1. INTRODUCTION (Cont…) Objective
Understand different methods that used to analyse stress and strain in solid body
Apply various principles to solve problems in solid mechanics
Analyse forces of solid body cause by external force
Analyse the result of solid mechanics experiments

2. INTRODUCTION (Cont…) Learning Outcome
Apply the concepts of stress, strain, torsion and bending and deflection of bar and beam in engineering field
Explain the stress, strain, torsion and bending
Calculate and determine the stress, strain and bending of solid body that subjected to external and internal load
Use solid mechanic apparatus and analyse the experiments result
Work in-group that relates the basic theory with application of solid mechanics

3. TOPICS Topic cover Stress and strain Torsion
Introduction to stress and strain, stress strain diagram
Elasticity and plasticity and Hooke’s law
Shear Stress and Shear strain
Load and stress limit
Axial force and deflection of body
Torsion
Introduction, round bar torsion, non-uniform torsion.
Relation between Young’s Modulus E,  and G
Power transmission on round bar

4. TOPICS (Cont…) Topic cover Shear Force and bending moment
Introduction, types of beam and load
Shear force and bending moment
Relation between load, shear force and bending moment
Bending Stress
Introduction, Simple bending theory
Area of 2nd moment, parallel axis theorem
Deflection of composite beam

5. TOPICS (Cont…) Topic cover Non Simetric Bending Shear Stress in beam
Introduction, non-simetric bending
Product of 2nd moment area, determination of stress
Shear Stress in beam
Introduction, Stream of shear force
Shear stress and shear strain in edge beam
Deflection of Beam
Introduction
Equation of elastic curve, slope equation and integral deflection
Statically indeterminate Beams and shaft

6. REFERENCES
James M. Gere (2006) “ Mechanics of Materials”. 6th Edition, Thompson
R.C. Hibbeler (2003) “ Mechanics of Materials”. 5th Edition, Prentice Hall
Raymond Parnes (2001), “Solid Mechanics in Engineering”. John Willey and Son

7. Stress and strain
DIRECT STRESS
When a force is applied to an elastic body, the body deforms. The way in which the body deforms depends upon the type of force applied to it.
Compression force makes the body shorter.
A tensile force makes the body longer

8. Tensile and compressive forces are called DIRECT FORCES
Stress is the force per unit area upon which it acts.
….. Unit is Pascal (Pa) or
( Simbol – Sigma)
Note: Most of engineering fields used kPa, MPa, GPa.

9. Strain is the deformation per unit of the original length.
DIRECT STRAIN ,
In each case, a force F produces a deformation x. In engineering, we usually change this force into stress and the deformation into strain and we define these as follows:
Strain is the deformation per unit of the original length.
The symbol
called EPSILON
Strain has no unit’s since it is a ratio of length to length. Most engineering materials do not stretch very mush before they become damages, so strain values are very small figures. It is quite normal to change small numbers in to the exponent for 10-6( micro strain).

10. MODULUS OF ELASTICITY (E)
Elastic materials always spring back into shape when released. They also obey HOOKE’s LAW.
This is the law of spring which states that deformation is directly proportional to the force. F/x = stiffness = kN/m
The stiffness is different for the different material and different sizes of the material. We may eliminate the size by using stress and strain instead of force and deformation:
If F and x is refer to the direct stress and strain , then
hence
and

11. The stiffness is now in terms of stress and strain only and this constant is called the MODULUS of ELASTICITY (E)
A graph of stress against strain will be straight line with gradient of E. The units of E are the same as the unit of stress.
ULTIMATE TENSILE STRESS
If a material is stretched until it breaks, the tensile stress has reached the absolute limit and this stress level is called the ultimate tensile stress.

12. STRESS STRAIN DIAGRAM

13. STRESS STRAIN DIAGRAM Elastic behaviour
The curve is straight line trough out most of the region
Stress is proportional with strain
Material to be linearly elastic
Proportional limit
The upper limit to linear line
The material still respond elastically
The curve tend to bend and flatten out
Elastic limit
Upon reaching this point, if load is remove, the specimen still return to original shape

14. STRESS STRAIN DIAGRAM Yielding
A Slight increase in stress above the elastic limit will result in breakdown of the material and cause it to deform permanently.
This behaviour is called yielding
The stress that cause = YIELD POINT
Plastic deformation
Once yield point is reached, the specimen will elongate (Strain) without any increase in load
Material in this state = perfectly plastic

