CE6306 STRENGTH OF MATERIALS NOTES II Auto IV Sem Regulation 2013

P.M.SUBRAMANIAN,ASST PROF, DEPT OF AUTOMOBILE ENGINEERING

CE 6306 SOM II AUTO IV SEM LEARNING MATERIAL 1

II AUTO IV SEM - CE 6306 STRENGTH OF MATERIALS



PART- A

Two 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.

The external force act on the body while stress is induced in the material of the body.

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 of dimension of the body to the original dimension is known as strain. Strain

is dimensionless.

3. Enumerate the types of strain.

Tensile strain, Compressive strain, Volumetric strain, Shear strain

4. Differentiate between tensile strain and compressive strain.

If there is increase in length of a body due to external force, the ratio of increase of length to the

original length of the body is known as tensile strain. If there is decrease in length of a body due

to external force, the ratio of decrease of length to the original length of the body is known as

compressive strain.

5. Define Volumetric strain.

The ratio of change in volume of the body to the original volume when body is subjected to a

single force or a system of forces is called volumetric strain.

6. Define normal stress

Normal stress is the stress which acts in a direction perpendicular to the area. It is denoted by

.It is further divided in to tensile and compressive stress.



7. Define tensile stress

The stress induced in a body, when subjected to two equal and opposite pulls, as a result of

which there is an increase in length, is known as tensile stress.

8. Define compressive stress.

The stress induced in a body, when subjected to two equal and opposite pushes, as a result of

which there is a decrease in length, is known as compressive stress.

9. 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 and corresponding strain is known as shear strain. The shear

stress is the stress which acts tangential to the area. It is represented by τ , Shear Strainφ

10. Define Elasticity.

The property by virtue of which certain materials return back to their original position after the

removal of the external force is called elasticity.



11. What is meant by elastic limit of the material?

There is a limiting value of force up to and within which the deformation completely disappears

on the removal of the force. The value of the stress corresponding to this limiting force is known

as the elastic limit of the material.

12. Give example for ductile, brittle and malleable materials.

Ductile materials steel, copper

Brittle materials wrought iron

Malleable materials cast iron

13. Define Poisson’s ratio

The ratio of lateral strain to the linear/longitudinal strain is a 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 expressed as

14. Write the relationship between modulus of elasticity, modulus of rigidity and

Poisson’s ratio

The relationship between modulus of elasticity, modulus of rigidity and Poisson’s ratio is

given by E= 2C (1+µ)

E=Modulus of elasticity C=Modulus of rigidity µ= Poisson’s Ratio

15. State Hooke’s law.

Hooke’s law states that when a material is loaded within elastic limit, the stress is proportional

to the strain produced by stress, or Stress/strain=constant. This constant is termed as modulus of

elasticity.

16. Define modulus of rigidity/Shear Modulus

The ratio of shear stress to the corresponding shear strain within the elastic limit is known as

modulus of rigidity or shear modulus and is denoted by C or G or N



17. Define modulus of elasticity/Young’s Modulus/Modulus of rigidity/Elastic Modulii.

The ratio of tensile stress or compressive stress to the corresponding strain is constant known as

modulus of elasticity or young’s modulus and is denoted by E.

18. Define factor of safety

It is defined as the ratio of ultimate tensile stress to the working stress or permissible stress.

19. Give the relationship between modulus of elasticity, bulk modulus and poison’s ratio.

E=3K(1-2 µ)

Where

E = Young’s modulus K = Bulk modulus µ= Poisson’s Ratio

20. Define Bulk modulus.

When a body is subjected to the mutually Perpendicular like and equal direct stresses, the ratio of

the direct stress to the corresponding volumetric strain is found to be a constant for a given

material when the deformation is within a certain limit called as the bulk modulus of the

material and is denoted by K.

21. What is stability?

The stability may be defined as an ability of a material to withstand high load without

deformation.

