Engineering Mechanics: Stresses, Strains, Displacements by Coenraad Hartsuijker, J. W. Welleman (auth.)

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

From the reviews:

"This is the second one of 2 volumes … through Hartsuijker and Welleman (both, Dolft Univ. of Technology). … The recommendations and functions are good provided; functions contain either simple and complex degrees. The labored out examples properly illustrate techniques. Figures and tables are transparent and support realizing of the thoughts. … In precis, the booklet is particularly good written and is a great addition to the literature of engineering mechanics. Summing Up: instructed. Lower-division undergraduates via professionals." (M. G. Prasad, selection, Vol. forty five (7), 2008)

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Extra resources for Engineering Mechanics: Stresses, Strains, Displacements

Example text

If join B is unloaded (Fx,B = 0), then the normal force N is continuous: 1 Field boundaries (locations) are indicated by a sub-index and the fields (regions) are indicated by an upper index. 13 The joining conditions related to u and N. (a) At a join of two adjacent fields, the displacement u must be continuous: BC uAB B = uB . (b) The force equilibrium of a small bar segment at a join of two fields gives NBAB = NBBC + Fx,B . 33 34 ENGINEERING MECHANICS. VOLUME 2: STRESSES, DEFORMATIONS, DISPLACEMENTS NBAB = NBBC .

Question: Determine the change in length of the column due to the compressive force F . 2 Bar Subject to Extension Comment: This problem requires some mathematical skill, such as the substitution of variables. Solution: For the change in length of the non-prismatic column with constant normal force we have N 1 dx = EA E =N 1 dx. A Since the area A = A(x) of the cross-section is a function of x, it has to remain inside the integral. 18b). If /2 is the change in length of the total column, then is the change in length of half the column: 1 2 = N E /2 1 dx, A(x) 0 which, with N = −F , implies =− 2F E /2 0 1 dx.

Or EAu = −qx . 7) For a prismatic bar, the extension problem reduces to an equation involving just the second derivative in the axial displacement u. 12 A bar divided into fields. The boundary conditions are found at the bar ends and at the joins of two adjacent fields. Boundary conditions: joining and/or end conditions The differential equation for extension can be solved through repeated integration whether or not EA is constant and the bar is prismatic. Each integration gives an (still unknown) integration constant.

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