PHYSICS, CHEMISTRY AND ENGINEERING 175 



That is, the moment at the end of a member can be ex- 

 pressed in terms of the changes in the slopes at the ends of 

 the member and in terms of the deflection of one end of the 

 member relative to the other end. 



Neglecting the change in length of a member due to axial 

 stress, the deflections of all columns in a story of a bent are 

 equal, and the deflection of the girders are equal to zero. If 

 the connections between the columns and girders are perfectly 

 rigid all members intersecting in a point are subjected to the 

 same angular strain at that point. The unknown quantities 

 for each story of a bent are therefore one change in slope, or 

 0, for each intersection of a column with a girder, and one 

 deflection for the story as a whole. That is, there are as 

 many unknowns per story as there are columns plus one. 



If the point in which a girder intersects a column is consid- 

 ered by itself since it is in equilibrium the algebraic sum of 

 the moments acting upon the points equal zero. A moment 

 equation therefore can be written for each intersection of a 

 column with a girder, or as many equations can be written 

 for each story as there are columns in the bent. 



If all of the columns in a story of a bent are considered 

 together, the algebraic sum of the moments at the tops and 

 bottoms of all of the columns equals the total sheer in the 

 story multiplied by the story height. 



All of the above moments are moments at the ends of the 

 girders and columns. As explained above these moments can 

 be expressed in terms of the changes in slopes, at the ends of 

 the members and the deflections of one end of a member rel- 

 ative to the other end. The total number of equations in one 

 story of a bent is therefore equal to the number of columns 

 in the bent plus one. The number of unknowns in the equa- 

 tions for one story of a bent is equal to the number of equa- 

 tions for the story, but the equations for one story contain 

 unknowns from the story above and from the story below the 

 one in question. It is therefore impossible to isolate the 

 equations for one story and determine the unknowns. There 

 is no story to contain unknowns above the top story, and the 

 bottoms of the columns of the bottom story are usually as- 

 sumed to be fixed. Under these conditions there are as many 



