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ll 7 
a 
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MOMENTS AND CENTROIDS 61 
the beam are supposed to be concentrated loads, i.e. loads acting at 
definite points. When a load is distributed over the whole length or 
a part of the length of a beam the bending moment and shearing force 
i s are determined graphically by dividing the part of the beam 
carrying the distributed load into a number of parts, and assuming the 
loads on these parts to be concentrated loads acting at the middle points 
of these parts, and then proceeding as for concentrated loads. 
Bending moment and shearing force diagrams are further considered 
in Chapter VII. 
Exercises Vb. 
1. Referring to Ex. 5, Fig. 39, p. 41, determine the moment of inertia of the 
given forces about a point 1 inch to the right of A. The forces are in lbs, 
2. Determine the moment of inertia of the figure shown at Ex. 5, Fig. 47, 
p- 49, about AB as an axis. 
3. Determine the moment of inertia of the figure shown at Ex. 9, Fig. 47, 
p. 49, (a) about AC as an axis, (b) about an axis parallel to AC and passing 
through the centroid of the figure. 
4. Find the greatest and least moments of inertia of a section of a 
stanchion built up of an I and two channel joists, as shown in 
Fig. 69. For the I section the over-all depth is 8 inches, the | i 
greatest moment of inertia is 111°6 inch units, and the least is 
22 inch units. For the channel the over-all width of base is 
12 inches, the flange width is 3} inches, and the thickness 
throughout is } inch. Neglect the rivets. [U.L.] 
5. A cast-iron beam section is shown in Fig. 70. Find g, the 
distance of the centre of gravity of this section from the bottom, 
and determine I, the moment of inertia of the section about an 
= peseing through the centre of gravity and perpendicular to TFia. 69. 
the web. 
6. Fig. 71 shows the section of a Carnegie Z-bar column. The web plate 
and the Z-bars are 4 inch thick throughout, Find the square of the least 
radius of gyration of this section. 
7. The cross section of a built up column is shown in Fig. 72. The angles 
i5--— 
a 
Fira. 70. Fie. 71. Fig. 72. Fig. 73. 
are 3} inches x 34 inches x $ inch, and the plates are $ inch thick. Find the 
square of the least radius of gyration of this section. 
8. The cross section of a Phcenix column is shown in Fig. 73. Find the 
square of the least radius of gyration of this section. 
9. Calculate the greatest and least moments of inertia of a T-iron section 
5 inches wide, 4 inches deep, and 4 inch thick. Construct the inertia curve 
and momental ellipse for this section. Linear scale, full size, Inertia scale, 
$4 inch to 1 unit of moment of inertia, the moment of inertia being in inch 
units. 
10. A Z-bar section has a total depth of 5 inches, each flange is 3 inches 
wide over-all, and the thickness throughout is 3 inch. Find the principal axes 
of inertia, and construct the inertia curve and momental ellipse for this section. 
State the value of the square of the least radius of gyration. 
