1 ©Lifting Equipment Engineers Association 2012 – Unit 1.5 UNIT 1.5 - STRESS AND STRAIN IN LIFTING EQUIPMENT Contents Introduction 1. Tensile, compressive and shear forces 2. Stress and strain 3. Tensile test 4. Elasticity, Hooke’s Law and Young’s Modulus 5. Bending stresses 6. Stress calculations 6.1 Tensile and compressive stress 6.2 Shear stress and strain 7. Conclusions 2 ©Lifting Equipment Engineers Association 2012 – Unit 1
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  1 © Lifting Equipment Engineers Association 2012 – Unit 1.5 UNIT 1.5 - STRESS AND STRAIN IN LIFTING EQUIPMENT Contents Introduction 1. Tensile, compressive and shear forces 2. Stress and strain 3. Tensile test 4. Elasticity, Hooke’s Law and Young’s Modulus 5. Bending stresses 6. Stress calculations 6.1 Tensile and compressive stress 6.2 Shear stress and strain 7. Conclusions  2 © Lifting Equipment Engineers Association 2012 – Unit 1.5 Introduction  This unit looks at stress and strain in simple terms as they relate to lifting equipment. The tester and examiner is not called upon to carry out stress calculations, and indeed may not be qualified to do so. However, it is important to have an understanding of their effects on the equipment being examined and possibly tested. This unit considers stress, strain and related matters as they affect lifting equipment, and therefore the methods of testing and safe use. 1. Tensile, compressive and shear forces Figure 1 is a diagrammatic representation of the four basic loading conditions that occur in lifting equipment. (a)   (b) (c) (d)  Figure 1 (a) Shows an item in straight pull. It is in tension and subject to a tensile force or load,  eg a sling leg under load. (b) Shows an item being squeezed. It is in compression and subject to a compressive force or load,  eg a jack body under load. When two contacting parts are caused to slide upon each other in opposite directions parallel to their plane of contact by the application of a load they are in shear and subject to a shear force or load. (c) Shows an example of single shear  . For example, if two plates are bolted together and subject to a tensile force the bolt would be subjected to the shear stress set up between the two plates. (d) Shows an example of double shear  . For example, the pin of a shackle where the load completely fills the jaws is in double shear. 2. Stress and strain 2.1 Stress When a force is applied to an item, the material it is made of tries to resist the force. For a given material, the larger the cross-sectional area, the better it is able to resist the force. This is because the limiting factor is the stress not the amount of force.  3 © Lifting Equipment Engineers Association 2012 – Unit 1.5 Stress  is the force per unit area. The SI unit for stress is the Newton per square metre, expressed as N/m². The accepted multiples used are kN/m²  and  MN/m². When calculating stress, the material section is usually measured in mm giving an answer in N/mm 2 . This is easy to convert as 1 N/mm 2  = 1MN/m².   Note 1: Strictly speaking the SI unit of stress has its own name which is Pascal, named after the French scientist. It is abbreviated to Pa. 1Pa = 1N/m 2 This unit was used for a while in standards but has now fallen out of favour and recent standards use N/m 2  or the accepted multiples. Note 2:  When the metric system was first introduced a transitional unit kilogram force ‘kgf’ and its multiple tonne force ‘tonnef’ were initially used. This then resulted in a unit of stress, kilogram force per square millimetre, expressed as a kgf/mm 2 .  Although it was widely used in standards and other technical publications during the 1970s, its use has been discontinued. It may be encountered in some older publications, for example in the context of the breaking strength of wire ropes. The following conversion factor should be used. 1 kgf/mm² = 9.81 MN/m²  In the imperial system the basic unit of stress is the ton per square inch, expressed as ton/inch² . For smaller units it is pounds per square inch,  lbs/inch² . The accepted conversion factors are 1 ton/inch² = 15.44 MN/m² 1lb/inch² = 6.894 kN/m² 2.2 Strain In everyday language stress and strain are synonymous and we often use one to mean the other. However they are not the same and it is important that we understand their true meanings and use them correctly when discussing their effects. They are closely related, both being the result of a force applied to the item. The force on the item puts the material from which the item is made under stress. To resist that stress, the material deforms. If it is in tension it gets longer and if it is in compression it gets shorter. We can see this clearly in every day items such as an elastic band which stretches when pulled. All materials deform to some extent when under stress, if only by a very small amount. The way that deformation is measured is by relating the amount of deformation to the srcinal length. The relative deformation is called Strain . The strain is determined by dividing the change in length by the srcinal length thus: unitsnohasthereforeand ratioaisThis   LengthOriginal LengthinChange =Strain    4 © Lifting Equipment Engineers Association 2012 – Unit 1.5 3. Tensile test  A tensile test reveals a great amount of information about the material and quantifies the important properties of the material. Testers and examiners need to know these properties and how they are determined in order to understand various material specifications and relate these to their suitability for making lifting equipment.  A tensile test is made as follows. A standard size test piece of material is subjected to increasing loads applied in a controlled manner. A graph is plotted as the material elongates and eventually fails. The result is a Load/Extension  diagram as shown in Figure 2. This is also a diagram of Stress/Strain  as the load results in stress and the extension is a measure of the strain. Figure 2 Figure 2 shows a typical graph for a mild steel sample obtained by plotting Load (Stress) against Elongation (Strain). Five definite points can be seen as the line of the graph is produced. These indicate the positions of the Limit of Proportionality , the Elastic Limit , the Yield Point , the Tensile Strength  and the Ultimate Breaking Stress . With mild steel samples these points can be clearly seen as the graph starts as a straight line, which then deforms and then takes on a distinctive curve. But with alloy steels they become less distinct as the line tends to be fairly straight. This unit therefore only considers mild steel, although the same is true of all materials. (A)  Limit of Proportionality . Initially as the force is applied the stress and strain are proportional until point A is reached. This is the point at which the graph is no longer a straight line. This point is known as the Limit of Proportionality. (B)  The Elastic Limit . This is the point up to which the material remains elastic. Within the elastic limit the test piece will return to its srcinal dimensions if the load is removed. (With mild steel this point practically corresponds with the Limit of Proportionality. This is not generally true of other materials or for materials that have been overstrained). When this point has been exceeded the extension is permanent and is referred to as Plastic Deformation.  
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