22. Give example for gradually applied load and suddenly applied load.

Example for gradually applied load

When we lower a body with the help of a crane, the body first touches the platform on which it is

to be placed. On further releasing the chain, the platform goes on loading till it is fully loaded by

the body. This is the case of gradually applied load.



Example for suddenly applied load

When we lower a body with the help of a crane, the body is first of all, just above the platform

on which it is to be placed. If the chain breaks at once at this moment the whole load of the body

begins to act on the platform. This is the case of suddenly applied load.

23. What is resilience?

The strain energy stored by the body within elastic limit, when loaded externally is called

resilience.

24. Define strain energy.

Strain energy is the energy absorbed or stored by a member when work is done on it to deform it.

25. Distinguish between suddenly applied and impact load.

When the load is applied all of a sudden and not step wise is called is suddenly applied load. The

load which falls from a height or strike and body with certain momentum is called falling or

impact load.

26. Define proof resilience?

The maximum strain energy stored in a body up to elastic limit is known as proof resilience.

27. Define strain energy density.

Strain energy density as the maximum strain energy stored in a material within the elastic limit

per unit volume. It is also known as modulus of resilience.

28. Differentiate between longitudinal and lateral strain.

The ratio of axial deformation to the original length of the body is known as longitudinal or

linear strain. Lateral strain is the strain at right angles to the direction of applied load. If

longitudinal strain is tensile, the lateral strain will be compressive. If longitudinal strain is

compressive then lateral strain will be tensile. Every longitudinal strain in direction of load is

accompanied by lateral strains of the opposite kind in all directions perpendicular to the load.

,

28. Write the expression for total change in length of bar of different lengths and of

different diameters when subjected to an axial load P.



29. Write the expression for total extension of a uniformly tapering circular rod of

diameters D1 and D2 when the rod is subjected to an axial load P.

30. What is meant by composite bar?

A composite bar is 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.

31. Define Thermal stress and write the expression for thermal stress and thermal strain.

The stresses induced in a body due to change in temperature are known as thermal stress.

32. Write the expression for elongation of a bar due to its own weight.

33. Write the expression for volumetric strain of a rectangular bar subjected to three forces

which are mutually perpendicular.

33. Write the expression for volumetric strain of a cylindrical rod subjected to an axial

tensile load P.



34. Give the relationship between modulus of elasticity, modulus of rigidity and poisson’s

ratio.

35. State the principle of complementary shear stresses.

A set of shear stresses across a plane is always accompanied by a set of balancing shear stresses of

same intensity across the plane and normal to it.

36. Define principal planes and principal stresses.

The planes which have no shear stress are known as principal planes. They carry only normal

stresses. The normal stresses acting on a principal plane are known as principal stresses.

37. Write the expression for normal stress, tangential stress and principal plane position for a

member subjected to two direct stresses in two mutually perpendicular directions

accompanied by simple shear stress.

38. Write the expression for major, minor principal stress, max shear stress and condition for

max shear stress for a member subjected to two direct stresses in two mutually perpendicular

directions accompanied by simple shear stress.

39. Explain the Mohr’s Circle.

It is a graphical method of finding normal, tangential and resultant stresses on an oblique plane.The

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



UNIT - II TRANSVERSE LOADING ON BEAMS AND STRESSES IN BEAM

1. What are the different types of beams?

1. Cantilever beam: A beam which is fixed at one end and free at the other end is known as

cantilever beam.

2. Simply supported beam: A beam supported or resting freely on the supports at its both ends is

known as simply supported beam

3. Fixed beam: A beam whose both end are fixed or built-in walls is known as fixed beam.(Built

in or encastred beam)

4. Overhanging beam: If the end portion of a beam is extended beyond the support is known as

overhanging beam.

5. Continuous beam: A beam which is having more than two supports is known as continuous

beam

2. Sketch the different types of beams?

Cantilever beam Simply supported beam Fixed beam

Overhanging beam Continuous beam

3. Name the various types of load.

1. concentrated load or point load 2. Uniformly varying load 3. Uniformly distributed load

4. Differentiate concentrated load and uniformly distributed load.

Concentrated load is one which is considered to act at a point where as uniformly distributed

load which is spread over the beam. The rate of loading is uniform along the length of beam for

uniformly distributed load.



