A Presentation on shear stress strain curve & modulus of rigidity

1. Welcome To My Presentation
Presented byAfsana Ishrat Khan
Dept. of Civil Engineering
4th Year 2nd Semester
ID: 10.01.03.039

2. Course No.
: CE 416
Course Title
: Pre-stressed Concrete Lab.
Course Teacher : Sabreena Nasrin Madam &
Munshi Galib Muktadir Sir
Topic Of Presentation
“Shear Stress-Strain Curve
&
Modulus Of Rigidity”

3. Shear Stress
• Shear stress that acts parallel to a surface. It can
cause one object to slide over another. It also
tends to deform originally rectangular objects
into parallelograms. The most general definition
is that shear acts to change the angles in an
object. Shear stress = τ = Force(F)/Area(A)

4. Shear Strain
• It is the amount of deformation perpendicular to
a given line rather than parallel to it. The ratio
turns out to be tan A, where A is the angle the
sheared line makes with its original orientation..
Generally, shear strain = γ = Δx/l

5. Shear Stress-Strain Curve
• The relationship between the shear stress and shear
strain for a particular material is known as that
particular material's Shear Stress-Strain curve.
• Shear stress-strain curves are an extremely important
graphical measure of a material's mechanical
properties

6. Cont'd

7. Various Stress-Strain Curves For
Different Materials
• Linear elastic material: A linear elastic material
is one in which the strain is proportional to stress
as shown below:

8. Cont'd
• Rigid Materials: It is the one which do not
experience any strain regardless of the applied
stress.

9. Cont'd
• Perfectly plastic: A perfectly plastic i.e. nonstrain hardening material is shown below:

10. Cont'd
• Rigid Plastic material(strain hardening):
A rigid plastic material i.e. strain hardening is
depicted in the figure below:

11. Cont'd
• Elastic Perfectly Plastic material: The elastic
perfectly plastic material is having the
characteristics as shown below:

12. Cont'd
• Elastic – Plastic material: The elastic plastic
material exhibits a stress Vs strain diagram as
depicted in the figure below:

13. Typical Stress-Strain Curve For Ductile
Material

14. Modulus of Rigidity
(Definition)
• Modulus of rigidity is the ratio of shear stress to
the displacement per unit sample length (shear
strain). More specifically modulus of rigidity (or
Shear Modulus) is the coefficient of elasticity for
a shearing force.
• In materials science, shear modulus or modulus
of rigidity, denoted by G defined as the ratio
of shear stress to the shear strain, i.e. G = τ / γ

15. • where,
τ=F/A= shear stress, F=force, A=area on which
the force acts, γ = Δx/l= shear strain,
Δx=transverse displacement, l= initial length.
Shear modulus' derived SI unit is the pascal (Pa)

16. Modulus of Rigidity
(PURPOSE)
• Modulus of rigidity, or the shearing modulus,
is used to determine how elastic or bendable
materials will be if they are sheared, which is
being pushed parallel from opposite sides.
This property becomes the useful part of
many calculations, and it is called the
coefficient of elasticity during shearing.

17. THANK YOU