CHAPTER III. 



THE LAWS OF EQUILIBRIUM AND THEIR APPLICATION. 



29. The Problem. The problem to be considered is that of 

 keeping structures and their parts at rest or in equilibrium. In 

 order to hold a structure in equilibrium, it is necessary that the 

 external forces acting on it shall be in equilibrium. In order that 

 any part of a structure shall be in equilibrium, it is necessary 

 that the internal forces (stresses), or internal and external forces 

 acting on it shall be in equilibrium. This is a problem in statics 

 (if the structure is statically determinate) ; the unknowns are the 

 reactions and the stresses, .and these are determined so as to 

 satisfy the condition of equilibrium by means of the simple laws 

 of equilibrium expressed in the form of equations. 



If ail the external forces acting on a structure are fully 

 known, the stresses in it can be found, and from these the defor- 

 mation of any part or the deflection at any point. The external 

 forces should, therefore, be determined first-, these are the loads 

 and reactions. 



Live loads for bridges and buildings are usually taken from 

 standard specifications; dead loads must be estimated when not 

 specified, and are taken uniformly distributed or concentrated, 

 depending upon the construction. Having the loads, the reactions 

 at the supports and the stresses are determined by the application 

 of the laws of equilibrium. Before stating these certain proper- 

 ties and relations of forces will be defined. 



30. Properties and Relations of Forces. Three things are 

 necessary to fully determine a force ; its magnitude, its point of 

 application, and the direction in which it acts. The point of 

 application is not important, and may be considered to be any 

 point in the line of action of a force. The line of action of a force 

 is a line of indefinite length, passing through the point of appli- 

 cation in the direction of the force, any part of which laid off to 

 some scale will represent the magnitude of the force; an arrow 

 placed on the line representing the force fully determines the 

 direction in which the force acts. Only co-planar forces forces 

 whose lines of action are in the same plane will be considered. 



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