12 PRACTICAL STRUCTURAL DESIGN 



The factor of safety = ~- 

 Mb 



A Moment is the product of a force multiplied by the distance 

 through which it acts. 



In Fig. 1 the load P, acts through a distance L r The formula is 



M = PL, 



Forces act through the center of gravity of bodies, and a load 

 is a force, for it tends to bend the beam down. The length L t is 

 measured from the center of the support to the center of gravity 

 of the load. 



For a uniformly distributed load the center of gravity is at the 

 center, which for the beam will be one-half of L, so the formula 

 for the bending moment due to the uniformly distributed load is 



L WL 

 M = Wx^ = -^~ 



The total moment on the beam, when W is the weight of the 

 beam, is WT 



M or M b = PL,+^ 



In Fig. 6 a cantilever beam carries two concentrated loads. For 

 this condition 



For more than two loads the formula will be the same, it being 

 only necessary to obtain the moment for each load and for the 

 weight of the beam and add them together. 



When the load is in pounds and the distance to the center of 

 gravity is in feet the bending moment is in foot pounds. When 

 the distance is in inches the bending moment is in inch pounds. 

 A bending moment in foot pounds is converted into inch pounds 

 by multiplying by 12. A bending moment in inch pounds is 

 converted into foot pounds by dividing by 12. 



The f ollowing examples will illustrate the foregoing formulas : 



1. A cantilever beam projecting 10 ft. beyond a wall and weigh- 

 ing 50 Ibs. per lineal foot carries a concentrated load of 400 Ibs. 

 at a point 7 ft. from the wall. Find the bending moment in foot 

 pounds. 



The total load is 500 Ibs. (weight of beam) + 400 Ibs. = 900 Ibs. 

 Assume the beam to be fastened in the wall 1 ft. and the center of 



