Titlebook: Intermediate Mechanics of Materials; J. R. Barber Textbook 2011Latest edition Springer Science+Business Media B.V. 2011 beams.bending.cyli

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Unsymmetrical Bending,The elementary theory of the bending of beams is restricted to the case where the beam has a cross section with at least one axis of symmetry. In the present chapter, we shall generalize the theory to beams of arbitrary cross section. All the remaining assumptions of the beam theory will remain unchanged.

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Non-linear and Elastic-Plastic Bending,In this chapter, we shall consider the question of determining the stress distribution and curvature when a beam is subjected to bending moments sufficient to cause plastic deformation. The same analytical procedure can also be used for the bending of beams made of materials such as rubber, which have a non-linear elastic constitutive behaviour.

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Thick-walled Cylinders and Disks,In this chapter, we shall consider a class of problems in which the stresses and displacements depend only on the radius . in the cylindrical coordinate system (.,. , .). The problems are therefore . (i.e. there is no variation with the angle .) nor is there any variation with the distance . along the axis.

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Introduction, are important because, in combination with fundamental tests on engineering materials, they enable us to determine the loading conditions under which material failure will occur. Deformations may also be important insofar as they affect the kinematic function of a device.

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Energy Methods, acting between them. We then use the equations of equilibrium, geometrical conditions and stressstrain laws to develop a system of governing equations. In some cases, the equilibrium equations alone are sufficient to determine the internal forces and the problem is described as .. By contrast, in .

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Shear and Torsion of Thin-walled Beams,s of loading that give rise to normal stresses σ. on transverse planes .=., where c is a constant. It is also worth noting that the combination of an axial force and a bending moment is equivalent to an equal axial force with a different line of action (see for example §5.5.2).

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Beams on Elastic Foundations,es arises in civil engineering, where buildings or other structures are supported on a soil base. Other less obvious examples include steel components supported on extended rubber bushings, floating structures (where the support is provided by the buoyancy force) and the transmission of load between

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Curved Beams,ss section is uniform along the length, which is much larger than any other linear dimension. However, the resulting equations are so simple that engineers routinely apply them outside this restrictive context and this usage is appropriate as long as we recognize that the resulting approximation may