle of Twist, Radians, l = Length of Shaft, m

8. Write down the expression for torque transmitted by hollow shaft.
Π Do
4 – Di
4
Torque transmitted by a hollow shaft – T = -------τ[-----------------]
16 Do
Where Do = Outer Diameter of hollow shaft
Di = Inner diameter of Hollow shaft
Τ = Shear stress induced in the outer surface of the shaft
9. Write down the equation for maximum shear stress of a solid circular
section in diameter D when subjected to torque T in a
solid shaft.
The maximum shear stress induced at the outer surface of the solid shaft.
10. Define torsional rigidity
Tensional rigidity or stiffness of the shaft is defined as the product of modulus
of rigidity (C) and polar moment of inertia of the shaft (J).
Tensional rigidity = C x J.
11. What is composite shaft?
A shaft made up of two or more different materials and behaving as a single
shaft is known as composite shaft.
12. What is a spring? Name two important types of spring.
Springs are elastic bodies which absorb energy due to resilience. The
absorbed energy may be released as and when required. The two important
types of springs are
1. Laminated or leaf springs
2. Helical springs
13. State any two functions of springs.
1. It will absorb energy when it is loaded and releases the absorbed
energy as and when required
2. It will act as cushion
14. Define helical springs specify the type of helical springs
Helical springs are the thick spring wires coiled in to a helix
The two types of helical springs are
(i) Close coiled helical springs
(ii) Open coiled helical springs.

15. What is solid length of a spring?
The solid length of spring means the distance between the coils when the
coils are touching each other. There is no gap between the coils. The soilid
length is given by
Solid length = Number of coils x Diameter of the wire = nX d
16. Define spring rate (stiffness).
The stiffness of the spring is defined as the load per unit deflection.
W
S = ---------
δ
Where W = Load and δ = Deflection
17. Define pitch of the spring.
The distance between to consecutive coils is known as pitch of the spring.
18. What is spring index (C)?
The term Spring index in relation to springs it means the ratio of the mean
diameter of the spring to the diameter of the wire. The preferred index range
is 4 to 12.
19. What is free length of spring?
This is the length over all of the spring in the fully unloaded position (free
position).
21. What are the differences between closed coil & open coil helical springs?
Closed coil Open coil
The wire is coiled so close that the The spring wire is coiled in such away
plane containing each turn is nearly that, there is a large gap between the
at right angle to the axis of helix two consecutive turns and takes
compression load also.
The helix angle is less than 10o The helix angle is greater than 10o
Due to loading, spring will elongate Due to loading, spring will contract
22. What is the use of wahl’s factor?
(i) The whals factor is used to account the stress due to direct
shear and curvature stress of spring.
(ii) It is used to calculate shear stress induced in a helical spring bt
considering shear stress due to twisting.
23. What kind of stress is introduced when an axial load acts on a
closed coil spring?
Shear stress is introduced when an axial load acts on a closed coil
spring.In addition direct shear stress due to load is introduced. Stress
due to curvature of the wire is also introduced.

24. What are the assumptions made in a closed coil helical spring
subjected to axial load?
The assumptions are
1. An element of an axially loaded helical spring, behaves essentially as a
straight bar in pure tension.
2. The planes perpendicular to the bar axis do not warp or distort during
deformation.
25. List out the uses of helical springs.
Automobiles and railway carriages
Shock absorbers
Reciprocating mechanisms and clock springs.
UNIT – IV DEFLECTION IN BEAMS
1.What are the methods for finding out the slope and deflection at a section?
(i) Double Integration Method
(ii) Moment Area method
(iii) Macaulay’s method
(iv) Conjucate beam method
2. State mohr’s theorems.
(i) The change of slope between any two points is equal to the net area of the
B.M Diagram between these points divided by EI
(ii) The total deflection between any two points is equal to the moment area of
B.M Diagram between the two points about the last point divided by EI.
3. What is the relation between slope and deflection?
If y= deflection
Slope = dy/dx
4. State the equation for bending moment and shear force.
BM = EI d2y/dx2
SF = EI d3y/dx3
5. Give expression for determining slope at the supports of a simply supported
beam carrying a point load at the centre.
Өa = Өb =
6. Give expression for determining deflection of a simply supported beam
carrying a point load at the centre.
yc= -

7. Give expression for determining slope and deflection of a simply supported
beam carrying a UDL over the entire span.
Өa = Өb =
yc =
8. What are the steps to be followed in determining slopes and deflections at
any point of a beam using Macaulay’s method?
(i) Brackets are to be integrated as a whole.
(ii) Constants of integrations are written after the first term
(iii) The section, for which B M equation is to be written, should be taken in
the last part of the beam.
9. What is the condition for maximum deflection in a beam.?
For maximum deflection, the slope dy/dx must be equal to Zero.
10. State the expression for determining slope in area moment method.
Area of BMD
Өb = ------------------
EI
11. State the expression for determining deflection in area moment method.
AX
y = ---------
EI
12. What is a column?
A vertical member of a structure, which is subjected to axial compressive
load and is fixed at both of its ends is known as a column.
13. What is a strut?
Strut is a member of a structure which is not vertical or whose one or both
of its ends are hinged or pin jointed.
14. Specify how the long and short column will fail?
All short columns fail due to crushing where as long column will fail due to
buckling or crushing.
15. What is buckling load?
The load at which the column just buckles is known as buckling load or
critical load or crippling load.

