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Strength of Materials: Simple Stresses and Strains

Learn about strength of materials, classification of loads, stress and strain, and types of stresses and strains in this C-16 curriculum lesson module.

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Strength of Materials: Simple Stresses and Strains

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  1. e – Lesson Module for C-16 Curriculum State Board of Technical Education & Training Andhra Pradesh Year/Semester : III Semester Branch : Mechanical engg Subject : M-302, Strength of Materials Unit -1 : Simple stresses and Strains Duration : 50 mins Prepared by : S V V RAMANA, Sr. Lecturer in M.E Government Polytechnic, Gannavaram Guided by : D V S S N V PRASAD BABU SL/ME Government Polytechnic, Gannavaram C-16-M-302-1

  2. Objectives On completion of this period, you would be able to know about • Strength of Material • Classification of Loads • Stress and Strain • Types of stress and Strain C-16-M-302-1

  3. Need of the subject • The main objective of the study of Strength of materials is to provide the future engineer with the means of analyzing and designing load bearing structures and various machines. • Both the analysis and design of a given structure involve the determination of stresses and deformations. • This chapter is devoted to the concept of stress. C-16-M-302-1

  4. Important terminology • Prismatic bar: Straight structural member having the same cross-sectional area Athroughout its length • Axial force : Load Pdirected along the axis of the member Free-body diagram disregarding weight of bar • Examples: members of bridge truss, spokes of bicycle wheels, columns in buildings, etc. C-16-M-302-1

  5. Strength • Strength is the ability of the material or structure to resist the influence of the external forces acting upon it. • Engineering Mechanics studying the rigid bodies, • Strength of Materials studies the bodies possessing the ability to deform, i.e. the ability to change its initial shape and dimensions under the action of external forces. C-16-M-302-1

  6. Classification of Loads I. According to application of load with respect to time: 1. Static load -­‐‑ Load is gradually applied. 2. Sustained load -­‐‑ Load, such as the weight of a structure, is constant over a long time. 3. Impact load -­‐‑ Load is rapidly applied. 4. Cyclic load -­‐‑ Load can vary and even reverse its direction II. According to application of load with respect to area: 1. Concentrated load --‐‑ Load is applied to an area much smaller than the loaded member. 2. Distributed load --‐‑ Load is spread along a large area. Example :the weight of books on a bookshelf. C-16-M-302-1

  7. Classification of Loads III. According to the effect produced on the member • Tensile load: It acts axially i.e. along the axis of the body and has pulling tendency. It produces some degree of elongation . • Compressive load: It acts axiallyand it has pushing tendency. It produces some degree of contraction. • Shearing load: It consists of equal and parallel opposite forces acting on surfaces of the body. These forces tend to cause the sliding of the surfaces w.r.t. another. • Bending load: It is produced by two couples and produces certain degree of curvature. • Twisting or torsional load: It is produced by two couples applied at opposite ends. It causes certain degree of twist in the members. ` C-16-M-302-1

  8. Classification of Loads Figure : (a) tensile; (b) compressive; (c) shear; (d) bending; (e) torsion; (f) combined. C-16-M-302-1

  9. Types of Loading Tensile Compressive Shear Torsion C-16-M-302-1

  10. types of loads (CLICK HERE) C-16-M-302-1

  11. Stress • When a structural member is under load, its ability to withstand that load depends upon the internal force, cross sectional area of the element and its material properties. • The ratio of the internal force to the cross sectional area will define the ability of the material in withstanding the loads . • The intensity of force distributed over the given area or simply the force per unit area is called the stress. • Stress is the internal response of a material to externally applied loads. • The stresses acting perpendicular to the surfaces considered are normal stresses In SI units, P: Force is expressed in newtons (N) A: Cross sectional area in squaremeters. σ: Stress has units of newtons per square meter or Pascals (Pa). σ (sigma) : Greek letter C-16-M-302-1

  12. Types of Stresses There are three important stresses, namely • Tensile stress 2. Compressive stress 3. Shear stress • Tensile and compressive stresses are called direct stresses • Direct stress: When a force is applied to an elastic body, the body deforms. The way in which the body deforms depends upon the type of force applied to it, which is tensile or compressive. C-16-M-302-1

  13. Tensile stress: This occurs when tensile load is applied • Tensile stress (ft) = tensile load area of cross-section ft = P A • Stress unit are or Pascals. Most of engineering fields used kPa, MPa, GPa. A tensile force makes the body longer C-16-M-302-1

