COLUMNS AND STRUTS 169 
_ 12. A vertical mild steel post in a bridge consists of a central plate 18 
nche ae inch, a pair of angles 4 inches x 4 inches x} inch at each 
of the plate, and a plate 12 inches wide by } inch thick con- 
ed to each pair of angles so as to form an i section (Fig. 240). 
t th is 20 feet, and each end is firmly riveted to the flanges of the 
main girder. Find the safe load by Rankine’s formula. [Inst.O, E.] 
_ 13, A cast-iron column 10 feet long is fixed at the ends and has an 
I section 6 inches deep, with flanges 5 inches wide and web 1 inch Fia, 240. 
Find the thickness of the flanges so that with a factor of 
) ¢ 6 pee eran will carry safely a load of 85 tons. Use the Rankine- 
_ 14. If P denotes the buckling load of a column by Euler’s formula, and W 
‘denotes the buckling load of the same column by the Rankine-Gordon formula, 
o if F denotes the crushing load of a very short column of the same section 
‘and same material, show that W =>" if the constant a in the Rankine-Gordon 
aM 7; 
x. 
ik for a column with fixed ends. 
15. A hollow 2 egg steel strut has to be designed for the following 
conditions. Length 6 feet, axial load 12 tons, ratio of internal to external 
diameter 0°8, factor of safety 10. Determine the necessary external diameter of 
the strut and the thickness of the metal, if the ends of the strut are firmly built 
in. Use the Rankine-Gordon formula, taking f=21 tons per square inch, and a 
for rounded ends=1/7500. [U.L.] 
@ r 
