Strength of material for Mechanical EngineeringPPT.pptx

Stress

1. Strength of material By: Tewodros B elayneh (MSc) Department of Mechanical E ngineering Gambella University Gambella , E thiopia

2. CHAPTER ONE Stress and Strain

3. Contents Definition of stress and strain Definition of young’s modulus & poison ratio Relationship b/n Stress and Strain Classification of stress and strain Plane stress Mohr circle diagram

4. Definition of stress Stress ( ) When a material is subjected to an external force, a resisting force is set up within the component. This internal resistance force per unit area acting on a material or intensity of the forces distributed over a given section is called the stress at a point. therefore Where F is force(N) A is original area(m 2 ) The unit of stress will be expresses in N/ m 2 .  

5. Definition of strain 2. Strain ( ) When a material is subjected to an external force, the material will displace from its original position. Strain can be defined as the displacement per unit original length. Therefore Where ∆L is change in length(mm) L is original length(mm) strain is a dimensionless parameter  

6. Definition of Young’s modulus & P oison ratio 1 . Young’s Modulus (E) Young’s modulus is a material property which is developed due to the application of the external force and deformation on the material. Can be expressed as the ratio of stress and strain. Therefore Where is stress(N/mm 2 ) is strain The unit of young’s modulus is the unit of stress.  

7. Conti. 2 . Poison ratio (v) a material property developed due to the application of the external force and deformation on the material. Can be expressed as the ratio of lateral strain to longitudinal strain. Mathematically; Poison ratio is a dimensionless parameter.  

8. Stress and S train Relation Hooke’s low ‘’With in the proportionality limit the ratio of stress applied to strain is constant’’ This constant is also known as young’s modulus modulus of elasticity or elastic modulus Mathematically;  

9. Conti.

10. Classification of stress Stress can be classified as follows Types of stress Normal stress Shear stress Tensile stress Compressive stress Bending stress Torsional stress

11. Tensile stress If >0, the stress is tensile. i.e. The fibers of the component tend to elongate due to the external force. A member subjected to an external force P and tensile stress distribution due to the force is shown in the given figure  

12. Compressive stress If A member subjected to an external compressive force P the fibers of the component tend to shorten due to the external force, i.e. if < 0, the stress is compressive. compressive stress distribution due to the force is shown in the given figure.  

13. Shear stress When forces are transmitted from one part of a body to other, the stresses developed in a plane parallel to the applied force are the shear stress. Shear stress acts parallel to plane of interest. Forces P is applied transversely to the member AB as shown. The corresponding internal forces act in the plane of section C and are called shearing forces.

14. Plane stress Plane stress is a two dimensional state of stress Plane stress is state of stress in which is z , τ xz τ yz is zero A stress which is induced in a thin metal sheet or thin vessels.  

15. Conti. The plane which have no shear stress is called the principal plane. The magnitude of normal stresses acting on the principal plane is called principal stress this are: Principal stresses are the maximum and minimum normal stresses on an element, occurring at specific orientations. 1. Maximum principal stress 2. Minimum principal stress Mathematically; Principal angle defining principal plane;

16. Mohr circle diagram A graphical representation of the state of stress at a point . Simplifies the calculation of principal stresses and maximum shear stresses

17. Thank you