By Coenraad Hartsuijker, J. W. Welleman (auth.)

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"This is the second one of 2 volumes … by way of Hartsuijker and Welleman (both, Dolft Univ. of Technology). … The innovations and purposes are good offered; functions contain either simple and complex degrees. The labored out examples well illustrate recommendations. Figures and tables are transparent and aid knowing of the recommendations. … In precis, the e-book is especially good written and is a great addition to the literature of engineering mechanics. Summing Up: suggested. Lower-division undergraduates via professionals." (M. G. Prasad, selection, Vol. forty five (7), 2008)

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Extra info for Engineering Mechanics: Stresses, Strains, Displacements

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At the join of two adjacent fields the boundary condition is called a joining condition. At the end of a field without an adjacent field, the boundary condition is called an end condition. Joining conditions: There are always two conditions per join: one relates to the displacement u, the other relates to the normal force N = EAu . 2 Bar Subject to Extension Joining condition related to the displacement u At a join of two fields, the displacement u must be continuous – holes cannot suddenly appear in the bar!

For the variation of the displacement u we find EAu = 1 2 G x 2 − Gx or, rewritten, u= G EA 1 2 x2 2 − x . The variation of the normal force N is N = EAu = G x −1 . Note that the normal force N is proportional to the slope of the u diagram. Note in particular that u = −G /(2EA) at the top, and N = −G at the base. 20 The column with associated u and N diagrams. 20 shows the u diagram and N diagram. 4. Since the structure is statically determinate, the variation of the normal force could be derived directly from the equilibrium there, without using the strain-displacement (kinematic) and stress-strain (constitutive) equations.

The normal centre then coincides with the centroid of the crosssection,1 as we shall see in Chapter 3. Solution b: We can also work in a xyz coordinate system with the x¯ axis chosen along an arbitrary fibre that need not coincide with the bar axis. 11): A, ¯ My¯ = y¯ N = yσ Mz¯ = z¯ N = z¯ σ A. 11 The bending moments My and Mz when the x axis is not chosen along the bar axis, and the point of application of Nx does not coincide with the normal centre NC of the cross-section. 1a) A = bending moment acting in the xy plane, Mz¯ = σ z¯ dA = σ A z¯ dA A = bending moment acting in the xz plane.

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