The Mechanics of Engineering Structures by David W A Rees

Author:David W A Rees [Rees, David W A]
Language: eng
Format: epub
Publisher: Imperial College Press
Published: 2015-11-19T22:00:00+00:00

Substituting Eq. 8.35b into Eq. 8.34 enables σ to be found from:

Applying Considére’s tensile instability condition to Eq. 8.35a:

shows that, at the inception of necking, the ultimate stress and strain are σu = Bnn and εu = n. Hence Eq. 8.36a gives the plastic buckling stress as a fraction of its ultimate tensile strength:

Equation 8.36b allows for the determination of constraint factor c experimentally given the material properties n and σu for a strut whose ends are not pinned.

Example 8.12 A pinned-end steel strut 1.5 m long has the cross section shown in Fig. 8.16. Find Engesser’s prediction to the plastic buckling load given that the Hollomon law σ/σc = 5ε1/3 describes the compressive stress–strain curve in the region beyond the yield stress σc = 300 MPa. Compare this with the elastic buckling loads predicted from the Perry-Robertson and Fidler formulae. Take E = 207 GPa.

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