Introduction to
Mechanics of Deformable
Bodies
What is Mechanics of Deformable
Bodies?
 Also known as Mechanics of materials/ Strength of materials
 Deals with the relations between externally applied loads and their
internal effect on bodies. Moreover, the bodies are no longer
assumed to be ideally rigid; the deformations, however small, are of
major interest. The properties of the material of which a structure or
machine is made affect both its choice and dimensions that will
satisfy the requirements of strength and rigidity.
Analysis of Internal Forces
 Axial Force. This component measures the pulling (or pushing) action over
the section. A pull represents a tensile force that elongates the member,
whereas a push is a compressive force that shortens it.
 Shear Force. These are the components of the total resistance to sliding the
portion to one side of the exploratory section past the other.
 Torque. This component measures the resistance to twisting the member.
 Bending moments. These components measures the resistance to bending
the member about the Y and Z axes.
Analysis of Internal Forces
y
Bending Moment
(My , Mz)
z
Shear Force (Py , Pz)
Torque (Mx)
x
Axial Force (Px)
Simple Stress
 When a force is transmitted through a body, the body tends to change its shape or deform. The body is said to be
strained.
Applied Force (F)
 Simple Stress =Cross Sectional Area (A)

Units: Usually N/m2 (Pa), N/mm2, MN/m2, GN/m2 or N/cm2

Note: 1 N/mm2 = 1 MN/m2 = 1 Mpa

Simple stress may be tensile or compressive and result from forces acting perpendicular to the plane of the cross-section
Shearing Stress
 Shearing Stress is the stress due to the shearing force applied to the resisting
area.
Applied Force (F)
 Stress =Cross Sectional Area (A)
 Where: A= (π/4)(d)2
Torsion
 Is a shear stress that acts on a transverse cross-section which is caused by
the action of a twist. Torsional shear stress can be thought of as the shear
stress produced on a shaft due to twisting.
Tc
 Torsion = J

T= torque

c= distance of farthest fiber

J= polar moment of inertia
 For Solid Shaft
16T
 ST = π 𝐷2
For Hollow Shaft
16TD
ST = π (𝐷4 −𝑑4)
Bearing Stress
 Stress caused by a force which is perpendicular to the resisting area. It is the
contact pressure between two separate bodies.
Applied Force (F)
 Stress =Cross Sectional Area (A)
Bending/ Flexural Stress
 Bending stress is the normal stress that an object encounters when it is
subjected to a large load at a particular point that causes the object to
bend and become fatigued.
 Rectangular Section
Circular Section
Mc 6M
 Sf = I =
bh3
Mc 32M
Sf = I = π𝐷3

M = bending moment

I = moment of Inertia

C = distance from farthest fiber
Thermal Stress
 Thermal stress is the stress produced by any change in the temperature of
the material. Thermal stress is induced in a body when the temperature of
the body is raised or lowered and the body is not allowed to expand or
contract freely. Thermal stress includes both heat and cold stress.
Eδ
 St = L
St = E (ΔT)

E = modulus of elasticity

Δ = Elongation

= coefficient of thermal expansion