Basics of mechanics stresses and strains (1)
- 1. Basics of Mechanics, Stresses & Strains Sunita Lakshani M Tech(Structure) Lecturer Civil Dept 12/8/2018 1
- 2. Introduction of Basics: Engineering Mechanics Statics(Body is @rest) Dynamics (Body is in Motion) Kinamatics Kinetics 12/8/2018 2
- 3. Force: Force can be defined as a push or a pull that changes or tends to change the state of rest or uniform motion of an object or changes the direction or shape of an object. It is vector quantity it is represented by magnitude and direction. System of a forces: Coplanar Force system Parallel Non coplanar Non-parallel Non ConcurrentCollinear Non-parallel Non ConcurrentConcurrent Parallel Concurrent 12/8/2018 3
- 4. System of forces • Coplanar Forces: All forces acting on body/point lie in single plane. • Non- coplanar Forces: All forces acting on body/point lie in different plane. • Coplanar collinear Forces: If the forces are having common line of action, then they are known as collinear whereas if the forces intersect at a common point, then they are known as concurrent. If forces acting parallel and in a plane is coplanar parallel forces. A force system may be coplanar or non-coplanar. • Coplanar non-concurrent forces: All forces do not meet at a point, but lie in a single plane. 12/8/2018 4
- 5. Laws of forces: • Lamis Therom: states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces. Consider three forces A, B, C acting on a particle or rigid body making angles α, β and γ with each other. 12/8/2018 5
- 6. Parallelogram of forces • The law of parallelogram of forces states that if two vectors acting on a particle at the same time be represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point their resultant vector is represented in magnitude and direction by the diagonal of the parallelogram. 12/8/2018 6
- 7. Couple: A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. The SI unit of the moment of a couple is Newton meter (Nm). A good example for moment of couple is the force applied on steering wheel in which force applied on one point of the wheel is equal in magnitude to the force measured at the point perpendicular on the wheel. 12/8/2018 7
- 8. Moment: The turning effect of a force is known as the moment. It is the product of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn. • •SI unit of moment of a force is Newton-metre (Nm). •It is a vector quantity. •Its direction is given by the right-hand grip rule perpendicular to the plane of the force and pivot point which is parallel to the axis of rotation. r=F× dr =F×d ,where r is the moment of force/torque F is the force d is the perpendicular distance from the line of action of the force to the pivot 12/8/2018 8
- 9. Mechanical Properties of Materials: • Elasticity: the ability of an object or material to resume its normal shape after being stretched or compressed; stretchiness. • Yield (or Proof Strength)Stress needed to produce a specified amount of plastic or permanent deformation. (Usually a 0.2 % change in length). • Ultimate Tensile Strength (UTS):The maximum stress a material can withstand before fracture. • Ductility: The amount of plastic deformation that a material can withstand without fracture. • Hardness: The resistance to abrasion, deformation, scratching or to indentation by another hard body. This property is important for wear resistant applications. • Toughness: This is commonly associated with impact loading. It is defined as the energy required to fracture a unit volume of material. Generally, the combination of a high UTS and a high ductility results in a higher toughness. 12/8/2018 9
- 10. • Fatigue Strength and Endurance Limit: Fatigue failure results from a repeated cyclic application of stress which may be below the yield strength of the material. This is known to be the most common form of mechanical failure of all engineering components. The number of stress cycles needed to cause fatigue failure depends on the magnitude of the stress. Below a certain stress level material does not fail regardless to the number of cycles. This is known as endurance limit and is an important parameter in many design applications. • Creep Resistance: The plastic deformation of a material which occurs as a function of time when the material is subjected to constant stress below its yield strength. For metals this is associated with high temperature applications but polymers may exhibit creep at low temperatures. • Malleability: is a substance's ability to deform under pressure (compressive stress). If malleable, a material may be flattened into thin sheets by hammering or rolling. Malleable materials can be flattened into metal leaf. Many metals with high malleability also have high ductility. 12/8/2018 10
