المادة: مقاومة المواد sub.: strength of materials

و – – المنشات قسم الهندسة كلية الكوفة جامعةالمائية الموارد

الثانية المرحلةuniversity of Kufa – College of engineering –structures and water resources department

2nd class. :المواد مقاومة sub.: strength ofالمادة

materials- الجزء : المواد مقاومة موضوع على التعرف المحاضرة من 2الهدف

Aim of the lecture:

To understand the strength of materials concept- part2

1.2 STRENGTH OF MATERIALSsubject which concerned with the behaviour and calculations of

the response of the bodies subjected to external loads .

1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

The mass of an object is defined from its acceleration when a force is applied, i.e. from the

equation F = Ma, not from gravity.

Gravity is normally the largest force acting on a structure. The gravitational force on a mass M is:

The gravitational force on an object is called its weight. Thus an object will have a weight of 9.81N

per kg of mass

sm/ 9.81 = g where

Mg= F2

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Types of strengthIn engineering the term strength is always

defined and is probably one of the following

         Compressive strength          Tensile strength          Shear strength

depending on the type of loading.

Compression, tension, bending and shear

ShearStress

This cylinderis in Tension

Forces

Flexural (bending)stress

This cylinder is

in compressio

n

Tension and Compression

Structures lab

Testing for strength

Applying Loads

StressThis is a measure of the internal resistance in a material to an externally applied load. For direct compressive or tensile loading the

stress is designated and is defined as:

stress = load W

area A

Types of stress

Compressive stress

Compressive load

Tensile load

Compressive load Tensile load

Tensile Stress

Measuring: Stress = Load/area

Shear StressSimilarly in shear the shear stress is a measure of the internal resistance of a material to an externally applied shear load.

The shear stress is defined as:

shear stress = load W

area resisting shear A

Shear stress

Shear force

Shear Force

Area resisting shear

Ultimate StrengthThe strength of a material is a measure of the stress that it can take when in use. The ultimate strength is the measured stress at failure but this is not normally used for design because safety factors are required.

The normal way to define a safety factor is :

stressePermissibl

stressUltimate

loadedwhen stress

failureat stress = factorsafety

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

StrainWe must also define strain. In engineering this is not a measure of force but is a measure of the deformation produced by the influence of stress. For tensile and

compressive loads:

Strain is dimensionless, i.e. it is not measured in metres, killogrammes etc.

 For shear loads the strain is defined as the

angle This is measured in radians

strain = increase in length x

original length L

shear strain shear displacement x

width L

Shear stress and strain

Shear force

Shear Force

Area resisting shear Shear displacement (x)

Shear strain is angle L

Units of stress and strainThe basic unit for Force and Load is the

Newton (N) which is equivalent to kg m/s2. One kilogramme (kg) weight is equal to 9.81

N .In industry the units of stress are normally

Newtons per square millimetre (N/mm2) but this is not a base unit for calculations.

The MKS unit for pressure is the Pascal. 1 Pascal = 1 Newton per square metre

Pressure and Stress have the same units 1 MPa = 1 N/mm2

Strain has no dimensions. It is expressed as a percentage or in microstrain (s) .

A strain of 1 s is an extension of one part per million. A strain of 0.2% is equal to 2000 s

Measuring: Strain = extension/length

Elastic and Plastic deformation

Stress

Strain

Stress

Strain

Permanent Deformation

Elastic deformation Plastic deformation

Stress-Strain curve for steelYield

Elastic

0.2% proof stress

Stress

Strain0.2%

Plastic

Failure

Steel Test in LaboratoryHigh Tensile Steel

0

10000

20000

30000

40000

-1 0 1 2 3 4

Extension mm (extensometer)

Lo

ad N

Energy absorbed

Stress(force)

Strain (distance)Final strain

Area = average stress final strain = Energy absorbed= work done

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Modulus of ElasticityIf the strain is "elastic" Hooke's law may be

used to define

Young's modulus is also called the modulus of elasticity or stiffness and is a measure of how much strain occurs due to a given stress. Because strain is dimensionless Young's modulus has the units of stress or

pressure

A

L

x

W =

Strain

Stress = E Modulus Youngs

Measuring modulus of elasticity

Initial Tangent and Secant Modulus

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Flexural Strength

d=depth

deflection x

Span L

Tension region

Compression region

b=breadth

Load W

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Fatigue

Stress

Strain

Failure

1.2 STRENGTH OF MATERIALS1.2.1 Mass and Gravity1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Poisson’s RatioThis is a measure of the amount by which a

solid "spreads out sideways" under the action of a load from above. It is defined as :

) lateral strain) / (vertical strain ( and is dimensionless.Note that a material like timber which has

a "grain direction" will have a number of different Poisson's ratios corresponding to loading and deformation in different

directions.

How to calculate deflection if the proof stress is applied and then partially removed.If a sample is loaded up to the 0.2% proof stress and then unloaded to a stress s the strain x = 0.2% + s/E where E is the Young’s modulus

Yield

0.2% proof stress

Stress

Strain0.2%

Plastic

Failure

s

0.002 s/E

Conclusion:When the loads (forces) applied at any body their were resistance to theses force called strength of the body material (stress) and their were a deformation happened due to these loads called (strain) , the both subject are explained in our lecture with their types, examples, and calculations. 1.2.1 Mass and Gravity

1.2.2 Stress and strength1.2.3 Strain1.2.4 Modulus of Elasticity1.2.5 Flexural loads1.2.6 Fatigue Strength1.2.7 Poisson's ratio1.2.8 Creep

Now we are waiting your questions , notes , misunderstanding , and opinions about the subject or it’s applications in different fields especially most engineering analysis and design depend on our current subject, also in next lecture we take more mathematical examples to explain the concepts and applications.

references : المصادر1- R.C. Hibbeler “ Mechanics of materials “ 8th edition , 2011 2- F. L. Singer “ strength of materials “ 10th edition , 2008 3- Pete Claisse “ lectures in strength of materials concepts “ 2010 محاضرات مقومة المواد لجامعة بابل -4

1992لألستاذ عبد الرضا محمد