Strength properties

1. STRENGTH OF MATERIALS
1
. Behaviour of Reinforced Concrete
. Strength of Materials
. Different Effects When Subjected to Different
Mechanical Stresses.

2. Behaviour of Reinforced Concrete
2
• Concrete in Compression and Tension

3. Behaviour of Reinforced Concrete
3
• Concrete in Compression and Tension
• Steel reinforcing bars are provided in Tension Zone.
• Design Strength of high yield steel are about 10-50 of
design compressive strength of concrete.
• So relatively small areas are required.
Exaggerated deformed view of bridge beam

4. Behaviour of Reinforced Concrete
4
• Concrete in Compression and Tension
• Steel reinforcing bars are provided in Tension zone in span.
• Then tension zone over supports.
• Shear reinforcements
• Other considerations: Continuity/Ties

5. Behaviour of Reinforced Concrete
5
• Reinforced Concrete_ A Composite material
• Two materials are more or less
complementary
• When combined Steel provides tensile
strength and some shear strength.
• Concrete is good in compression and
helps to provide durability and fire
resistance.

6. Strength of Materials
6
• Stress
• When an external force is applied (P) on a material it deforms and consequently
internal forces (R) are induced in the material. As the deformation increases the
internal forces also increases. This continues until internal forces = external forces
and thus the deformation stops.
• This internal force for unit of cross sectional area (A) is called stress and is
mathematically defined as external force per unit area.
• Stress is force divided by area
When We consider direct Normal) stress..

7. 7
• Stress
Mathematically,
Since resisting force equals to the applied load i.e. P = R. So
Where,
•R = Resisting force induced in the body.
•P = Load applied on the body.
•A = Cross Section area of the body.
Units:
N/ m2 or N/mm2
Strength of Materials

8. 8
• Strain
• When an external force (P) is applied on a body, there is some change (dl) occur in
the dimension of the body. The ratio of this change of dimension in the body to its
original dimension (l) is called strain.
Strength of Materials
Strain = (change in length)/(original length)
e = dl/l

9. 9
• Hook 'Law
Strength of Materials
For relatively small deformations of an object,
the displacement or size of the deformation is
directly proportional to the deforming force or
load. Under these conditions the object returns
to its original shape and size upon removal of
the load. Robert Hooke
1635-1703

10. 10
• Hook 'Law
Strength of Materials
Hooke’s Law Equation in Terms of Stress and Strain
According to this law,
Within the elastic limit, stress is proportional to the strain. Thus,
Hooke’s Law equation can be expressed in terms of stress and strain;
Stress α Strain or stress / strain = constant = E
Stress = Young’s modulus of elasticity × Strain
σ = E ε
Where,
σ is the stress,
E is the modulus of elasticity also known as Young’s modulus of
elasticity
ε is the strain

11. 11
• Stress Vs Strain Relationship
Strength of Materials
A
B C
D E
OA-Elastic proportionate region
AB- Elastic Non proportionate region
BC-Plastic plateau
CD-Strain hardening
DE-Necking

12. 12
Properties of Stress Strain Diagram
Strength of Materials
• Elastic region_ The elastic limit on a stress-strain curve is the point where the
behaviour of the material switches from elastic to plastic. If the stress (and
therefore strain) applied to a material is lower than the elastic limit, both the
stress and strain will return to zero (recover) when the load is removed This
internal force for unit of cross sectional area (A) is called stress and is
mathematically defined as external force per unit area.
• Plastic plateau_ Having significant plastic deformation without increasing the
stress.
• Strain Hardening (Work hardening)_ Strengthening of material by plastic
deformation due to dislocation of molecules generated within the crystal
structure.
• Necking _Reduces the cross sectional area, just before necking material
reaches its maximum tensile stress called “Ultimate Tensile Strength” UTS.
• Damage and Fracture_ Continuously reduces the cross section area and stress.
When fracture, release heat and sound etc. (This is how strain energy releases)
• Ductility_ Ability to undergo large plastic deformation before rupture.
• Area under the curve: Toughness
• Toughness: Amount of energy that can be absorbed before
rupture
• Brittle_ Brittle material can withstand little or no plastic strain

13. 13
• Poisson's Effect
Strength of Materials
Poisson effect,
the deformation (expansion
or contraction) of a material
in directions perpendicular
to the specific direction
of loading
 The value of Poisson's ratio
is the negative of the ratio
of transverse strain to
axial strain.
 Most materials have
Poisson's ratio values
ranging between 0.0 and
0.5.

14. 14
• Young’s Modulus
Strength of Materials
The Young’s modulus of
elasticity is the elastic
modulus for tensile and
compressive stress in the
linear elasticity regime of a
uniaxial deformation

15. 15
Strength of Materials
• Low C % steel (Mild) show more ductile behaviour while high C%
steel (Tor steel, HT bars) shows brittle behaviour.
• Brittle material has no well defined yield point compared to mild
steel. (For tor steel 0.2% proof stress is defined)
• E does not chanced with the types of steel 200GPa
• Stress Vs Strain Relationship of Steel types

16. 16
Strength of Materials
• Concrete is a brittle material.
• When the grade increases brittleness is also increases.
• There is no well defined yield point.
• Instead of young’s modulus, secant modulus Ecm of elasticity is
defined.
• Stress Vs Strain Relationship of Concrete grades

17. 17
Creep
Creep _ It is a time dependent deformation under a sustained load.
Generally occurs at high temperature (thermal creep), but can also
happen at room temperature.
Creep Stages
1. • Primary Creep: starts at a
rapid rate and slows with
time.
2. • Secondary Creep: has a
relatively uniform rate.
3. • Tertiary Creep: has an
accelerated creep rate and
terminates when the
material breaks or ruptures.

18. 18
Fatigue
What Is Material Fatigue?
Material fatigue is a phenomenon where structures fail when subjected to a cyclic load.
This type of structural damage occurs even when the experienced stress range is far below
the static material strength. Fatigue is the most common source behind failures of
mechanical structures (Machine bases).
This process until a component finally fails under repeated loading which can be divided
into three stages:
1. During a large number of cycles, the
damage develops on the microscopic level
and grows until a macroscopic crack is
formed.
2. The macroscopic crack grows for each
cycle until it reaches a critical length.
3. The cracked component breaks because it
can no longer sustain the peak load.
For certain applications, the second stage
cannot be observed. A microscopic crack
instead grows rapidly, causing sudden failure
of the component.