Footnotes

^* Historical reviews of mechanics of materials and the theory of elasticity are given in Refs. 1.1 through 1.5.

^* Further discussion of uniaxial compression stress is found in Section 11.6, where we take up the classification of columns.

^* In this case, the body is not in static equilibrium, and the inertia force terms –ρa_x, –ρa_y, and –ρa_z (where a_x, a_y, and a_z are the components of acceleration) must be included in the body force components F_x, F_y, and F_z, respectively, in Eqs. (1.14).

^* More details and illustrations of these assumptions are given in Chapter 3.

^* After Otto Mohr (1835–1918), professor at Dresden Polytechnic. For further details, see Ref. 1.7, for example.

^* For a detailed discussion of the elastic properties of various classes of materials, see, for example, Refs. 2.1 and 2.11.

^* See, for example, Refs. 2.13 and 2.14.

^* See, for example, Refs. 3.8 through 3.14.

^* A summary and complete list of publications dealing with contact stress problems are given by Refs. 3.13 through 3.19.

^* For further details, see Ref. 4.1 and texts on material science, for example, Refs. 4.2 through 4.4.

^* From Ref. 4.14. For further details related to failure criteria for metal fatigue, see Refs. 4.8 and 4.15 through 4.17.

^* For a detailed discussion, see Ref. 5.3.

^* For an extensive discussion of springs, see Refs. 6.5 and 6.6.

^* For a general function , defined in area coordinates, the integral of f over any triangular area A is given by

where α, β, γ are constants.

^* Refer, for example, to Ref. 8.2.

^* For a detailed presentation of a number of practical problems, see Refs. 9.1 through 9.3.

^* For a more rigorous mathematical treatment and an extensive exposition of energy methods, see Refs. 10.1 through 10.8.

^* The range of L_e/r depends on the material under consideration. In the case of structural steel, for example, long columns are those for which about L_e/r > 100; for intermediate columns, 30 < L_e/r < 100, and for short struts, L_e/r < 30.

^* The specifications of the AISC are given in Ref. 11.5. Similar formulas are available for aluminum and timber columns; see, for example, Ref. 11.6.

^* For a complete discussion of this subject, see Refs. 11.7 through 11.10.

^* For a detailed discussion of problems in plasticity, see Refs. 12.1 through 12.3.

^* This approach was introduced by Navier in 1820. For details, see Refs. 13.1 and 13.2.