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Simple Stress and StrainIn any engineering structure the individual components or members will be subjected to external forces arising from the service conditions or environment in which the component works. If the component or member is in equilibrium, the resultant of the external forces will be zero but, nevertheless, they together place a load on the member which tends to deform that member and which must be reacted by internal forces set up within the material.There are a number of different ways in which load can be applied to a member. Loads may be classified with respect to time:(a) A static load is a gradually applied load for whichequilibrium is reached in a relatively short time.(b) A sustained load that is constant over a long period of time,such as the weight of a structure (called dead load). Thistype of load is treated in the same manner as a static load;however, for some materials and conditions of temperatureand stress, the resistance to failure may be different undershort time loading and under sustained loading.(c)An impact load is a rapidly applied load (an energy load).Vibration normally results from an impact load, andequilibrium is not established until the vibration iseliminated, usually by natural damping forces.(d)An repeated load is a dead that is applied and removedmany thousands of times.(e) A fatigue of alternating load is a load whose magnitude andsign are changed with time.It has been noted above that external force applied to a body in equilibrium is reacted by internal forces set up within the material. If, therefore, a bar is subjected to a uniform tension or compression, i.e.a force, which is uniformly applied across the cross-section, then the internal forces set up are also distributed uniformly and the bar is said to be subjected to a uniform normal tress, the stress being defined asStress=load/area=P/AStress may thus be compressive or tensile depending on the nature of the load and will be measured in units of newtons per square meter (N/m2) or multiple of this.If a bar is subjected to an axial load, and hence a stress, the bar will change in length. If the bar has an original length L and changed in length by an amount QL, the stain produced is defined as follow: Train=change in length/original length=QL/LStrain is thus a measure of the deformation of the material and is non-dimensional, i.e. it has no units; it is simply a ratio of two quantities with the same unit.Since, in practice, the extensions of materials under load are very small, it is often convenient to measure the strains in the form of strain *10-6, i.e. microstrain, when the symbol used becomes UE.Tensile stresses and strains are considered positive in sense. Compressive stresses and strains are considered negative in sense. Thus a negative train produces a decrease in length.A material is said to be elastic if it returns to its original, unloaded dimensions when load is removed. A particular form of elasticity which applies to a large range of engineering materials, at least over part of their load range, produces deformations which are proportional to the loads producing them. Since loads are proportional to the stresses they produce and deformations are proportional to the strains, this also implies that, whilst materials are elastic, stress is proportional to strain, Hooke’s law therefore states thatStress trainThis law is obeyed within certain limits by most ferrous alloys and it can even be assumed to apply to with reasonable accuracy.Whilst a material is elastic the deformation produced by any load will be completely recovered when the load is removed; there is no permanent deformation.Within the elastic limits of materials, i.e. within the limits inwhich Hooke’s law applies, it has been shown thatTress/train=constantThis constant is given the symbol E and modulus of elasticityOr Young’s modulus. ThusE=tress/strainYoung’s modulus E is generally assumed to the same in tension or compression and for most engineering materials had a high numerical value. Typically, E=200*109N/m2 for steel, so that it will be observed from Eq. that trains are normally very small.In most common engineering applications strains rarely exceed 0,1%. The actual of Young’s modulus for any material is normally determined by carrying out a standard test on a specimen of the material.。
应力应变英语Stress and Strain in EngineeringStress and strain are fundamental concepts in the field of engineering, as they are crucial in understanding the behavior of materials and structures under various loading conditions. These two interrelated quantities are essential for the design, analysis, and optimization of engineering systems, from small components to large-scale structures.Stress, in the context of engineering, can be defined as the internal force per unit area acting within a material or structure. It is a measure of the intensity of the internal forces that arise due to the application of external loads or constraints. Stress can be classified into different types, such as normal stress, shear stress, and torsional stress, depending on the direction and nature of the forces acting on the material.Normal stress is the stress that acts perpendicular to the surface of a material, and it can be either compressive or tensile. Compressive stress occurs when the material is subjected to forces that tend to push it together, while tensile stress occurs when the material issubjected to forces that tend to pull it apart. Shear stress, on the other hand, is the stress that acts parallel to the surface of a material, causing the material to slide or deform in a particular direction.Strain, on the other hand, is a measure of the deformation of a material or structure due to the application of stress. It is the change in the size or shape of a material relative to its original dimensions. Strain can be classified into different types, such as normal strain and shear strain, just like stress.Normal strain is the change in the length of a material divided by its original length, and it can be either compressive or tensile. Shear strain, on the other hand, is the change in the angle between two originally perpendicular lines in the material, caused by the application of a shear stress.The relationship between stress and strain is governed by the material's mechanical properties, which can be determined through various testing methods. The most fundamental relationship between stress and strain is described by Hooke's law, which states that for small deformations, the stress in a material is proportional to the strain. This linear relationship is valid for many materials, such as steel and aluminum, within their elastic range.However, not all materials exhibit a linear stress-strain relationship.Some materials, such as rubber and certain polymers, exhibit a non-linear relationship, where the stress-strain curve is curved and the material exhibits more complex behavior, such as viscoelasticity or plasticity.Understanding the stress-strain relationship of materials is essential for the design and analysis of engineering structures and components. By knowing the stress and strain values, engineers can determine the safety and reliability of a structure under various loading conditions, as well as optimize the design to ensure that the material is being used efficiently and effectively.For example, in the design of a bridge, engineers need to consider the stresses and strains that will be experienced by the structure due to the weight of the bridge, the traffic load, and environmental factors, such as wind and earthquakes. By analyzing the stress and strain distribution within the bridge, engineers can ensure that the structure is designed to withstand the expected loads without exceeding the material's strength or deformation limits.Similarly, in the design of a mechanical component, such as a gear or a shaft, engineers need to consider the stresses and strains that will be experienced by the component during operation. By analyzing the stress and strain distribution within the component, engineers can optimize the design to minimize the risk of failure and ensurethe component's reliability and longevity.In conclusion, stress and strain are fundamental concepts in engineering that are essential for the design, analysis, and optimization of engineering systems. By understanding the relationship between stress and strain, engineers can ensure the safety, reliability, and efficiency of their designs, ultimately contributing to the advancement of technology and the betterment of society.。