Concentrated load uniformly distributed load

5. What is meant by uniformly varying load.

The rate of loading varies from point to point along the beam in which load is zero at one end

and increases uniformly to the other end. It is known as triangular load.

6. Define shear force at a section of a beam.

The algebraic sum of the vertical force at any section of a beam to the right or left of the section

is known as shear force.

7. Define bending moment at a section of a beam.

The algebraic sum of the moments of all the force acting to the right or left of the section is

known as bending moment.

8. What is meant by point of contraflexure?

It is the point where the bending moment is zero where it change sign from positive to negative

or vice –versa.(point of inflexion)

9. Mention the different types of supports?

1. Fixed support

2. Hinged support

3. Roller support

10. State the relationship between the load and shear force.

The rate of the change of shear force is equal to rate of loading = -w



11. State the relationship between shear force and bending moment.

The rate of change of bending is equal to the shear force at the section. = F

12. What will be the shape of bending moment and shear force diagrams for different types

of load.

13. Define clear span and effective span.

The horizontal distance between the supporting walls is called the clear span of the beam. The

horizontal distance between the lines of action of end –reaction is called effective span.

14. What is section modulus?

The ratio of Moment of Inertia of a section about the neutral axis to the distance of the outer

most layer from the neutral axis is known as Section Modulus. It is denoted by Z.

15. What is moment of resistance?

Due to pure bending, the layers above the NA are subjected to compressive stress whereas the

layers below the NA are subjected to tensile stress. Due to these stresses, the forces will be

acting on the layers. These forces will have moment about the N.A. The total moment of these

forces about the NA for a section is known as moment of resistance of that section.



16. State the theory of simple bending?

If a length of a beam is subjected to a constant bending moment and no shear force (i.e. zero

shear force) then the stresses will be set up in that length of the beam due to B.M. only and that

length of the beam is said to be in pure bending or simple bending. The stresses set up in that

length of beam are known as bending stress.

17. Write the bending equation?

Where

M = bending moment in N mm σ = bending stress in N/mm2

I = moment of inertia about N.A. in mm4 Y = distance of the fibre from N.A. in mm

R = radius of curvature in mm E = young’s modulus of beam N/mm2

18. What are the assumptions made in the theory of simple bending?

1. The material of the beam is perfectly homogeneous and isotropic.

2. The beam material is stressed, within its elastic limit and thus obeys Hooke’s law. The value

of Young’s modulus of elasticity is same in tension and compression.

3. The transverse sections, which were plane before bending, remain plane after bending also.

4. Each layer of the beam is free to expand or contract, independently, of the layer, above or

below it.

5. The beam is initially straight and all longitudinal filaments bend in to circular arcs with a

common centre of curvature.

19. A cantilever beam of span 3 m carries a point load of 10 kN at the free end. What is the

value of support moment?

The value of support moment = 3 X10 = 30 kN m

20. Define neutral axis of a cross section

While beam subjected to bending there will be a layer which is neither shortened nor elongated

termed as neutral layer or neutral surface. The line of intersection of the neutral layer on a cross-

section of a beam is called the neutral axis(NA). There is no stress at the axis.

21. Differentiate shear force and bending moment diagrams.

Shear force diagram shows the variation of the shear force along the length of the beam. Bending

moment diagram shows the variation of the bending moment along the length of the beam.



22. Describe the sign convention for shear force.

The shear force at a section will be considered positive when the resultant of the forces to the left

of the section is upwards, or to the right of the section is downwards. The shear force at a

section will be considered negative when the resultant of the forces to the left of the section is

downwards or to the right of the section is upwards.

23. Describe the sign convention for bending moment.

The bending moment at a section will be considered positive if it tends to bend the beam to a

curvature having concavity at the top and will be considered negative if it tends to bend the beam

to a curvature having convexity at the top. The positive BM is called sagging moment and

negative BM is called hogging moment.

