Syllabus For The Subject Mechanics of Solids


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

1.7                      Loads

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

2.3 Load-extension relationships

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)

6.3               Assumptions made

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 obtain1and )

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


9.13Unit load method

9.14Plastic collapse of beams

9.15Residual stresses in beams

 Example for practice 9


10    Theories of Elastic failure


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


 Example for practice 10


11    Thick cylinders and spheres


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


12.2Axially loaded struts

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

12.8Eccentrically loaded struts

12.9Struts with initial curvature

12.10            Perry-Robertson formula

12.11            Dynamic instability

        Example for practice 12


13    Unsymmetrical bending of beams


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


14.2Vertical shearing stresses

14.3Horizontal shearing stresses

14.4Shear centre

14.5Shear centre position for closed thin-walled tubes

14.6Shear deflection


      Example for practice 14


15    The matrix displacement method


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


16.2Electrical resistance strain gauges

16.3Types of electrical resistance strain gauge

16.4Gauge material

16.5Gauges adhesives


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






















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