Downloaded from https://www.everyspec.com STRUCTURES test is called the ultiniate sirfs. Since all ratio of the lateral strain to the axial strain stresses are . sed on the original cros- in a uniaxially stressed material. As men- sectional area of the specimen, the ultimate tioned earlier, a cylindrical tensile test speci- stress corresponds to the maximum load, and men subjected to an axial load produces an it may be considered as indicaive of the axial strain. This axial strain is always ac- strength of the material. Relatively few companied by a lateral strain smaller in members in airplane and missile structures, magnitude, and opposite in sign [Figure however, are critical in tension.
The ultimate 2-2(a) ]. For most engineering materials strems of a material in compression is net Poisson's Ratio has a value of approximately quite as clear-cut because of the column 0.3. action. Even when the column action is pre- vented by lateral constraints or by the pro- 2-1.8. Fatigue. The physical properties of portions of the test specimen only some materials discussed so far have been based materials such as wood and stone will exhibit on static tests in which the load is slowly ap- a definite value of the ultimate stress. For plied without repetition.
It is well known that most metals, an arbitrary criterion must be some structural elements are subject to vi- used to define this quantity. When the design brations which cause the stresses to fluctuate. criterion is associated with failure or rupture Under these conditions, failure can occur at SL t a stress level which may be considerably oh suctuall nirner, then the ultimate stress assumes major iUmprtance as a ma- lower than the ultimate stress previously dis- terial propeyty. cussed. This type of failure is known as 2-1.6. Tarigent and Secant Modulus, Modu- fatigue failure. 2-1.of TaRget Ind sestucatMualsnalyses The fatigue strengtl. of a structural ele- lus of Rigid.
In some structural analyses ment is probably the least amenable to analy- (column buckling, for example), a so-called sis and hence the most difficult of the various tangent modulus is used. This quantity is design strengths to evaluate. Unfortunately, simply the slope of the stress-strain curve at its determination is not confined !o a knowl- any point. Below the proportional limit, the edge of the nature and magnitude of L%-, tangent modulus is everywhere equal to the fluctuating stresses and some simply physical Young's Modulus. Some investigators use the properties.
it is known that the "atigue concept of a secant modulus, which is the strength of a specimen is affected by size, ratio of stress to strain at any point. Young's local discontinuities, and heat treatment, to Modulus and the secant modulus are also mention a few of the parameters. Investiga- equal below the proportional limit. Torsion tors in this field have nevertheless made sig- stress-strain diagrams can also be plotted nificant strides by their analytical studies from torsion tests on round tubes or round and extensive experimental programs. solid sections.
The initial slope of this curve, The data used by design engineers in de- analogous to Young's Modulus, yields the termining fatigue strength are based on tests modulus of elasticity in shear, referred to cf standar.1 specimens (smooth or notched) as the Modulus of Rigidity. subject to controlled fluctuating stresses, in 2-1.7. Poisson's Ratio. For homogeneous, which the number of cycles to failure is re- isotropic materials, the Modulus of Rigidity corded. Part (a) of Figure 2-3 shows a peri- is related to Young's Modulus in the follow- odic variation of stress to which a fatiguc ing manner:
specimen may be subjected and defines the G = E/2( ± v) (2-1) important stress parameters affecting fatigut where life. In part (b) of The figure, a characteristic E is 'Young's Modulus curve is presented which gives results of G is Modulus of Rigidity fatigue tests on a specimen. The curve is v is Poisson's Ratio drawn for a mean stress value of zero, and Pqisson's Ratio is the absolute value of the relates the stress to the number of cycles to f 10 -a