24. Describe about bending stress.

The beam undergoes deformation due to shear force and bending moment. The material of the

beam will offer resistance against these deformations. Thus the stresses introduced by bending

moment are known as bending stresses.

24. What is meant by pure bending?

If the length of the beam is subjected to a constant bending moment and no shear force, then the

stresses will be set up in the length of the beam due to BM only. The length of beam is said to be in

pure bending or simple bending.

25. Explain how section modulus represent the strength of the section.

The bending stress will be maximum, when the distance of outer most layer from NA is maximum.

M is the maximum bending moment or moment of resistance offered by the section. The moment of

resistance is maximum when section modulus is maximum. Thus section modulus represent the

strength of the section.



26. What is meant by flitched beam?

Flitched beam is a composite beam made up of two or more different materials assumed to be

rigidly connected together and behave like a single piece. The strain at the common surfaces will

be same for both materials. Total moment of resistance will be equal to the sum of the moments

of individual sections.

27. Enumerate the section modulus for various sections.

28. Give the expression for shear stress in a section of a beam.

29. Describe the shear stress distribution for a rectangular section.

30. Describe the shear stress distribution for a circular section.



31. Describe the shear stress distribution for a I section.

32. Provide the expression for max shear stress distribution for different sections.



UNIT-3 TORSION

1. Define torsion

A shaft is said to be in torsion, when equal and opposite torques are applied at the two ends of

the shaft. The torque is equal to the product of the force applied (tangentially to the ends of shaft)

and radius of the shaft.

2. What are the assumptions made in the theory of torsion?

(i) The material of the shaft is uniform throughout.

(ii) The twist along the shaft is uniform.

(iii) Cross sections of the shaft, which were plane before twist, remain plane after twist.

(iv) All radii which are straight before twist remain straight after twist.

(v) The shaft is uniform circular section throughout.

3. Write torsional equation.

Where, T = Torque,

J= Polar Moment of Inertia

t= Shear Stress

r= Radius of section

G= Shear modulus

θ= Angle of twist

L=length of shaft

4. Write the expression for power transmitted by a shaft.



5. Define polar modulus.

Polar modulus is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is

also called torsional section modulus. (Zp)

6. Define torsional rigidity

Torsional rigidity or stiffness of the shaft is defined as the product of modulus of rigidity (G or

C) and the polar moment of inertia of the shaft (J). Torsional rigidity = C X J

It is also defined as the torque required to produce a twist of one radian per unit length of the

shaft.

7. Why hollow circular shafts are preferred when compared to solid circular shafts?

The torque transmitted by the hollow shaft is greater than the solid shaft, thereby hollow shaft is

efficient than the solid shaft. Hollow shaft is stronger than solid shaft. For transmitting same

torque for the given length, material solid shaft weighs more compared to hollow shaft.

8. Distinguish between close and open helical coil springs.

If the angle of the helix of the coil is so small that the bending effects can be neglected, then the

spring is called a closed–coiled spring. Close –coiled spring is a torsion spring. Thepitch between

two adjacent turns is small. If the slope of the helix of the coil is quite appreciable then both the

bending as well as torsional shear stresses are introduced in the spring, then the spring called

open coiled spring.

9. Define stiffness of a spring? In what unit it is measured?

Stiffness of a spring is defined as load per unit deflection. It is denoted by K and unit is N/mm.

10. What is a spring?

Springs are elastic members which distort under load and regain their original shape when load is

removed. They are elastic bodies which absorb energy due to resilience. The absorbed energy

may be released as and when required.



11. State the types of stresses when a closed-coiled spring is subjected to

1. Axial load

2. Axial twisting moment

1. Axial load: torsion (neglecting the effects of bending and direct shear)

2. Axial twisting moment: pure bending

12. What kind of stress introduced when an axial load acts on a close and open coiled

spring.

