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 - الجزء 2 Aim of the lecture: To understand the strength of materials concept- part2

1.2 STRENGTH OF MATERIALS subject which concerned with the behaviour and calculations of the response of the bodies subjected to external loads Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio 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

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Types of strength In 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 Shear Stress This cylinder is in Tension Forces Flexural (bending) stress This cylinder is in compression

Tension and Compression

Structures lab

Testing for strength

Applying Loads

Stress This 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:

Types of stress Compressive stress Compressive load Tensile load Compressive load Tensile load Tensile Stress

Measuring: Stress = Load/area

Shear Stress Similarly 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 Shear force Shear Force Area resisting shear

Ultimate Strength The 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 :

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Strain We 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

Shear stress and strain Shear force Shear Force Area resisting shear Shear displacement (x) Shear strain is angle  L

Units of stress and strain The basic unit for Force and Load is the Newton (N) which is equivalent to kg m/s 2. One kilogramme (kg) weight is equal to 9.81 N. In industry the units of stress are normally Newtons per square millimetre (N/mm 2 ) 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/mm 2 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 steel Yield Elastic 0.2% proof stress Stress Strain 0.2% Plastic Failure

Steel Test in Laboratory

Energy absorbed Stress (force) Strain (distance) Final strain Area = average stress  final strain = Energy absorbed = work done

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Modulus of Elasticity If 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

Measuring modulus of elasticity

Initial Tangent and Secant Modulus

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Flexural Strength d=depth deflection x Span L Tension region Compression region b=breadth Load W

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Fatigue Stress Strain Failure

1.2 STRENGTH OF MATERIALS Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio Creep

Poisson’s Ratio This 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 Strain 0.2% Plastic Failure s 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 Mass and Gravity Stress and strength Strain Modulus of Elasticity Flexural loads Fatigue Strength Poisson's ratio 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.

المصادر : references 1- R.C. Hibbeler “ Mechanics of materials “ 8 th edition, F. L. Singer “ strength of materials “ 10 th edition, Pete Claisse “ lectures in strength of materials concepts “ محاضرات مقومة المواد لجامعة بابل للأستاذ عبد الرضا محمد 1992