Strength of materials Two mark Question with answers

K. Rajesh/AP Mech/RMKCET
R.M.K COLLEGE OF ENGINEERING AND TECHNOLOGY
RSM NAGAR, PUDUVOYAL - 601 206
DEPARTMENT OF MECHANICAL ENGINEERING
CE8395-STRENGTH OF MATERIALS
Two-mark Questions and Answers
UNIT 1 - Stress, Strain and Deformation of solids
1. Define Principal Stresses And Principal Plane? (Nov 2006 , Nov 2007, May 2008 , May
2009, 2011,May 2014)
Principal Plane: The planes which have no shear stress are known as principal planes.
Principal Stress: The magnitude of normal stress, acting on a principal planes are known
as principal stresses.
2. Give The Relation Between Modulus Of Rigidity And Modulus And Bulk Modulus?
(May 2008 ,May2012)
E = 2g(1+µ)
E = 3k(1-2µ)
Where : E – Youngs Modulus
G – Modulus Of Rigidity
K – Bulk Modulus
µ – Poission Ratio
3. How Will You Find Major Principal Stress And Minor Principal Stress? Also
Mention To Locate The Direction Of Principal Planes? (May 2007)
4. Define Poisson Ratio And Bulk Modulus? (Nov 2007,May 2009,May 2010 , May 14)
Poisson Ratio: When a rod is stretched within the elastic limit the ratio of lateral strain to
the longitudinal strain is constant for the given material.
Poission ratio, µ=Lateral strain/Linear strain
Bulk Modulus :When a body is stressed within its elastic limit the ratio of direct stress to
the corresponding volumentric strain is constant this is known as bulk modulus.
Bulk Modulus, K = Direct stress/Volumetric strain

5. Explain the effect of change of temperature in a composite bar ?(Nov 2007)
Whenever there is some increase or decreases in the temperature of a bar, consisting of
two or more different materials, it causes the bar to expand or contract. On account of
different coeffecients of linear expansions, the two materials do not expand or contract
by the same amount, but expand or contract by different amounts.
e1 +e2 =t(α1-α2)
6. Define Proof Resilience And Modulus Resilience ? (May 2008,May 2013,May 2014)
Proof resilience: The maximum strain energy that can be stored in material within its
elastic limit is known as proof resilience.
Modulus of Resilience: It is the proof of a material per unit volume.
Modulus of resilience = proof resilience/volume of the body
7. What is thermal Stress?(May 2009, May 2015)
Thermal stress are the stresses induced in a body due to change in temperature. When the
thermal expansion of the material is not restricted then no stress acts on the material. If
expansion is restricted by some means then thermal stress acts on the material.
8. What is mohr’s circle method?(may 2009)
Mohr’s circle is a graphical method of finding normal, tangential and resultant stresses on
an oblique plane.
9. State Hooke’s Law? (May 2010, May 2013)
It states that when a material is loaded, within its elastic limit, the stress is directly
proportional to the strain. The constant of proportionality is called as young’s modulus.
10. Define Elasticity? (May 2012)
The material return back to their original position after the removal of the external force is
called elasticity.
Stress 𝛼 Strain 𝜎 𝛼 𝑒, 𝜎 = 𝐸 𝑒

UNIT 2 - Transverse loading and stresses on beams
1. Sketch (a) the bending stress distribution (b) shear stress distribution of a beam in
rectangular cross section. (MAY 2006, NOV 2006, MAY 2011)
2. Mention assumptions in theory of simple bending ? (MAY 2007,MAY 2014)
The material is perfectly homogeneous and isotropic.It obeys Hooke’s law
The value of young’s modulus is same in tension as well as in compression.
Transverse sections, which are plane before bending, remains plane after bending.
The resultant force on a transverse section of the beam is zero.
3. Define point of contraflexure or inflexion?(may 2008,may 2010,may2012,may 2013)
The point where the bending moment changes its sign or zero is called the point of
contraflexure.
4. Write down the bending moment equation?
The bending equation is M/I = E/R =σb/Y
Where,
M – Bending moment I – Moment of inertia of the section
Y – Distance from the neutral axis E – Young’s modulus of the material
R – Radius of curvature of the beam σb- Bending stress at that section.
5. What is the value of BM corresponding to a point having a zero shear force? (May
2010)
The value of bending moment is maximum when the shear force changes its sign or zero .
In a beam ,that point is considered as maximum bending moment .
6. Mention and sketch any two types of supports and lording for the beams ? (May
2011)