Close coiled helical spring —shear stress

Open coiled helical spring —bending stress shear stress

13. Describe the effect of torsion.

Due to torsion, torques will be applied at two ends of the shaft resulting in twisting moment. It

causes shear stresses and shear strains in the material of the shaft.

14. Give the expression for maximum torque transmitted by a circular solid shaft.

The maximum torque transmitted by a circular solid shaft is given by

D = Diameter of the shaft.

15. Give the expression for maximum torque transmitted by a hollow circular shaft.

The maximum torque transmitted by a hollow circular shaft is given by

16. Derive the expression for polar modulus of solid shaft.



17. Derive the expression for polar modulus of hollow shaft.

18. What is meant by strength of shaft?

The strength of a shaft means the maximum torque or maximum power the shaft can transmit.

19. What is meant by composite shaft?

Composite shaft is made up of two or more different materials and behaving as a single shaft.

The total torque transmitted by a composite shaft is the sum of the torques transmitted by each

individual shaft. But the angle of twist in each shaft will be equal.

20. Write the expression for total strain energy stored in the solid shaft due to torsion.

21. Write the expression for total strain energy stored in the hollow shaft due to torsion.



22. Enumerate the various types of spring.

Types of springs:

1. Helical springs a. Closed-coiled spring b. open-coiled helical spring

2. Laminated or Leaf springs a. full-elliptic b.semi elliptic ,c. cantilever

3. Torsion spring 4. Circular spring

23. State the applications of laminated or leaf spring.

The laminated springs are used to absorb shocks in railway wagons, coaches and road vehicles

such as cars, lorries.

24. Give the expression for maximum bending stress developed in the plate of the spring.

24. Give the expression for central deflection of the leaf spring.

23. What is meant by solid length of the spring?

The solid length of the spring means the distance between the coils when the coils are touching

each other. There is no gap between the coils. The solid length is given by

Solid Length = Number of coils X Dia of wire = n X d



24. Give the relation of maximum shear stress induced in a shaft subjected to twisting

moment.

25. Give the expression for shear stress variation of a circular shaft subjected to torsion.

The shear stress at any point varies linearly from the axis to the surface. The shear stress is

maximum on the surface of the shaft and is zero at the axis of the shaft.

26. Explain about Helical springs.

27. Give the expression for maximum shear stress induced in the wire of a close-coiled

helical spring which carries an axial load.

27. Give the expression for strain energy stored in close coiled helical spring which carries

an axial load.



28. Give the expression for the deflection of the spring at the centre due to axial load.

28. Give the expression for stiffness of the spring due to axial load.



UNIT 4 DEFLECTION OF BEAMS

PART- A

1. Write the maximum value of deflection and slope for a cantilever beam of length of

length L, constant EI and carrying concentrated load W at the end.

Maximum deflection at the free end ‘B’of a cantilever due to the load W at ‘B’

2. Write the maximum value of deflection and slope at ends for a simply supported beam of

a length L, constant EI and carrying a central concentrated load W.

Maximum deflection at a mid span of simply supported beam due to a central load

3. Write the value of fixed end moment and deflection for a fixed beam of span L and

constant EI carrying central concentrated load W.

Fixed end moment due to central concentrated load ,

(1/4 th of SSB)



4. What are the different methods used for finding deflection and slope of beams?

(i) Double integration method

(ii) Mecaulay’s method

(iii) Strain energy method

(iv) Moment area method

(v) Unit load method

5. State the two theorems in moment area method.

Mohr’s Theorem-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

Mohr’s Theorem-II: The total deflection between any two points is equal to the moment of the

area of the B.M diagram between the two points about the last point(i.e. B) divided by EI.

6. Write the differential equation of deflection of a bent beam.

7. What is meant by elastic curve?

The deflected shape of a beam under load is called elastic curve of the beam, within elastic limit.

8. When Macaulay’s method is preferred?

This method is preferred for determining the deflections of a beam subjected to several

concentrated loads or a discontinuous load. Macaulay’s method is simple compared to double

integration method in finding the slope and deflection at any point in a beam.