16. Give the expressions for a column by Euler’s formula for different end
conditions.
P = When both ends are hinged
P = When one end is fixed and other end is free
P = When both ends are fixed
P = When one end is fixed and other end is hinged.
17. What is effective length of a column?
The effective length of a given column with given end conditions is the
length of an equivalent column of the same material and cross section with
hinged ends, and having the value of crippling load equal to that of the
given column.
18. What is slenderness ratio?
Slenderness ratio is the ratio of the effective length of the column to the
least radius of gyration.
Mathematically, Slenderness ratio =
19. State the limitation of Euler’s formula.
If the slenderness ratio is small, the crippling stress will be high. But for the
column material, the crippling stress cannot be greater than the crushing
stress. Hence when the slenderness ratio is less than a certain limit,
Euler’s formula gives a value of crippling stress greater than the crushing
stress. In this limiting case, we can find the value of l/k for which crippling
load equal to crushing stress.
20. Specify the expression for Rankine’s formula.
= +
P = Crippling load by Rankine’s formula
Pc = Crushing load
PE = Crippling load by Euler’s formula

UNIT – V Analysis of Stressesin Two Dimensions
1. When will you call a cylinder as thin cylinder?
A cylinder is called as a thin cylinder when the ratio of wall thickness
to the diameter of cylinder is less than 1/20
2. In a cylinder will the radial stress vary over thickness of wall?
No, in the cylinders radial stress developed in its wall is assumed to be
constant since the wall thickness is very small as compared to the
diameter of the cylinder.
3. What is the ratio of circumferential stress to longitudinal stress of a thin
cylinder?
4. What is the maximum principal stress in a thin cylindrical?
The maximum principal stress in a thin cylinder is circumferential
stress.
5. What is the maximum shear stress in a thin cylinder? Circumferential
strains,
6. For a thin cylinder, write down the equation for strain along the
circumferential direction.
7. For a thin cylinder, write down the equation for strain along the
longitudinal direction
8. Write the expression for hoop stress in thin cylinder due to internal presser
P.
9. Write the expression for longitudinal stress in thin cylinder due to internal
presser P.

10. For a thin cylinder, write down the expression for volumetric strain.
11. What is the circumferential stress in a thin spherical shell subjected to
internal presser ‘P’?
12. Write is the volumetric strain in a thin spherical shell subjected to internal
presser ‘P’
13. Write the circumferential strain in thin spherical shell.
14. In a thin cylindrical shell if hoop strain is 0.2×10-3 and longitudinal strain
is 0.005×10-3, find out volumetric strain.
Volumetric strain, ev = 2ec ea
= 0.2 × 10-3 +0.005 × 10-3
ev = 0.25 × 10-3
15. Different between thin cylinder and thick cylinder.
Thin cylinder Thick cylinder
1. Ratio of wall thickness to the
diameter of cylinder is less that
1/20.
2. Circumferential stress is
assumed to be constant
throughout the all thickness.
1. Ratio of wall thickness to the
dia., of cylinder is more than
1/20.
2. circumferential stress varies
from inner to outer wall
thickness
16. Distinguish between cylindrical shell and spherical shell.
cylindrical shell
spherical shell
1. Circumferential stress is
twice the longitudinal stress.
2. It withstands low pressure
than spherical shell for the
same diameter.
1. Only hoop stress presents.
2. It withstands more pressure than
cylindrical shell for the same
diameter.

17. Write the equation for the change in diameter and length of a thin cylinder
shell, when subjected to an internal pressure.
18. What is the effect of riveting a thin cylindrical shell?
Riveting reduces the area offering the resistance. Due to this, the
circumferential and longitudinal stresses are more. It reduces the
pressure carrying capacity of the shell.
19. What do you understand by term wire winding of thin cylinder?
In order to increase the tensile strength of a thin cylinder to withstand
high internal pressure without excessive increase in wall thickness,
they are some times pre-stressed by winding with a steel wire under
tension.
20. Define principal stresses and principal plane.
Principal stress: The magnitudes of normal stress, acting on a
principal plances are known as principal stresses.
Principal planes: The planes which have no shear stress are known as
principal planes.
21. Give the expression for maximum shear stress in a two dimensional stress
system.
22. What is the radius of Mohr’s circle?
Radius of Mohr’s circle is equal to the maximum shear stress.
23. A bar of cross sectional area 600mm2 is subjected to a tensile load of
50KN applied at each end. Determine the normal stress on a plane inclined
at 30° to the direction of loading.
A = 600 mm2
Load, p = 50KN
θ = 30°
Normal stress, σn = p cos2θ = 83.33× cos2 30° = 62.5N/mm2
24. Give the expression for stresses on an inclined plane when it is subjected
to a axial pull.
Normal stress, σn = p cos2θ
Shear stress, σt = p/2 sin2θ
25. What is the use of Mohr’s circle?
To find out the normal, tangential, resultant stresses and principal
stress and their planes.

26. What are the planes along which the greatest shear stresses occur?
Greatest shear stress occurs at the planes which is inclined at 45° to its
normal
27. Write the expression for a normal stress on an inclined plane in a block
which is subjected to two mutually perpendicular normal stresses and
shear stresses?
28. At a point in strained material is subjected to a compressive stress of
100N/m2 and shear stress of 60 N/mm2.determine graphically or otherwise
the principal stresses.
σ = -100 N/mm2
q = 60 N/mm2
29. In case of equal like principal stresses, what is the diameter of the Mohr’s
circle?
Zero.
30. What is the value of maximum shear stress when the principal stresses are
σ1 compression and σ2 tension?

STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

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STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)