7. What is meant by shear flow? (May 2013)
Shear flow is defined as the gradient of stress through the body.
8. What is bending moment and shear force in a beam (May 2015)
Bending moment at any cross section is defined as algebraic sum of the moments of all the
forces which are placed either side from that point.
Shear force at any cross section is defined as algebraic sum of all the forces acting either
side of beam.
9. State the theory of simple bending.
When a beam is subjected to bending load, the bottom most layers is subjected to tensile
stress and top most layers is subjected to compressive stress. The neutral layer is subjected
to neither compressive stress nor tensile stress. The stress at a point in the section of the
beam is directly proportional to its distance from the neutral axis.
10. What is neutral axis of a beam section? How do you locate it when a beam is under
simple bending? (May 2015)
The line of intersection of the neutral layer on a cross section of a beam is known as neutral
axis. The layer above the neutral layer have been shortened and layer below have been
elongated and neutral layer remains in the same length to the original.

UNIT 3 - Torsion
1. What is Torsional rigidity or stiffness of the shaft? (May 2007,May 2012, May 2013, May
2015)
Product of rigidity modulus and polar moment of inertia is called torsional rigidity
Torsional rigidity = JG
Where, J=Polar moment of inertia, G=modulus of rigidity.
2. Define stiffness of the spring or spring rate and give its expression. (May2010, May 2011)
The spring stiffness or spring constant is defined as the load required per unit deflection of the
spring.
K= N/mm
Where
W – load, δ – deflection
3. Define torsion and give examples for it. (May 2009, May 2011, May 2014)
When a shaft is said to be in torsion when equal and opposite torques are applied at the two
ends of the shaft. This torques is equal to the product of the for applied and radius of the shaft.
Eg: 1.twisting of a shaft,
2. When opening the lid of a common plastic drinks bottle, a torque T applied to the cap is
gradually increased until the plastic connectors between the cap and the bottle experience shear
failure.
4. Write short note on types of springs. (May 2014)
Laminated springs - where the energy is stored due to bending
Helical springs- it is of two types open coil and closed coil springs. In this the energy is stored
due to axial pull or push of the spring
Torsion springs- the energy stored is due to the twist or torque applied to it.
5. Write down the equation of torsion with various terms involved in it. (May 2007, 2012)
T/J = Gθ/L = τ/R
T-torque, J-polar moment of inertia, G or C- modulus of rigidity, θ-angle of twist, τ-shear
stress, R- Radius of the shaft
6. How will you find maximum shear stress induced in the wire of a closed coiled helical
spring carrying an axial load? (May 2007)
𝝉 =
𝟏𝟔𝒘𝑹
𝝅𝒅 𝟑
Where, τ = Shear stress, w – Load acting on the spring, R-mean radius of the spring,
d-diameter of the wire

7. Write the assumption for finding out the shear stress of a circular shaft, subjected to
torsion. (May 2010)
1. Material of the shaft is uniform throughout
2. The twist along the shaft is uniform
3. The shaft is uniform circular section throughout.
4. All radii which are straight before twist remains straight after twist
8. Difference between open coil and closed coil springs. (May 2006,2007,2012,2013)
Sl.
no
Closed coil helical spring Open coil helical spring
1
The spring wires are coiled very
closely, each turn is nearly at right
angles to the axis of helix.
The wires are coiled such that there is a gap between
the two consecutive turns.
2 Helix angle is less than 10o
Helix angle is large (>10o
)
3 The gap between two turns is small There is large gap between two consecutive turns
4
Axial pull produces only torsion on the
material of the spring
These springs takes compressive as well as tensile
loads
9. Define strength of the shaft. (Nov 2007)
The maximum torque or power transmitted by the shaft is called as strength of the shaft.
For solid shaft, 𝑇 =
𝜋
16
𝜏𝑑3
For hollow shaft, T = 𝑇 =
𝜋
16
𝜏 (
𝐷 𝑜
4−𝐷 𝑖
4
𝐷 𝑜
)
10. Define polar modulus of a section (may 2008)
Polar modulus is defined as the ratio of polar moment of inertia and the radius of the shaft.
Zp=J/R
J= polar moment of inertia, R= radius of the shaft

