USEFUL DATA 



The distance to the point of zero shear, provided the shear changes sign in the span, is 



Xi = — for span li 



X2 = — for span U 



The bending moment at this point. 



M=M\-\-V iXi ^ for span h 



M = 3/2+^2X2 r^ for span U 



If the sign of this moment is plus, it is the maximum positive moment. If the sign 

 is minus, it is the minimum negative moment and indicates that no positive moment 

 exists at any point of the span. 



By changing the subscripts as previously mentioned the formulas may be applied 

 to any span. 



CONCENTRATED LOADS 



For concentrated loads the theorem is expressed by the formula. 



Ml 



ii h 



I ^ 7ri A T 



Ms 



Vt 



h + 12 



1 *2 



-0:2- 

 V2 



v/ 



ly 



Bs 



Ri 



Fig. 5 



Applied to spans ^3 and Z4, Fig. 5, the formula would be written as follows: 

 The shears will then be: 



(3 



n = F3-(P,+P',) 



F4=^^^+P4(l-ifc4) 



Knowing the moments at the supports, the shears and moments at any section may 

 be obtained as in the case of continuous beams with uniformly distributed loads. 



Careful attention must be paid to the use of the proper algebraic signs in the fore- 

 going equations. 



Equal Spans. Uniform load over all spans: Diagram 10, page 45, gives 

 moment coefficients of tcP at critical sections of contmuous beams of from two to 



39 



