Force causes stress and strain in materials. Stress is the internal resisting force within a material when an external force acts on it. It is calculated by dividing the applied force by the material's cross-sectional area. Normal stress acts perpendicular to a surface, while shear stress acts parallel. The Young's modulus quantifies a material's resistance to elastic deformation from stress, and is calculated from the material's stress and strain. The shear modulus similarly quantifies a material's resistance to shear deformation from parallel forces. These moduli are important properties for understanding how materials deform under different types of loads.

1. Force, Stress, Strain and Factor
of Safety
By
Dr. Mrinal Kanti Manik
Director
LDC Institute of Technical Studies,
Soraon
Prayagraj, UP-211004
L D C Institute of Technical Studies Soraon, Prayagraj, UP-111004, India

2. What is Force and it’s unit?
Force is definition as physical power or strength possessed by a living being that
will change/tends to change the motion of an object. SI unit is Newton, Dyne in CGS
The man is lifting a load
The spring is loaded with gravity force
Unbalance weight in fulcrum

3. Engineering-stress definitions
Stress is the internal resisting force acting within the material to resist
externally applied force.
Normal force causing shear
**(Suppose force acting in this figure is
100Newton on the Surface having 4X4
cm2 in dimension then)
Stress= Force/cross sectional area.
= 100/4x4
=100/16
=6.25 N/cm2

4. Normal Stress Shear Stress
When a force acts perpendicular or "normal" to the surface of an
object, it exerts a normal stress.
On the other hand when force acts parallel to the surface of an
object, it exerts a shear stress.
Normal stress and Shear stress

5. Poisson's ratio of a material defines the ratio of
transverse strain (x direction) to the axial strain (y
direction) as shown in the fig.
Poisson’s ratio

6. Mathematicaly Stress &Strain

9. Hook’s law state that the stress in the material is directly proportional
to the strain within the elastic limit.

12. Calculate Stress and Strain of the spring where dia. of the spring wire is 4mm.
** Calculate young’s modulus of the wire under test when diameter of the wire is taken
as 6mm, 8mm and 1cm.

13. Young’s Modulus
An elastic modulus (also known
as modulus of elasticity) is a quantity
that measures an object or substance's
resistance to being deformed
elastically (i.e., non-permanently)
when a stress is applied to it.
Modulus of elasticity is a measure of
the stress–strain relationship and is
an important parameter in the
evaluation of the deformation
response of concrete/materials under
working loads.

14. Young’s Modulus

16. Shear modulus or modulus of rigidity
Shear modulus or modulus of rigidity, denoted by G, or sometimes S
or μ, is defined as the ratio of shear stress to the shear strain:
 Modulus of elasticity is used to calculate the deformation of an
object when a deforming force acts at right angles to a surface of the
object.
Modulus of rigidity is used to calculate deformations when a
deforming force acts parallel to the surface of an object.
Bulk modulus is the measure of the decrease
in volume with an increase in pressure.

17. Relation amongst all the Modulus

21. EXAMPLE -3.
A metal cube of side 0.20 m is subjected to a shearing force
of 4000 N. The top surface is displaced through 0.50 cm with
respect to the bottom. Calculate the shear modulus of
elasticity of the metal.
Solution
Here, L = 0.20 m, F = 4000 N, x = 0.50 cm = 0.005 m and Area
A = L2 = 0.04 m2
Therefore, Shear modulus