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Building Design and Construction Handbook - Merritt - Ventech!

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5.60 SECTION FIVE<br />

After extensive testing <strong>and</strong> analysis, prevalent engineering opinion favors the<br />

Engesser equation for metals in the inelastic range:<br />

2 Pt � Et<br />

2<br />

� (5.91)<br />

A (kL/r)<br />

This differs from Eqs. (5.88) to (5.90) only in that the tangent modulus E t (the<br />

actual slope of the stress-strain curve for the stress P t/A) replaced the modulus of<br />

elasticity E in the elastic range. P t is the smallest axial load for which two equilibrium<br />

positions are possible, the straight position <strong>and</strong> a deflected position.<br />

5.7.5 Column Curves<br />

Curves obtained by plotting the critical stress for various values of the slenderness<br />

ratio are called column curves. For axially loaded, initially straight columns, the<br />

column curve consists of two parts: (1) the Euler critical values, <strong>and</strong> (2) the Engesser,<br />

or tangent-modulus critical values.<br />

The latter are greatly affected by the shape of the stress-strain curve for the<br />

material of which the column is made, as shown in Fig. 5.44. The stress-strain<br />

curve for a material, such as an aluminum alloy or high-strength steel, which does<br />

not have a sharply defined yield point, is shown in Fig. 5.44a. The corresponding<br />

FIGURE 5.44 Column curves: (a) stress-strain curve for a material that does not have a sharply<br />

defined yield pont: (b) column curve for this material; (c) stress-strain curve for a material with a<br />

sharply defined yield point; (d) column curve for that material.

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