StressStrain_01_Surface_and_Contact_Forces

StressStrain_01_Surface_and_Contact_Forces - Section 3.1...

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Section 3.1 Solid Mechanics Part I Kelly 29 3.1 Surface and Contact Stress The concept of the force is fundamental to mechanics and many important problems can be cast in terms of forces only, for example the problems considered in Chapter 2. However, more sophisticated problems require that the action of forces be described in terms of stress , that is, force divided by area. For example, if one hangs an object from a rope, it is not the weight of the object which determines whether the rope will break, but the weight divided by the cross-sectional area of the rope, a fact noted by Galileo in 1638. 3.1.1 Stress Distributions As an introduction to the idea of stress, consider the situation shown in Fig. 3.1.1a: a block of mass m and cross sectional area A sits on a bench. Following the methodology of Chapter 2, an analysis of a free-body of the block shows that a force equal to the weight mg acts upward on the block, Fig. 3.1.1b. Allowing for more detail now, this force will actually be distributed over the surface of the block, as indicated in Fig. 3.1.1c. Defining the stress to be force divided by area, the stress acting on the block is A mg = σ (3.1.1) The unit of stress is the Pascal (Pa): 1Pa is equivalent to a force of 1 Newton acting over an area of 1 metre squared. Typical units used in engineering applications are the kilopascal, kPa ( Pa 10 3 ), the megapascal, MPa ( Pa 10 6 ) and the gigapascal (P a 10 9 ). Figure 3.1.1: a block resting on a bench; (a) weight of the block, (b) reaction of the bench on the block, (c) stress distribution acting on the block The stress distribution of Fig. 3.1.1c acts on the block. By Newton’s third law, an equal and opposite stress distribution is exerted by the block on the bench; one says that the weight force of the block is transmitted to the underlying bench. The stress distribution of Fig. 3.1.1 is uniform , i.e. constant everywhere over the surface. In more complex and interesting situations in which materials contact, one is more likely to obtain a non-uniform distribution of stress. For example, consider the case of a metal ball being pushed into a similarly stiff object by a force F , as mg (a) (c) mg (b)
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Section 3.1 Solid Mechanics Part I Kelly 30 illustrated in Fig. 3.1.2. 1 Again, an equal force F acts on the underside of the ball, Fig. 3.1.2b. As with the block, the force will actually be distributed over a contact region . It will be shown in Part II that a circular contact region will arise where the ball and object meet 2
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 1 taught by Professor Staff during the Fall '11 term at Auckland.

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StressStrain_01_Surface_and_Contact_Forces - Section 3.1...

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