RECTANGULAR BEAMS 133 



wl 2 

 per cent more steel than the beam designed with i for both 



positive and negative moments. 



Building laws, however, often require the beams and girders 

 to be figured as simply supported. In such cases to obtain a safe 

 structure and at the same time one that is as economical as 

 possible under the conditions, the beam over the supports should 

 have about six-tenths of the amount of steel that is employed in 

 the middle of the beam. 



The spans of a continuous beam are generally taken as the 

 distance between the centers of supports. This is the simplest 

 plan to follow in the majority of cases and is always on the side 

 of safety. If the support is exceptionally wide, an arbitrary 

 length of span may be taken which should not be less than the 

 net span between supports plus the total depth of the member 

 which is being designed. 



For occasional concentrated loads which act in connection with 

 uniform live and dead loads, and for loads produced by beams 

 running into girders, the maximum moment may be computed 

 with sufficient accuracy by considering the beam or girder simply 



X 



FIG. 65. 



supported, and then reducing this maximum moment by the 

 same ratio used in the distributed loading. For example, sup- 

 pose the maximum moment due to given concentrated loads is K 

 (considering the beam supported), then if 1/12 wl* is used in 

 distributed loading instead of 1/8 wl 2 required for the supported 

 beam, 8/12 of K, or 2/3K, may be used for the concentrated 

 loads. The negative bending moment with concentrated loading 

 may be taken the same as the maximum positive moment due to 

 concentrated loading, reduced as already explained. If the 

 principal live loads on a beam are concentrated as, for example, 

 upon a girder bridge, the moments and shears at all points must 



