## Syllabus For The Subject Mechanics of Solids

MECHANICS OF SOLID

1 . Statics

1.1                      Introduction

1.2                      Plane pin-jointed trusses

1.3                      Criterion for sufficiency of bracing

1.4                       Elementary mathematics

1.5                      Equilibrium consideration

1.6                      Bending moment and shearing force

1.8                      Types of beam

1.9                      Bending moment and shearing force Diagrams

1.10                  Points of contraflexure

1.11                 Relation between bending moment (M), shearing force (F),and intensity of load (w)

1.12                  Cables

1.13                 Suspension bridges examples for practice1

2.Stress and strain

2.1 Introduction

2.2 Hook’s law

2.4 Proof stress

2.5 Ductility

2.6 Shear stress and shear strain

2.7 Poisson’s ratio (v)

2.8 Hydrostatic stress

2.9 Relationship between the material constant E,G,K & v

2.10  Three-dimensional stress

2.11 composite materials

2.12 Thermal strain

2.13 Compound materials

2.14 Failure by fatigue

2.15 failure due to creep Examples for practice

3 .Geometrical properties of symmetrical section

3.1               Introduction

3.2               Centroid

3.3               Second moment of area

3.4               Polar second moment of area

3.5               Parallel axes theorem

3.6               Perpendicular axes theorem

3.7               Calculation of I through numerical integration

Examples for practice 3

4                   Bending stresses in beams

4.1               Introduction

4.2               Proof of / =M/I=E/R

4.3               Sectional modulus (Z)

4.4               Anticlastic curvature

4.5               Composite beams

4.6               Flitched beams

4.7               Composite ship structures

4.8               Composite structures

4.9               Combined bending and direct stress

Examples for practice 4

5                   Beam deflection due to bending

5.1               Introduction

5.2               Repeated integration method

5.3               Macaulay’s method

5.4               Statically indeterminate beams

5.5               Moment –area method

5.6               Slope-deflection equations

Examples for practice 5

6                   Torsion

6.1               Introduction

6.2               Torque(T)

6.4               Proof of / =T/J=G / 6.5               Flanged couplings

6.6               Keyed couplings

6.7               Compounds shafts

6.8               Tapered shafts

6.9               Close-coiled helical springs

6.10          Torsion of thin-walled non-circular sections

6.11          Torsion of thin-walled rectangular sections

6.12          Torsion of thin-walled open section

6.13          Elastic-plastic torsion of circular-section shafts

Examples for practice 6

7                   complex stress and strain

7.1               Introduction

7.2               To obtai

7.3               To obtain 1and )

7.4               Mohr’s stress circle

7.5               Combined bending and torsion

7.6               Two-dimensional strain systems

7.7    Principal strains(£1and£2 )

7.8    Mohr’s circle of strain

7.9    Stress-strain relationship for plane stress

7.10Stress-strain relationship for plane strain

7.11Pure shear

7.12Strain rosettes

7.13Computer program for principal stress and strains

7.14The constitutive laws for a lamina of a composite in global co-ordinates

Examples for practice 7

8        Membrane theory for thin-walled circular cylinders and spheres

8.1    introduction

8.2    circular cylindrical shells under uniform internal pressure

8.3    thin-walled spherical shells under uniform internal pressure

8.4    bending stress in circular cylinders under uniform pressure

8.5    circular cylindrical shell with hemispherical ends

Example for practice 8

9        Energy methods

9.1    Introduction

9.2    The method of minimum potential (Rayleigh-Ritz)

9.3    The principal of virtual work

9.4    The principal of  complementary virtual work

9.5    Castigliano’s first theorem

9.6     Castigliano’s second theorem

9.7    Strain energy  stored in a rod under axial loading

9.8    Strain energy stored in a beam subjected to couples of magnitude  M at its ends

9.9    Strain energy due to a torque T stored in a uniform circular section shafts

9.10Deflection of thin curved beams

9.11Suddenly applied and impact loads

9.12Resilience

9.14Plastic collapse of beams

9.15Residual stresses in beams

Example for practice 9

10    Theories of Elastic failure

10.1Introduction

10.2Maximum principal stress theory (Rankine)

10.3 Maximum principal strain theory(St Venant)

10.4Total strain energy theory(Beltrami and Haigh)

10.5Maximum shear stress theory (Tresca)

10.6Maximum shear strain energy theory (Hencky and von Mises

10.7Yield loci

10.8Conclusions

Example for practice 10

11    Thick cylinders and spheres

11.1Introduction

11.2Derivation of the hoop and redial stress equation for a thick-walled cylinder

11.3Lam’e line

11.4Compound cylinders

11.5Plastic yielding of thick tubes

11.6Thick spherical shells

11.7Rotating discs

11.8Plastic collapse of discs

11.9Rotating rings

Example for practice 11

12    The bulking of struts

12.1Introduction

12.3Elastic instability of very long slender struts

12.4Struts with various boundary conditions

12.5Limit of application of Euler theory

12.6Rankine-Gordon formula

12.7Effects of geometrical imperfections

12.9Struts with initial curvature

12.10            Perry-Robertson formula

12.11            Dynamic instability

Example for practice 12

13    Unsymmetrical bending of beams

13.1Introduction

13.2Symmetrical-section beams loaded asymmetrically

13.3Unsymmetrical sections

13.4Calculation of bending

13.5Mohr’s circle of inertia

13.6Stresses in beams of asymmetrical section

Example for practice 13

14    shear stresses in bending and shear defections

14.1Introduction

14.2Vertical shearing stresses

14.3Horizontal shearing stresses

14.4Shear centre

14.5Shear centre position for closed thin-walled tubes

14.6Shear deflection

14.7Warping

Example for practice 14

15    The matrix displacement method

15.1Introduction

15.2The matrix displacement method

15.3The structural stiffness matrix [K]

15.4Elemental stiffness matrix for a plane rod

Example for practice 15

16    Experimental strain analysis

16.1Introduction

16.2Electrical resistance strain gauges

16.3Types of electrical resistance strain gauge

16.4Gauge material

16.6Water-proofing

16.7Other strain gauges

16.8Gauge circuits

16.9Photo elasticity

16.10            Moire fringes

16.11            Brittle  lacquer techniques

16.12            Semi conductor strain gauges

16.13            Acoustical gauges