24 PRACTICAL STRUCTURAL DESIGN 



The maximum bending moment for a single load is always under 

 the load. If the weight of the beam is included the moment under 



the load is 



,, D 7 wb 2 



M = R& - \ 



in which w = weight of beam per lineal foot. 



Example. A beam with a length of 15 ft. between centers of 

 supports carries a load of 600 Ibs. at a point 5 ft. from the left 

 support. The weight of the beam per lineal foot is 9 Ibs. What 

 is the bending moment? 



First. For load only. 



,, Pab 600x5 X 10 

 M = -y- = - = - = 2000 ft. Ibs. 

 L 15 



Second. For load and beam. 



Pa wL 600x5 135 



= 267 ' 5 lbs " 



on/,2 /Q v 1f)2\ 



M = RJ> - ~ = (267.5 x 10) - Ptg 1 = 2675 - 450 



= 2225 ft. lbs. 



Referring to Fig. 17, the load P acts through the center of 

 ( ____ a _____ _______ b ________ gravity, but the effect is 



lessened because the load is 



npi 



w i distributed over a portion of 



the beam instead of acting 

 at a point as it would were 

 the load round like a ball. 

 Fig. 17 Partially Distributed Load on a Consider the load of fiOO 



T T-fc i* rri CI C1L V_>vFHOlviC>l I lie lUct\_l Ul UUU 



Beam Resting on Two Supports as Shown 



lbs. in the last example to 



be distributed over a length of 3 ft. What is the total bending 

 moment under the load? 



_ wtf _ PI 



Writing this out it appears 



M = (267.5 X 10) - ? X 2 1Q2 !^p- = 2675 - 450 - 225 



= 2000 ft. lbs. 



