Simple Stress and Strain
In 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 which equilibrium 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). This type of load is treated in the same manner as a static load; however, for some materials and conditions of temperature and stress, the resistance to failure may be different under short 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, and equilibrium is not established until the vibration is eliminated, usually by natural damping forces.
(d)An repeated load is a dead that is applied and removed many thousands of times.
(e)A fatigue of alternating load is a load whose magnitude and sign 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 as
Stress=load/area=P/A
Stress 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/L
Strain 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 that
Stress train
This 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 in which Hooke’s law applies, it has been shown that
Tress/train=constant
This constant is given the symbol E and modulus of elasticity
Or Young’s modulus. Thus
E=tress/strain
react to stress的中文翻译Young’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.
   

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