  14. Compressive stress: This occurs when compressive load is applied • Compressive stress (fc) = compressive load area of cross- section fc = P A Compression force makes the body shorter. C-16-M-302-1

  15. Tensile and compressive stresses Tensile Stress Compressive Stress Forces on the external surface of a body Uniaxial compressive stress tends to reduce the length of the body (shorten the body) Uniaxial tensile stress tends to elongate the body C-16-M-302-1

  16. Shear Stress • Shear stress is defined a the component of force that acts parallel to a surface area • Shear stress is a stress state where the shape of a material tends to change without particular volume change. • The shape change is evaluated by measuring the change of the angle's magnitude (shear strain). Figure 2.24: Shear strain of cubic element subjected to shear stress. (a) Three dimensional view; (b) two--‐‑dimensional (or plane) view. C-16-M-302-1

  17. The corresponding average shear stress is, Shearing Stress • Forces P and P’ are applied transversely to the member AB. • Corresponding internal forces act in the plane of section C and are called shearing forces. • The resultant of the internal shear force distribution is defined as the shear of the section and is equal to the load P. • Shear stress distribution varies from zero at the member surfaces to maximum values that may be much larger than the average value. • The shear stress distribution cannot be assumed to be uniform. C-16-M-302-1

  18. Shear stress: This occurs when shear load is applied • Shear stress = shear load surface area Shear stress is denoted by the symbols fs or τ. Shear stress induced in below cases, When a pair of shears cut a material When a material is punched When a beam has a transverse load C-16-M-302-1

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  20. The shearing area for the pin at C, • The pin at A is in double shear and the shear stress at A, • The shear stress at C, C-16-M-302-1

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  22. Strain • It is important to avoid deformations caused by the loads applied to a structure so that they may prevent the structure from fulfilling the purpose for which it is intended. Photo: Collapse of a bridge • To determine the actual distribution of stresses within a member, it is necessary to analyse the deformations which take place in that member. • This topic deals with the deformations of a structural member such as a rod, bar or a plate under axial loading and shear loading. C-16-M-302-1

  23. DIRECT STRAIN (Tensile strain and Compressive strain) , In each case, a force P produces a deformation δ. In engineering, we usually change this force into stress and the deformation into strain and we define these as follows: Strain is the deformation per unit of the original length. The symbol called EPSILON Strain has no unit’s since it is a ratio of length to length. Most engineering materials do not stretch very mush before they become damages, so strain values are very small figures. It is quite normal to change small numbers in to the exponent for 10-6( micro strain). C-16-M-302-1

  24. Tensile Strain • A rod of uniform cross section with initial length as shown in figure L0 • Application of a tensile load P at one end of the rod results in elongation of the rod by δ. • After elongation, the length of the rod is L. • As the cross section of the rod is uniform, the elongation is also uniform throughout the volume of the rod. • The deformation per unit length of the rod along its axis is defined as the tensile (normal) strain. It is denoted by ε C-16-M-302-1

  25. Compressive Strain • A rod of uniform cross section with initial length as shown in figure L • Application of a Compressive load P at one end of the rod results in shorten of the rod by δ. • After shorten, the length of the rod is L0 • As the cross section of the rod is uniform, the shorten is also uniform throughout the volume of the rod. • The deformation per unit length of the rod along its axis is defined as the compressive (normal)strain. It is denoted by ε C-16-M-302-1

  26. Normal Strain examples C-16-M-302-1

  27. SHEAR STRAIN • The force causes the material to deform as shown. The shear strain is defined as the ratio of the distance deformed to the height . Since this is a very small angle , we can say that : Shear strain ( symbol called Gamma) C-16-M-302-1

  28. In summary:If we load a body and this leads to stress inside the body→ this will lead to strains in the deformable body. I.e. stress gives rise to strain. Load → Stress → Strain. • We can have stress without strain and strain without stress Strain without stress heat a unconstrained body (it will expand and no stresses will develop) Stress without Strain heat a body constrained between rigid walls (it will not be able to expand but stresses will develop). C-16-M-302-1

  29. Summary We have discussed about: • Types of loads • Definition of stress & strain • Types of stresses and strains C-16-M-302-1

  30. Quiz • The formula for Stress is • Load / Area • Load x Area • Load x Length • Load / Length C-16-M-302-1

  31. Quiz • The units for Stress is • N / mm2 • N / mm • N-mm • N-mm/s C-16-M-302-1

  32. Frequently asked Questions • What is Stress ? • List out the types of loads ? • What are the types of stresses ? • What are types of strains ? C-16-M-302-1

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