INTRODUCTION

Name : Mohamad Redhwan Abd Aziz

Post : Lecturer @ DEAN CENTER OF HND STUDIES

Subject : Solid Mechanics

Code : BME 2033

Room : CENTER OF HND STUDIES OFFICE

H/P No. : 019-2579663

W/SITE : Http://tatiuc.edu.my/redhwan

email : redhwan296@yahoo.com

INTRODUCTION (Cont..)

� Monday 11-1pm (L13/Mech lab)

� Tutorial

� Lab

� Tuesday 10-12pm (L9)

� Lecture

INTRODUCTION (Cont..)

� BME 2023 SOLID MECHANICS

� 3 CREDIT HOURS � 2 Hours for lecture

� 2 hours for lab/tutorial

� Assessment/marks distribution

� Quizzes/Assignments - 10%

� Test - 30%

� Lab report - 20%

� Final Exam - 40%

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

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

TOPICS

� Topic cover

� Stress and strain

• 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, υ and G

• Power transmission on round bar

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

TOPICS (Cont>)

� Topic cover � Non Simetric Bending

• 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

REFERENCES

1. James M. Gere (2006) “ Mechanics of Materials”. 6th

Edition, Thompson

2. R.C. Hibbeler (2003) “ Mechanics of Materials”. 5th

Edition, Prentice Hall

3. Raymond Parnes (2001), “Solid Mechanics in

Engineering”. John Willey and Son

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

σ

A

F

Area

ForceStress === σ

2/mN

Tensile and compressive forces are called DIRECT FORCES

Stress is the force per unit area upon which it acts.

>.. Unit is Pascal (Pa) or

Note: Most of engineering fields used kPa, MPa, GPa.

( Simbol – Sigma)

ε

L

xStrain == ε ε

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

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).

called EPSILON

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

AF σ= Lx ε=L

A

x

F

ε

σ=

ε

σ=

Ax

FL hence and

=Eε

σ=

Ax

FL

•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.

STRESS STRAIN DIAGRAM

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

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 STRESS@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

STRESS STRAIN DIAGRAM

� STRAIN HARDENING � 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

SHEAR STRESS τ

•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

�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.

A

F=τ and symbol is called Tau •Shear stress,

�The sign convention for shear force and stress is based on how it

shears the materials as shown below.

γ

L

x

γ

L

x=γ

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 :

( symbol called

Gamma)

Shear strain

•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.

MODULUS OF RIGIDITY (G)

•The gradient of the graph is constant so tconsx

Ftan=

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

tconAx

FL

x

Lx

A

F

L

x

A

F

tan===

τ=A

F

Where

L

x=γ

tconAx

FL

x

Lx

A

Ftan===

γ

τthen

•If we divide F by area A and x by the height L, the relationship is

still a constant and we get

This constant will have a special value for each elastic material

and is called the Modulus of Rigidity (G).

G=γ

τ

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.

τ

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

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

(σU) = ULTIMATE FORCE(PU) /AREA

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

SELECTION OF F.S.

1. Variations that may occur in the properties of the member under

considerations

2. The number of loading that may be expected during the life of the

structural/machine

3. The type of loading that are planned for in the design, or that may

occur in the future

4. The type of failure that may occur

5. Uncertainty due to the methods of analysis

6. Deterioration that may occur in the future because of poor

maintenance / because of unpreventable natural causes

7. The importance of a given member to the integrity of the whole

structure

WORKED EXAMPLE 8

0.6 m

SOLUTION

SOLUTION

SELF ASSESSMENT NO. 5

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 / δ) can be written as

AE

FL=δ

εσ E=

WORKED EXAMPLE 9

0.4 m

WORKED EXAMPLE 9

WORKED EXAMPLE 9

SELF ASSESSMENT NO. 6