- 11. Loads and Forces: External forces acting on body are termed as loads. These loads may arise due to dead loads of members, live loads, wind loads, earthquake effects, fluid pressures, support settlements, frictional resistance etc. Loads cause stresses, deformations, and displacements in structures. • Types of Loads/force Single Diagram: 12/8/2018 11
- 12. Stresses σ : Internal resistance per unit area offered by a material against externally applied load Stress = force / cross sectional area: where, σ = stress, F = force applied, and A= cross sectional area of the object. Units of stress : N/m-2 or Pa. Types of Stress: Tensile ,Compressive And Shear stresses. Strain ‘ε’ :Ratio of Change in dimension to original dimension, it is unit less quantity. If its linear dimension concern linear strain. If it is lateral dimension concern lateral strain. Young’s Modulus ‘E’: Ratio of Stress to strain called Young’s Modulus. E= σ/ ε its unit N/m-2 Elastic Constants: Young’s modulus , Bulk modulus &Rigidity modulus. Bulk Modulus ‘K’: Ratio of Stress to volumetric strain its unit N/m-2. Rigidity Modulus ‘G’: Ratio of shear stress to shear strain its unit N/m-2.12/8/2018 12
- 13. Types of Stresses: Tensile Stress: is the stress state caused by an applied load that tends to elongate the material in the axis of the applied load, or in other words, the stress caused by pulling the material. Compressive Stress: When equal and opposite forces are applied to a body, and the resistance offered by a section of the body is against the decrease in length. Shear Stress: When equal and opposite forces act tangentially on any cross-sectional plane of a body , tending to slide its one part over the other at that plane. 12/8/2018 13
- 15. Stress and Strain Diagram of Various materials • Relation between various elastic constants. E=2G(1+μ) E=3K(1-2 μ) E=9KG/(G+3K) Where μ Poisson’s Ratio its varies with material. 12/8/2018 15
- 16. Proportional Limit (Hooke's Law). From the origin O to the point called proportional limit, the stress-strain curve is a straight line. This linear relation between elongation and the axial force causing was first noticed by Sir Robert Hooke in 1678 and is called Hooke's Law that within the proportional limit, the stress is directly proportional to strain or σ∝ε or σ=kε The constant of proportionality k is called the Modulus of Elasticity E or Young's Modulus and is equal to the slope of the stress-strain diagram from O to P. Elastic Limit. The elastic limit is the limit beyond which the material will no longer go back to its original shape when the load is removed, or it is the maximum stress that may e developed such that there is no permanent or residual deformation when the load is entirely removed. 12/8/2018 16
- 17. Elastic and Plastic Ranges The region in stress-strain diagram from O to P is called the elastic range. The region from P to R is called the plastic range. Yield Point Yield point is the point at which the material will have an appreciable elongation or yielding without any increase in load. Ultimate Strength The maximum ordinate in the stress-strain diagram is the ultimate strength or tensile strength. Rapture Strength Rapture strength is the strength of the material at rupture. This is also known as the breaking strength. 12/8/2018 17
- 18. Modulus of Resilience Modulus of resilience is the work done on a unit volume of material as the force is gradually increased from O to P, in N·m/m3. This may be calculated as the area under the stress-strain curve from the origin O to up to the elastic limit E (the shaded area in the figure). The resilience of the material is its ability to absorb energy without creating a permanent distortion. Modulus of Toughness Modulus of toughness is the work done on a unit volume of material as the force is gradually increased from O to R, in N·m/m3. This may be calculated as the area under the entire stress-strain curve (from O to R). The toughness of a material is its ability to absorb energy without causing it to break. Working Stress, Allowable Stress, and Factor of Safety Working stress is defined as the actual stress of a material under a given loading. The maximum safe stress that a material can carry is termed as the allowable stress. The allowable stress should be limited to values not exceeding the proportional limit. However, since proportional limit is difficult to determine accurately, the allowable tress is taken as either the yield point or ultimate strength divided by a factor of safety. The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety. 12/8/2018 18
- 19. Strains: • Longitudinal Strain: Ratio of Change in linear dimension to original dimension. • Lateral strain: Ratio of Change in lateral dimension to original dimension. • Poisson’s Ratio: Ratio of Longitudinal strain to linear strain notation used as μ or 1/m. 12/8/2018 19