182 WOOD AND CAST-IRON COLUMNS 



u = 3,500 



/3,500X240\ 



-I ) =2,660 Ib. 



\ 100X10 / 



Since the factor of safety is 6, the safe bearing value per 

 square inch of sectional area is 2,660 -5- 6 = 443 Ib. The 

 area of the post being 100 sq. in., the safe load is 100 X 443 J 

 = 44,333 Ib. 



The column formulas in general use do not give a direct 

 method of calculating the dimensions of a post that will 

 safely support a given load. The usual method of obtain- 

 ing this information is to assume values for the dimen- 

 sions of the post* substitute these values in the formula, 

 and then solve for u, the ultimate average compression per 

 square inch of sectional area of post. If the assumed dimen- 

 sions give a value of u that is satisfactory for the given con- 

 ditions, they are accepted as correct. If, however, the 

 resulting value of u is smaller than desirable, it shows that 

 the sectional area is too small. Larger dimensions must 

 then be chosen and the solution repeated until a satisfactory 

 result is obtained. 



If, on the contrary, the value of u is much greater than the 

 required ultimate strength per square inch of the post sec- 

 tion, a smaller cross-sectional area is chosen and the corre- 

 sponding value of u is found. After a few trials, a size that 

 gives a satisfactory stress for the given conditions is found. 



EXAMPLE. Design to the nearest inch a white-oak post 

 that is to be 15 ft. long and that is to carry a load of 40, 000 Ib. 

 with a factor of safety of 5. The post is to be square in 

 cross-section. 



SOLUTION. Since a factor of safety of 5 is to be used, 

 the required post must crush under a load of 5X40,000 

 = 200,000 Ib. The ultimate compressive strength of white 

 oak, from the table on page 128, is 5,000 Ib. As a trial, 

 first try a 7" X 7" post. 



Substituting the correct values in the preceding formula, 



5,000X15X12 



u = 5,000 = 3,714 Ib. per sq. m. 



100X7 



The ultimate strength of the post is therefore 3,714 

 X7X7 = 181,986 Ib. But the required' ultimate strength is 



