CONCRETE DESIGN 285 



Substituting these quantities in the formula M Ss, then 

 ll,250 = d 2 X180. Thus, c? 2 = 62.5 and rf = 7.906, say 8, in. 



The modulus of rupture of concrete is usually less than 

 that of stone. 



The table on page 284 gives values found by the United 

 States Geological Survey. Three degrees of wetness are 

 recognized in mixing the concrete, namely, wet, medium, 

 and damp. Wet concrete is such that sufficient water is 

 added to make it semiliquid; damp concrete is decidedly 

 granular, with little tendency to lump; while medium concrete 

 is of a consistency between the other two mixtures. The 

 values given in the table are mostly for 1-2-4 mixtures. 

 A 1-3-6 mixture gives values at least 15% lower than the 

 1-2-4 mixture. 



The factor of safety employed is sometimes 4, but usually 

 6 or higher, as the strength of concrete is uncertain. 



EXAMPLE. Design a concrete beam 12 in. wide on a 12-ft. 

 span to carry 800 Ib. at its center. The safe working stress 

 is to be 100 Ib. per sq. in. 



Wl 800 X 12 X 12 

 SOLUTION. The moment is equal to - 



= 28,800 in.-lb. Assume the beam itself weighs 260 Ib. 

 per ft. Then the moment due to the dead load is 



260X12X12X12 



- = 56,160 in.-ib. The total moment is 

 8 



56,160 + 28,800 = 84,960 in.-lb. Substituting the correct 



values in the formula M = Si, then 84,960 = -- X100. 



6 



Therefore, d 2 = 424.8 and d = 20.6, say, 21 in. 



CONCRETE COLUMNS 



Plain-concrete and stone columns may be divided into two 

 classes, namely, those which are centrally loaded, and those 

 which are eccentrically loaded. The height of the column 

 should never be more than twelve times the least dimen- 

 sion of the cross-section and even less for stone and brick. 



Column Centrally Loaded. For a centrally loaded column 

 the allowable compressive stress per square inch is multiplied 

 by the area of the cross-section of the column to find the 



t 