15. STRESS STRAIN DIAGRAM STRAIN HARDENING NECKING
When yielding has ended, further load applied, resulting in a curve that rises continuously
Become flat when reached ULTIMATE STRESS
The rise in the curve = STRAIN HARDENING
While specimen is elongating, its cross sectional will decrease
The decrease is fairly uniform
NECKING
At the ultimate stress, the cross sectional area begins its localised region of specimen
it is caused by slip planes formed within material
Actual strain produced by shear strain
As a result, “neck” tend to form
Smaller area can only carry lesser load, hence curve donward
Specimen break at FRACTURE STRESS

16. SHEAR STRESS
Shear force is a force applied sideways on the material (transversely loaded).
When a pair of shears cut a material
When a material is punched
When a beam has a transverse load

17. Shear stress is the force per unit area carrying the load
Shear stress is the force per unit area carrying the load. This means the cross sectional area of the material being cut, the beam and pin.
Shear stress,
and symbol is called Tau
The sign convention for shear force and stress is based on how it shears the materials as shown below.

18. SHEAR STRAIN
The force causes the material to deform as shown. The shear strain is defined as the ratio of the distance deformed to the height
. Since this is a very small angle , we can say that :
Shear strain
( symbol called Gamma)

19. The gradient of the graph is constant so
MODULUS OF RIGIDITY (G)
If we conduct an experiment and measure x for various values of F, we would find that if the material is elastic, it behave like spring and so long as we do not damage the material by using too big force, the graph of F and x is straight line as shown.
The gradient of the graph is constant so
and this is the spring stiffness of the block in N/m.
If we divide F by area A and x by the height L, the relationship is still a constant and we get

20. If we divide F by area A and x by the height L, the relationship is still a constant and we get
Where
then
This constant will have a special value for each elastic material and is called the Modulus of Rigidity (G).

21. ULTIMATE SHEAR STRESS
If a material is sheared beyond a certain limit and it becomes permanently distorted and does not spring all the way back to its original shape, the elastic limit has been exceeded.
If the material stressed to the limit so that it parts into two, the ultimate limit has been reached.
The ultimate shear stress has symbol and this value is used to calculate the force needed by shears and punches.

31. DOUBLE SHEAR
Consider a pin joint with a support on both ends as shown. This is called CLEVIS and CLEVIS PIN
By balance of force, the force in the two supports is F/2 each
The area sheared is twice the cross section of the pin
So it takes twice as much force to break the pin as for a case of single shear
Double shear arrangements doubles the maximum force allowed in the pin

34. LOAD AND STRESS LIMIT
DESIGN CONSIDERATION
Will help engineers with their important task in Designing structural/machine that is SAFE and ECONOMICALLY perform for a specified function
DETERMINATION OF ULTIMATE STRENGTH
An important element to be considered by a designer is how the material that has been selected will behave under a load
This is determined by performing specific test (e.g. Tensile test)
ULTIMATE FORCE (PU)= The largest force that may be applied to the specimen is reached, and the specimen either breaks or begins to carry less load
ULTIMATE NORMAL STRESS
(U) = ULTIMATE FORCE(PU) /AREA

35. ALLOWABLE LOAD / ALLOWABLE STRESS
Max load that a structural member/machine component will be allowed to carry under normal conditions of utilisation is considerably smaller than the ultimate load
This smaller load = Allowable load / Working load / Design load
Only a fraction of ultimate load capacity of the member is utilised when allowable load is applied
The remaining portion of the load-carrying capacity of the member is kept in reserve to assure its safe performance
The ratio of the ultimate load/allowable load is used to define FACTOR OF SAFETY
FACTOR OF SAFETY = ULTIMATE LOAD/ALLOWABLE LOAD @
FACTOR OF SAFETY = ULTIMATE STRESS/ALLOWABLE STRESS

36. SELECTION OF F.S.
Variations that may occur in the properties of the member under considerations
The number of loading that may be expected during the life of the structural/machine
The type of loading that are planned for in the design, or that may occur in the future
The type of failure that may occur
Uncertainty due to the methods of analysis
Deterioration that may occur in the future because of poor maintenance / because of unpreventable natural causes
The importance of a given member to the integrity of the whole structure

37. WORKED EXAMPLE 8
0.6 m

38. SOLUTION

39. SOLUTION

40. SELF ASSESSMENT NO. 5

41. AXIAL FORCE & DEFLECTION OF BODY
Deformations of members under axial loading
If the resulting axial stress does not exceed the proportional limit of the material, Hooke’s Law may be applied
Then deformation (x / ) can be written as

42. WORKED EXAMPLE 9
0.4 m

43. WORKED EXAMPLE 9

44. WORKED EXAMPLE 9

45. SELF ASSESSMENT NO. 6