Solid Mechanics

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Solid object behaviour under the application of external load is analyzed in mechanics. The mechanics of the solid are called solid mechanics. Solid mechanics is a field of study that examines materials, structures, and the deformation of those under load.

Change on cross-section by internal forces or externally applied force is associated with solid mechanics. The strength of the failure of bodies, the elasticity of bodies or stress which may develop due to external load are some of the properties of the bodies in solid mechanics. The oratorical approach provides a similar result in solid mechanics.

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What is Solid Mechanics?

Solid mechanics is a branch of physical science that deals with the effects of forces, displacements, and accelerations on the motion of continuous solid media. In the context of solid mechanics, the forces are equivalent in the horizontal and vertical directions to let know the directional strain or deformation of the material.

The failure analysis of materials is done by comparing the internal stresses with the strength of the material. We consider the material to be intact if the stresses do not exceed the strength of the material made against the strength, which is brittle and does not have a yield point. There are exceptions to the rule that applies to nearly all materials under solid mechanics.

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Solid Mechanics Formula

Important solid mechanics formulae can be used for deflection under different load conditions, shear stress equations, torsion equations, and moment equations also for different types of support yield conditions. Some of these are-

  • Strain ( δ ) = PL/AE

Where; P = applied load on the beam, L = length of the beam, A= area of cross-section, E= modulus of elasticity

  • Bending moment equation M/I= F/Y= E/R
  • Torsional moment equation T/r= τ/J= G.θ/L

Where; M= Moment on beam, F = Shear force, T= Torsional force etc.

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Basic Principles of Solid Mechanics

The principles throughout the course are a part of the solutions to the problems examined in the course. They should be like demonstrations of understanding and application of the three principles.

  • Compatibility: It is compatible with the Displacement. Constraints on the geometry and/or deformation of structural elements in a given system are imposed by the nature of plausible deformation. Two solid objects can’t fit in the same space because elements have to change with each other.
  • Free Body Diagram: A part must have the proper reactions and/or internal forces applied if it is separated from or isolated from a body (also known as sectioning) or surroundings (also known as boundary conditions).
  • Stress-strain concept: The stress-strain is related to placement relations. Hooke’s Law links material properties and structural geometry in a structure.

Analysis of Solid Mechanics

The solid mechanics may be analyzed by the stress and strain relationship of the material. The concept of stress is to find the important material properties like elasticity, ductility, malleability, hardness and toughness that can be defined. When the external force is applied to the material body the nature of the material is affected either in cross-section or in geometry.

In solid mechanics, causes of external force may vary due to conditional services, due to work environment, due to contact with other materials/members, due to pressurized fluid or due to gravitational or inertia forces.

These applied external forces or developed internal forces raise a concept of stress as applied external forces opposed by material particles in equal and opposite directions may cause stress in solid mechanics.


Here a sample of material is under the load p as pull force. Let us consider it is a rectangular bar and it is having a cross-section area as “A” and when tensile force P is applied to it. The section is broken in two pieces at the section of XX as shown below-


Now the stress is considered as force P per unit area A as-

σ = P/A

Here we consider the total force on the proper cross-section area. If we take the random area with a differential limit of the area then we consider as-

σ = δP/δA

where δis indicated as a partial load or area of cross-section. To cover the whole area under total load we took a limit as limit 0 to A of the cross-section. The unit of the stress is like MPa = 106 Pa, GPa = 109 Pa, and KPa = 103 Pa.

In solid mechanics stress concept is classified by different types of stress as-

  • Normal stress
  • Shear stress
  • Bending stress
  • Bearing stress
  • Torsional stress

Stress-Strain Relationship

In general, after externally loaded on the material, strain is like deformation is developed and stress is induced between the molecules of the solid body of material. Now the relation is formed between stress and strain as when strain is changed how stress affects the materials body in solid mechanics.



When strain is at zero.

Stress is also zero for the material body.

When strain is 0.2% of the fracture strain.

Stress is reached to the yield point of the material sample.

When strain is 2% of the fracture strain.

Stress is reached to the plastic point of the material sample.

When strain is 20% of the total strain.

Stress of material is reaches to the necking point of the material sample.

When strain reaches the fracture point.

Stress is reached to the fracture point of material which is less than the yield point of the material sample.

The stress-strain is also classified as the engineering stress-strain concept of solid mechanics or the actual stress-strain concept of solid mechanics.

The actual stress is = Actual applied force/Cross section area of the necking portion

The engineering stress is = Applied force/Cross section area of the original sample portion

Where engineering stress is always greater than the actual stress.

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