226 STRENGTH OF MATERIALS 



the test, the strain diagram is drawn by using unit loads as ordinates 

 and relative elongations as abscissas. From this curve the elastic limit, 

 modulus of elasticity (Young's modulus), and modulus of elastic 

 resilience may be determined. 



The elastic limit is found by noting the point on the strain diagram 

 where it ceases to be a straight line. 



The modulus of elasticity is determined by dividing the stress by 

 the deformation for any stress below the elastic limit. 



The modulus of elastic resilience is denned as the amount of work re- 

 quired to deform a cubic inch of the material to its elastic limit. It is 

 therefore represented by the area under the strain curve up to the elastic 

 limit, or, expressed as a formula, 



(stress at elastic limit) 8 

 Mod. elastic resilience = - 



"2 modulus ot elasticity 



If in plotting the strain diagram the ordinates represent the stress 

 expressed in lb./in. 2 and the abscissas represent the convs pend- 

 ing unit elongations, the area under the curve up to the 

 elastic limit multiplied by the scale value in inch-pounds of 



each unit an -a 

 the modulus of clas- 

 tic resilience in inch- 

 pounds. 



The modulus of total 

 FIG. 149 



resilience is defined as 



the amount of work required to deform a cubic inch of the material 

 to rupture. It is therefore represented by the area under the whole 

 curve multiplied by the scale value of a unit area, that is, the number 

 of inch-pounds per unit area. 



In case the stresses are plotted in pounds and the corresponding 

 deformations in inches, the above method gives the work done on the 

 whole volume of the specimen included in the gauge length. To 

 obtain the modulus for such cases it is necessary, in addition to the 

 above, to divide by the volume of that portion of the specimen over 

 which the deformations were measured. 



Compression is measured by means of a compressometer, by methods 

 similar to those used in making tension tests. The strain diagram in 

 this case is a stress-compression curve. 



