Art. 11. 



MODULUS OF ELASTICITY. 



a pull of 20000 Ibs. will produce an elongation of 0.02 in., of 

 25000 Ibs., 0.025 in., etc. The constant ratio of stress to deforma- 

 tion is a physical constant, usually represented by ,and is called 

 the modulus (measure) of elasticity; for tension and compression, 

 it is the same and is called Young's Modulus. In the form of an 



equation. 



8 = -or EB 



(2)- 



For steel E is about 29000000 when 8 is in inches and s in 

 pounds per square inch, that is, the longitudinal deformation per 

 lineal inch is -^oo^ooo part of an inch for every pound stress per 

 square inch of cross section 2 . 



Referring to a steel bar as shown in Fig. 3, if W= 60000 Ibs., 

 6=2 in., 7t=3 in., =290 in., we have .4=6 sq. in., 5=10000 

 Ibs., per sq. in.; & = ^sVWVW = Wmr in -j Sir = -gffo = 0.1 in.; 



> \X A Q O \s A O 



It is evident that A\ will 



2900 ' 2900 



be but slightly smaller than A. 



The modulus of elasticity is a measure of the stiffness of a ma- 

 terial. Since 8 = -^-, for the same unit stress, the deformation 

 iv ill be least for the material having the greatest modulus of 

 elasticity. Steel and iron are stiffer than timber. Stiffness is 

 important in structures subjected to impact stresses. 



There is naturally considerable variation in the value of a 

 physical constant, particularly for some materials; the following 

 values of Young's Modulus may be taken as general values. 



YOUNG'S MODULI OF ELASTICITY, 3 

 White oak and long-leaf pine 1000000 to 2000000. 

 Wrought iron 26000000 to 30000000. 

 Steel 27000000 to 31000000 (includes all grades). 

 Cast iron 12000000 to 15000000 (increases with strength). 



iThis equation is easily remembered; it can not be Es= S because 

 this would give an absurdly large deformation. 



2 Some writers use the term coefficient of elasticity in place of 

 modulus of elasticity, but in order to have the coefficient in the form 

 usually given to physical constants, it would have to be the reciprocal 

 of the modulus. For steel, the coefficient of elasticity would be 

 75T5 i__ ?J?5 _ 0.000000'0345. Comparing this with the coefficient for ther- 

 mal expansion, the total change in length due to a change of tempera- 

 ture of t degrees equals 0.00000665 Lt and the total change in length 

 due to a change of stress of s pounds per square inch equals 

 0.0000000345 Ls. 



3 For further data with regard to the modulous of elasticity, see John- 

 son's Materials of Construction, Burr's Elasticity and Resistance of the 

 Materials of Engineering, Goodman's Mechanics Applied to Engineer- 

 ing, and Swing's Strength of Materials. 



