168 APPLIED MECHANICS 
Exercises X. 
1. A straight bar of steel 40 inches in length, 1 inch broad, and 4; inch in 
thickness, is bent into the form of a bow, having an elastic deflection of 2 inches 
in the middle, and the ends are united by the bow string. Taking the modulus 
E= 29,000,000 lbs. per square inch, what will be the tension on the string ? 
[Inst.C. E.] 
2. Apply the Rankine-Gordon formula to tind the buckling load for a cast- 
iron column 8 inches external diameter, 6 inches internal diameter, and 20 feet 
long. The column has fixed ends. 
3. A strut in a framed structure is formed of a steel pipe 6 inches external 
diameter, and 3} inch thick; it is 10 feet long, and has pin connections at each 
end. With a factor of safety of 5, to what load may it be submitted ? [Inst.C.E. 
4. Determine the value of the ratio L/k for which columns of cast-iron an 
mild steel of the same cross section, with hinged ends, have the same strength by 
the Rankine formula. ‘7 
5. Plot crippling load, in tons per square inch, and ratio L/k, for cast-iron 
columns with hinged ends, (a) by the Rankine-Gordon formula, (6) by Euler’s © 
formula, up to L/k=200. Take E=6000 tons per square inch. 
6. Find the proper diameter for a solid mild steel strut with pin ends, if its 
length is 120 inches, and if it has to carry a total load of 20 tons with a factor of 
safety of 7. Take the values of f and a (for flat ends) in the formula as 30 tons 
per square inch, and zp3gy respectively. [U.L.] 
7. Three solid cast-iron columns, each 3 inches in diameter, and 10 feet long, 
have their ends fixed, and each carries one-third of a load W. Find by the 
Rankine-Gordon formula the diameter of a single solid cast-iron column with 
fixed ends to replace these three columns, and find the percentage saving in 
weight of cast-iron. 
8. A hollow cast-iron column has to be designed to support a total load of 130 
tons ; the column is to be 15 feet in length, and the internal diameter is to be 
four-fifths of the external diameter, and it is desired to have a factor of safety 
10. Find the external and internal diameters of the column if the crushing 
load in tons per square inch for such a column is given by the formula 
Crushing load in tons per square inch = a , where L is the length 
. ste 5) 
of the column in inches, and D is the external diameter in inches. [B.E.] 
9. A hollow cast-iron column 20 feet long, with ends rigidly fixed, has 
to carry safely a load of 50 tons, If the factor of safety is 6, and the 
external diameter of the column is 8 inches, find the internal diameter. 
10. A steel strut is built up of two T section bars (Fig. 238) 
riveted back to back; the T’s are of the following section : 6 
inches x 43 inchesx 8 inch, The ends of the strut are rigidly 
secured, and its over-all length is 18 feet 6 inches. What gross 
load can this strut carry if it is to have a factor of safety 5? By 
the Rankine formula the buckling load in lbs. per square inch 
of such a strut=——4%,000 _ | where L is the length of the 
1+! _ (LY Fig. 238. 
30000\ & 
strut in inches, and & the least radius of gyration of the section. [U.L.] 
11. A column is built up of an [ rolled joist 20 inches deep ; flanges 7} inches — 
wide, and 1 inch thick; web $-inch thick; with two §-inch 
plates 12 inches wide riveted to each flange (Fig. 239). Find 
the least radius of gyration of the section. Taking a factor of 
safety of 6, find the working load if the column is 10 feet high 
= »where P is the 
ith fixed ends. he f 2 
with fixed ends. Use the formula P 2 Fia. 239. 
buckling load in tons, A the cross sectional area in square inches, and \ is 
the ratio of the length to the least radius of gyration. [Inst.C.E.] 