9. What are the boundary conditions for a simply supported end?

The boundary conditions for a simply supported end beam are:

(i) Deflection at the support is zero.

(ii) Slop exists at all points except at the point where deflection is maximum.

(iii) Bending moment is zero at the support.

10. What are the boundary conditions for a fixed end?

Both deflection and slope at the fixed support are zero.



11. What is meant by Double-Integration method?

Double-integration method used for finding deflection and slope at a section in a loaded beam.It

is used for single load.

12. Define the term slope.

Slope at any point on the bent beam is the angle through which the tangent at that point makes

with the horizontal.

13. What is meant by deflection of beams?

When a flexural member is subjected to transverse loads, the longitudinal axis of the beam

deviates from its original position because of the bending of the beam. This deviation at any

cross section is called as deflection.

14. When do you prefer Moment Area Method?

Even though the moment area method can be used for problems on slopes and deflections, it is

convenient to use this method for the following types of problems (with varying cross-section)

(i) Cantilever beams

(ii) Simply supported beams carrying symmetrical loading

(iii) Beams fixed at both ends.

15. What is meant by determinate beams?

The beams whose external reacts can be determined with the help of equations of static

equilibrium alone are called determinate beams.

16. What is meant by indeterminate beams?

The beams whose support reactions cannot be obtained with the help of static equations of

equilibrium alone are called indeterminate beams.

17. Give examples for determinate and indeterminate beams

Determinate beams: cantilever and simply supported beams

Indeterminate beams: fixed end beams, continuous beams and propped cantilever beams.



18. Give relation between slope, deflection, bending moment, shearing force and rate of

loading.

19. Write the maximum value of deflection and slope at ends for a simply supported beam

of a length L, constant EI and carrying a uniformly distributed load of w per unit length

over entire length.


of a length L, constant EI and carrying a eccentric point load W at distance of ‘a’ from

support A and at a distance of ‘b’ from Support B.(double integration method)




of a length L, constant EI and carrying a eccentric point load W at distance of ‘a’ from

support A and at a distance of ‘b’ from Support B.(Macaulay’s method)


length L, constant EI and carrying concentrated load W at distance ‘a’ from the fixed end

A.



, ,


length L, constant EI fixed at A, free at B and carrying a UDL of w per unit length.

,

23. Give the expression for slope at free end for cantilever beam for different loading

conditions.



24. Give the expression for deflection at free end for cantilever beam for different loading

conditions.

25. Write the relation between actual beam and conjugate beam.

26. What is meant by conjugate beam?

Conjugate beam is an imaginary beam of length equal to that of original beam but for which load

diagram is M/EI diagram. The load on conjugate beam at any point is equal to the B.M at that

point divided by EI.



27. State the significance of conjugate beam method.

The conjugate beam method is used to find the slope and deflection of such beams whose

flexural rigidity (EI) is not uniform throughout of its length.

28. Define the Shear force and bending moment in conjugate beam method.

The slope at any section of the given beam is S.F at the corresponding section of the conjugate

beam. The deflection at any point of the given beam is B.M at the corresponding point of the

conjugate beam.

29. Give the expression for deflection by moment area method.

30. State the advantages of fixed beam over simply supported beam.

30. Differentiate between fixed beam and continuous beam.

A beam whose both ends are fixed is known as fixed beam. A beam which is supported on more

than two supports is continuous beam.


constant EI carrying UDL over the entire length.

(1/5 th of SSB)


constant EI carrying eccentric load under point load.



UNIT 5 THIN CYLINDERS, SPHERES AND THICK CYLINDERS

1. When do you call a cylinder as a thin cylinder?

A cylinder is called a thin cylinder when the ratio of wall thickness to diameter of cylinder is less

than 1/20.The thickness of the wall of the cylindrical vessel is less than 1/15 to 1/20 of its

internal diameter. The stress distribution is assumed uniform over the thickness of the wall.

