6 STRESSES AND DEFOLIATIONS. Art. 9. 



steel than in other materials of construction. Cast iron and 

 timber, for example, can scarcely be said to have elastic limits, 

 but, practically, certain values may be assigned within which 

 the permanent deformations are negligible. 



9. Deformations. 1 Besides the longitudinal deformations 

 in the bars of Figs. 3 and 4, there are also transverse deforma- 

 tions ; the area of the cross section is contracted in tension and 

 expanded in compression, so that in one case A^ is less, and in the 

 other case A l is greater than A. Within the elastic limits the 

 deformations arc proportional to the stress, and depend upon its 

 intensity. 



The relation between the longitudinal and transverse defor- 

 mations has not been well determined for most materials, but for 

 metals the transverse deformation is usually taken from J- to J 

 (Poisson's Ratio) as much per inch as the longitudinal; this 

 ratio may be taken as 0.3 for iron and steel. 



10. Unit Stresses. If the forces IT 7 are applied uniformily 

 over the ends of a bar, the stress at any cross section will be 

 uniformily distributed, and the unit stress will be the stress 

 per unit of area. 



W W 



s = = (nearly) (1) 



AI A 



Within the elastic limit, deformations are so small that A 

 and A! are practically equal and, in any case, it is usually the 

 stress per unit of original area that is wanted. 



WORKING STRESSES for structures are the unit stresses used 

 in their design (24), and are taken well within the elastic limits. 

 If the elastic limits were exceeded in any part of a structure, it 

 would not return to its original shape, and might finally become 

 unfit for the purpose for which it was intended ; there might also 

 be a dangerous redistribution of stresses. We are, therefore, 

 chiefly concerned with stresses within the elastic limits. 



11. Modulus of Elasticity. According to Hooke's Law, de- 

 formations and stresses u-ithin the elastic limits, for any one kind 

 of stress, are proportional to each other. For example, if a bar of 

 steel having an elastic limit of 40000 Ibs. per square inch be sub- 

 jected to a pull of 10000 Ibs., producing an elongation of 0.01 in., 



1 The term strain is used by most writers to denote the deforma- 

 tion accompanying stress, but since engineers commonly use strain to 

 denote stress, the term is here avoided. 



