192 JOHN C. KOCH 



stresses, or stresses which the body may carry constantly or 

 repeatedly without damage, should always be well below this 

 limit. If the modulus of elasticity is known for a given material, 

 it is easy to' compute the deflections or deformations of beams or 

 other structures when the forces acting upon them are given. 

 Conversely, by measuring the deformations due to external loads 

 the stresses in various parts of a structure may be determined. 



Composition and resolution of forces 



16. The resultant of two or more forces acting in the same plane 

 is that single force which will produce the same effect as the 

 combined original forces. 



17. The components of a force are those forces which by their 

 combined action will produce the same effect as the original 

 force. 



In figure 2 let AB and BC represent both direction and mag- 

 nitude of two forces acting through the point B. Through A 

 and C if lines are drawn parallel respectively to BC and AB, 

 intersecting in the point D, the diagonal DB represents the 

 direction and magnitude of the resultant of the two forces AB 

 and BC. To balance AB and 5C a third force acting at B and 

 equal to DB but acting in the opposite direction would produce 

 equilibrium. 



18. Levers and moments. The simplest illustration of levers is 

 the see-saw. In figure 3 is shown a simple lever supported by 

 the fulcrum /. For equilibrium it is evident that if the weights 

 W and V are equal, their distances from the fulcrum must also 

 be equal. Also, if the weight W is greater than the weight V, 

 the lever arm of W must be less than that of F; and this rela- 

 tion must be such that W times its lever arm, m, or distance 

 from the point of support is equal to V times its lever arm, n. 

 That is, for equilibrium, W'm = V'n 



These products Wm and Vn are called moments and / is the 

 center of moments. This conception of the lever and of mo- 

 ments is one of the most important principles in mechanics. A 

 force acting on a body tending to rotate it about a certain point 



