62 APPLIED MECHANICS 
11.. Calculate the square’ of the least radius of gyration of an angle-iron 
section’5 inches.x 34 inches x3 inch, and construct, the 
inertia curve and momental ellipse for this section. 
12. Show that the momental ellipse for any regular 
polygon is a circle, 
13. A column is built up of two channel irons 12 
inches x 34 inches x 4 inch, and two plates each 4 inch 
thick, as shown in the section Fig. 74. Determine the 
dimension « in order that the greatest and least moments 
of inertia about axes through the centre of gravity of the 
section may be equal. 
14. Fig. 75 shows the British standard section for 
No. 1 standard rail for tramways, a rail which weighs 90 lbs. per yard. Deter- 
mine (1) the area of the section, (2) the distance of the centre of gravity of the 
section from the bottom, and (3) the moment of inertia of the section about an 
axis through the centre of gravity and parallel to the underside of the bottom flange. 
#5 
-------@)'----------------- 
------------26 
Fig. 75. Fig. 76. 
15. The section of a small cast-iron fly-wheel is shown in Fig. 76. Find (1) 
the weight of the wheel in lbs., taking the weight of 1 cubic inch of cast-iron 
= 0°26 lb., and (2) the radius of gyration of the wheel about its axis. 
16. A beam of 20 feet span, supported at the ends, is loaded at points 4, 9, 
and 17 feet from one apd, the loads being 24, 34, and 4} tons respectively. 
Construct, graphically, the bending moment and shearing force diagrams, and 
measure the bending monient and shearing force at the middle of the beam. 
diner scale, 4 inch to 1 foot. Force scale, } inch tol ton. Pole distance, 10 
eet. 
_17. A beam of 20 feet span, supported at the ends, carries a load of 20 tons 
uniformly distributed over its length. Determine, graphically, the bending 
