المادة: مقاومة المواد sub.: strength of materials
DESCRIPTION
جامعة الكوفة – كلية الهندسة –قسم المنشات و الموارد المائية المرحلة الثانية university of Kufa – College of engineering –structures and water resources department 2 nd class. المادة: مقاومة المواد sub.: strength of materials الهدف من المحاضرة : التعرف على موضوع مقاومة المواد-الجزء2 - PowerPoint PPT PresentationTRANSCRIPT
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