RECTANGULAR BEAMS 61 



or 



bd*= 

 Pf.j 



may be used to determine the size of beam necessary. 



Illustrative Problem. A beam is to be figured to safely withstand a 

 bending moment of 200,000 in.-lb., the ultimate compressive strength of 

 the concrete being taken at 2000 Ib. per square inch and the elastic limit of 

 the steel at 40,000 Ib. per square inch. rc = 15. 



= ^3(0.02) (15)+ | V<)2) 2 (15) 2 -| (0.02) (15) 



= 0.598 



/=l-3/8fc = 0.775. 



With a factor of safety of 3, the ultimate bending moment is 600,000 in.-lb. 

 and 



bd * = 600,000 _ 



(2/3) (2,000) (0.598) (0.775) 

 With b =8 in., then 



Q72 



d 2 = ^ = 121.5, ord =11 in. 

 o 



Also, 



a s = (0.02)(8)(ll)=1.76sq. in. 



Some designers consider the stress-deformation curve to be 

 a full parabola even at working loads and use working formulas 

 similar to those derived for a rectilinear variation of stress. The 

 results obtained in designing under such an assumption are not 

 as much on the side of safety as those obtained by the straight 

 line formulas. This method of figuring beams is more likely to 

 be found in practice where the allowable unit stress on the con- 

 crete as specified by a building code is considered lower than 

 conservative practice requires. 



Formulas for ultimate loads are open to the objection that 

 when a factor of safety is applied which will bring the stress in 

 the concrete to about a good working stress, the stress in the 

 steel becomes unduly low from a standpoint of economy. A 

 factor of safety of 3 or 4 as is usually taken leaves a high stress 

 in the concrete with the stress in the steel far below what is 



