18 



PRACTICAL STRUCTURAL DESIGN 



M P 



= 



(around) the load, with a lever arm = ^- The bending moment 



Zi 



under the load (middle of span) is 



L PL 



2 = ~r 



The reader is not to forget that in computing reactions, which 



take into account only the 

 weight, we use the clear 

 span (5), but in computing 

 the moment we use the 

 length (L) from the center 

 of bearing on the support. 

 In Fig. 9 a uniform load 

 (represented by the weight 

 of the beam) is carried on 

 two supports on which it 

 rests freely. 



Shear Diagram 



* ig. 7 A Cantilever Beam Supporting 

 an I-beam 



w 



Each reaction = -~-> in which W = wS. 



This gives two cantilevers with moments acting about the center 

 of gravity of the beam, which being in the middle of the span 



makes the length of the moment arms = j measured from the 



middle of the span to the center of gravity of each half span. 

 The bending moment is ^ i 



W 



" 2 



L 



4 



WL wSL 



_ _ r\r* 



8 



or 



W 



The load -= acts as a uni- 



*%- 



<L o __ 



t* 



_ Fig. 8 Concentrated Load at Mid- 



,. , ,. , ., span with Beam on Two Supports 



formly distributed load and 



not as a concentrated load at the end, although it is equal to the 

 reaction. 



The reader will notice that the multiplication sign (x) is not 

 used between letters, for when several letters are written together 

 in formulas it means they are to be multiplied together. If the 

 multiplication sign were used it might be mistaken for the letter 

 x when written. The multiplication sign is always used between 

 figures. Thus, WL stands for W x L, but 67 means sixty-seven 

 and does not mean 6 x 7 = 42. 