UNIT 4 - Deflection of Beams
1. Write the relation between slopes, deflection of radius of curvature of beam(May
2010)
Radius of curvature, 1/R= d2
y /dx2
Slope, θ =dy /dx
Deflection = y
2. List the four method for determining slope and deflection of loaded beams(May 2010,
Dec 2015, 2016)
1. Moment area of method.
2. Double integration method.
3. Macauly’s method.
4. Conjugate beam method.
3. Write the expression for deflection of a SSB carrying point load at centre(May2012).
Yc = -WL3
/48EI
θ b = -WL2
/ 16EI
4. State the Mohr’s theorem I and II or Moment area theorem(May2013, 2014).
Mohr’s Theorem I:
The change of slope between any points is equal to the net area of the BM diagram between
these points divided by EI.
Mohr’s Theorem II:
The total deflection between any two points is equal to the moment of the area of the BM
diagram between these two points about the last point divided by EI.
5. Define Maxwell’s theorem (Dec 2016, 2017)
The workdone by the 1st
system of loads due to displacement caused by a second system
of load equals to the workdone by second system of load due to displacement caused by
1st
system if load.
6. Define Resilience and Modulus of Resilience.
Resilience:The strain energy stored by the within elastic limit, when loaded externally is
called resilience. The maximum energy which a body stored energy elastic limit called
proof resilience.
Modulus of Resilience: It the mechanical property of material and it indicates the capacity
to real shocks of resilience per uint volume of pice is called modulus of resilience.
7. Define strain energy (2006, May2011, Dec 2014).
The energy which is absorbed in a body, when strained within the elastic limit, is known
as strain energy. Its unit is N-m or J.
8. State the two theorems of conjugate beam. (May 2018)
Theorem 1: The slope at a point in the real beam is numerically equal to the shear force at
the corresponding point in the conjugate beam.
Theorem 2: The displacement of a point in the real beam is numerically equal to the
bending moment at the corresponding point in the conjugate beam.

9. How will you use conjugate beam method for finding slope and deflection at any
section of a given beam?
In conjugate beam method the Shear force at any point is equal to the slope of the
beam and bending moment at any point is equal to the deflection of the beam.
10. What are the limitations of double integration method?
i. Difficult to find slope and deflection for beams carrying more than one load at the
same time
ii. Has limitations of using this method for varying cross section and beams having
different materials.

UNIT 5 - Thin cylinders, spheres and thick cylinders
1. List out the modes of failure in thin cylindrical shell due to an internal pressure.(May
2010)
• It may split up into two semi circular halves along the cylinder axis due to the
Circumferential or hoop stress.
• It may split into two cylinders due to the Longitudinal stress
2. What are assumptions involved in the analysis of thin cylindrical shells. (May 2011)
• Radial stress is negligible.
• Hoop stress is constant along the thickness of the shell.
• Material obeys Hooke‘s law.
• Material is homogeneous and isotropic.
3. List out the stress induced in cylindrical shell due to internal pressure. (May 2012)
• Hoop stress
• Longitudinal stress
4. How do you classify a cylinder or a shell into thin or thick?
In thin walled cylinder, thickness of the wall of the cylindrical vessel is less than 1/15 to
1/20 of its internal diameter. Stress distribution is uniform over the thickness of the wall. If the
ratio of thickness to its internal diameter is more than 1/20, then cylindrical shell is known as thick
cylinders. The stress distribution is not uniform over the thickness of the wall.
5.Define hoop and longitudinal stress. (May 2013)
Hoop stress or circumferential stress : The stress acting along the circumference of the cylinder
is called circumference or hoop stress.
Longitudinal stress: The stress acting along the length of the cylinder is known as longitudinal
stress.
6. Write down the Lami’s equation for thick cylinders. (Nov 2014)
Radial Stress, 𝑃𝑥 =
𝑏
𝑥2 − 𝑎,
Hoop Stress, 𝜎𝑥 =
𝑏
𝑥2 + 𝑎
7. Assumptions of Lami’s theorem. (Nov 2013)
a. The material is homogeneous and isotrophic
b. The material is stressed within the elastic limit
c. Plane section perpendicular to the longitudinal axis of the cyliner remain plane after the
application of internal pressure.
d. All the fibres of the material are to expand or contract independently without being
constrained by the adjacent fibres
8. Stress acting on a cylindrical or spherical shells. (May 2012)
The stresses set up in the walls of a thin cylinder owing to an internal pressure p are:
Circumferential or hoop stress σ= Pd/2t
Longitudinal or axial stress 𝜎=Pd/4t
Radial stresses
where d is the internal diameter and t is the wall thickness of the cylinder.

9.Define thin cylinder? (May 2011, Nov 2010)
If the thickness of the wall of the cylinder vessel is less than 1/15 to 1/20 of its internal diameter,
the cylinder vessel is known as thin cylinder.
10. Differentiate between thick and thin cylinder.
Sl.No Thin cylinder Thick cylinder
1.
The ratio of thickness to internal diameter
i.e t/d is less than 1/20.
The ratio of thickness to internal
diameter i.e t/d is more than 1/20.
2.
The stress distribution is uniform over the
thickness of the wall.
The stress distributed need not be
uniform over the thickness of the wall.
3. Radial stress is negligible
Radial stress has considerable effect on
the cyinder walls
4. Longitudinal stress is not constant Longitudinal is constant

Strength of materials Two mark Question with answers

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