2. In thin cylinder will radial stress vary over thickness of wall?

No, radial stress will be constant since the wall thickness is very small as compared to diameter

of cylinder. The hoop and longitudinal stress are constant and radial stress is small and can be

neglected.

3. What is the ratio of circumferential stress to hoop stress of a thin cylinder?

The ratio of circumferential stress to hoop stress is 2.

4. What is the maximum principal stress in thin cylinder?

It is the circumferential stress which is maximum.

5. What is the maximum shear stress in a thin cylinder?

6. What is the hoop stress due to internal pressure p in thin cylinder?

7. What is the expression for longitudinal stress due to internal pressure in thin cylinder?



8. For thin cylindrical shell write the expression for volumetric strain.

9. For thin cylindrical shell write the expression for circumferential strain.

10. For thin cylindrical shell write the expression for longitudinal strain.

11. Distinguish between thin cylinder and thick cylinder.

12. Distinguish between cylindrical shell and spherical shell

Cylindrical shell:

Circumferential stress is twice that of longitudinal stress. It withstands low pressure than

spherical shell for the same diameter.



Spherical shell:

Only hoop stress is present. It withstands more pressure than cylindrical shell for the same

diameter.

13. Distinguish between circumferential stress and longitudinal stress.

The stress acting along the circumference of the cylinder is called circumferential stress ( Hoop

Stress). The stress acting along the length of the cylinder (in longitudinal direction) is known as

longitudinal stress.

circumferential stress longitudinal stress

14. For thin spherical shell write the expression for circumferential stress.

15. For thin spherical shell write the expression for lateral strain.

16. For thin spherical shell write the expression for volumetric strain.

17. How to classify thick cylinders?

If the ratio of thickness to internal diameter is more than 1/20, then the cylindrical shell is called

as thick cylinders. The hoop stress will not be constant , will vary from a maximum value at the

inner circumference to a minimum vale at the outer circumference.

18. Give the expression for hoop stress and radial pressure in thick cylinders.



19. State the boundary conditions for thick cylinders.

20. Give the expression for hoop stress and radial pressure in thick spherical shell.



PART B QUESTION BANK

UNIT I

































UNIT IV





UNIT IV- CONJUGATE BEAM METHOD



UNIT IV- CANTILEVERS









CE 6306 STRENGTH OF MATERIALS

RAJALAKSHMI ENGINEERING COLLEGE

DEPARTMENT OF AUTOMOBILE ENGINEERING







































UNIT-I

STRESS, STRAIN AND DEFORMATION OF SOLIDS

Rigid bodies and deformable solids – Tension, Compression and Shear Stresses – Deformation

of simple and compound bars – Thermal stresses – Elastic constants – Volumetric strains –

Stresses on inclined planes – principal stresses and principal planes – Mohr’s circle of stress.

















































































UNIT-II

TRANSVERSE LOADING ON BEAMS AND STRESSES IN BEAM

Beams – types transverse loading on beams – Shear force and bending moment in beams –

Cantilevers – Simply supported beams and over – hanging beams. Theory of simple bending–

bending stress distribution – Load carrying capacity – Proportioning of sections – Flitched

beams–Shear stress distribution.



































































UNIT-III

TORSION

Torsion formulation stresses and deformation in circular and hollows shafts – Stepped shafts–

Deflection in shafts fixed at the both ends – Stresses in helical springs – Deflection of helical

springs, carriage springs.



























UNIT-IV

DEFLECTION OF BEAMS

Double Integration method – Macaulay’s method – Area moment method for computation of

slopes and deflections in beams - Conjugate beam and strain energy – Maxwell’s reciprocal

theorems.





































































.























UNIT-V

THIN CYLINDERS, SPHERES AND THICK CYLINDERS

Stresses in thin cylindrical shell due to internal pressure circumferential and longitudinal stresses

and deformation in thin and thick cylinders – spherical shells subjected to internal pressure

Deformation in spherical shells – Lame’s theorem.































Education

CE6306 STRENGTH OF MATERIALS NOTES II Auto IV Sem Regulation 2013