Mechanics of Materials

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About Mechanics of Materials

The solid mechanics as a subject may be defined as a branch of applied mechanics that deals with behaviors of solid bodies subjected to various types of loadings. This is usually subdivided into further two streams i.e. Mechanics of rigid bodies or simply Mechanics and Mechanics of deformable solids. The mechanics of deformable solids which is branch of applied mechanics is known by several names i.e. strength of materials, mechanics of materials etc.

Basic concept of Mechanics of Materials::

Decision making comes in every stage of design. Consider two cars of different makes. They may both be reasonable cars and serve the same purpose but the designs are different. The designers consider different factors and come to certain conclusions leading to an optimum design. Market survey gives an indication of what people want. Existing norms play an important role. Once a critical decision is made, the rest of the design features follow.

Mechanics of rigid bodies:

The mechanics of rigid bodies is primarily concerned with the static and dynamic behavior under external forces of engineering components and systems which are treated as infinitely strong and undeformable. Primarily we deal here with the forces and motions associated with particles and rigid bodies.

Mechanics of deformable solids:

The mechanics of deformable solids is more concerned with the internal forces and associated changes in the geometry of the components involved. Of particular importance are the properties of the materials used, the strength of which will determine whether the components fail by breaking in service, and the stiffness of which will determine whether the amount of deformation they suffer is acceptable. Therefore, the subject of mechanics of materials or strength of materials is central to the whole activity of engineering design. Usually the objectives in analysis here will be the determination of the stresses, strains, and deflections produced by loads. Theoretical analyses and experimental results have an equal role in this field.

Aim of Strength of Materials:

Aim of subject is to derive expressions for stress, strain and deformation under different loading conditions by using experimentally obtained elastic properties like E (Young’s Modulus) and u (Poisson’s ratio). Ultimate aim of design is to develop a drawing or a plan i.e. selection of appropriate shape, selection of appropriate material (calculation of dimensions by using strength of materials equations), selection of manufacturing process details in such a way that the resulting machine component should perform its functionality satisfactory.

Assumptions made while deriving Strength of Materials:

  1. Material is assumed to be homogeneous and isotropic.
  2. Material obeys Hooke’s law in elastic region i.e. Induced stress and strain are assumed to be within elastic region.
  3. Member is assumed to be prismatic i.e. cross-sectional dimensions remains same throughout the length of the member.
  4. Member is subjected to static loading.
  5. Self-weight of the member is neglected.
  6. Member is assumed to be under static equilibrium condition i.e. summation of all the forces in x, y & z direction is zero and summation of all the couples in x, y & z direction is zero.

Topics to be taught under Strength of Materials:

  1. Loading : Types of loading like transverse loading or axial loading.
  2. Types of stresses: only two basic stresses exist: (1) normal stress and (2) shear stress. Other stresses either are similar to these basic stresses or are a combination of these e.g. bending stress is a combination tensile, compressive and shear stresses. Torsional stress, as encountered in twisting of a shaft is a shearing stress.
  3. Types of strains: Likewise stress two strains are there (1) normal strains and (2) shear strains
  4. Strain Energy: Various topics like Resilience, Proof Resilience, modulus of resilience, Toughness, Modulus of toughness has been taught in this topic.
  5. Thermal Stresses: Cases like completely restricted expansion, thermal stresses in compound bars in series, parallel etc.
  6. Shear Force Diagram & Bending moment Diagram: SFD and BMD are drawn to locate the maximum shear force and bending moment in the beam so that design should be done accordingly.
  7. Principal stresses & Strains: Principal stresses and strains are to be drawn according to Mohr’s circle diagram. Principal stresses are those stresses which acted in a plane in such a way that the value of shear stress is zero in that plane.
  8. Theories of Failure: various theories like Maximum Principal stress theory, Maximum shear stress theory, Maximum Principal strain theory, Total Strain Theory, Maximum distortion energy theory are to be studied in this topic.

· Mechanics of Materials, Gere Timoshenko.
· NPTEL, Mechanical, Strength of Materials.

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