February 6, 1903 J 



SCIENCE. 



211 



electrical engineering, interpreting it 

 broadly if need be. 



Stress: J. Burkitt "Webb, Stevens Insti- 

 tute, Iloboken, N. J. 



Attention has often been called to the 

 fact that in mechanics a confusion exists 

 in the use of fundam 'atal terms, which 

 results in masaj^ cases fi-om faulty defini- 

 tions of the quantities caiployed. 



Stress is one of the more recent terms, 

 and a discussion of its meaning may lead 

 to a better understanding of it. 



An examination of authors shows that 

 it is a general designation for tension, com- 

 pression, shear, etc., in which authors agree ; 

 they differ, however, somewhat on minor 

 points, so that the composite idea to be 

 gained from a number of them is somewhat 

 confused. 



Its right to exist must depend upon its 

 applicability to a definite thing in nature 

 for which no better name exists, and we 

 will attempt to show what this thing is. 



When forces and moments are in equi- 

 librium upon a material body, a state is 

 produced therein which, viewed statically, 

 is called a stress, and, viewed geometrically, 

 a strain. Thus, if two equal and opposite 

 forces of m pounds each, or, as we may 

 express it, two forces m and — m in the 

 same line of action, be applied to the ends 

 of a rope, a state of tension ensues therein. 

 This is evident statically from its tendency 

 to contract, and geometrically from its 

 greater than normal length. 



The following distinct points are to be 

 noticed : 



{a) It i-equires two equal and opposite 

 forces to produce a tension, that is, it re- 

 quires a 'couple,' and the definition of 

 stress should be consistent therewith and 

 with the following general conceptions: 



A definite force applied at any point 

 of a free body produces in one second a 

 definite velocity of translation of its center 



of gravity. If a 'couple' of forces be 

 applied, each neutralizes the translation of 

 the other so that the center of gravity is 

 unaffected. The forces of the 'couple' 

 have, of course, parallel lines of action 

 whose distance apart is the lever arm of 

 the 'couple,' and the product of one of 

 the forces by the lever arm is the moment, 

 or torque, of the 'couple.' A definite 

 toi-que produces a definite angular velocity, 

 and may be neutralized by an equal and 

 opposite torque so as to leave the body un- 

 affected as to both translation and rotation. 

 It is unscientific to exclude, as some authors 

 do, from their definition of a 'couple' the 

 case when the lever arm is zero ; the ' coiiple ' 

 exists then as much as it ever does. 



But besides these Idnematic effects, which 

 may or may not be produced, we have the 

 static effect on the body itself, and a body 

 can not act as the medium for balancing 

 forces or moments vsdthout assuming a 

 state of stress, so that a 'couple,' whose 

 dynamic effect is reduced to zero by reduc- 

 ing to zero its lever arm, still causes stress 

 in the body. In a 'couple,' therefore, the 

 essential property of the forces themselves 

 is neutralized, and the dynamic or static 

 properties of the couple alone remain. 



A stress, thei'efore, is not a force, any 

 more than a 'couple' is, although appro- 

 priately measured in pounds or similar 

 unit used for forces. 



(&) Another point of difference between 

 a stress and a force is that a force is a 

 vector having direction, while a stress has 

 only a line of action. This is the more 

 evident when we consider that changing 

 the algebraic sign of a force reverses its 

 direction, and that to produce one stress, 

 say a tension, we require both the plus 

 and minus forces, thus interfering ^vith the 

 idea of direction. A stress has only a line 

 of action, and changing from plus to minus 

 has nothing to do with direction, but means 



