* MOMENTS AND UENTROIDS 49 
a ee ee 
alnCDma when subjected to a uniform pressure or stress A,Q will be 
the same as the resultant of the varying pressure or stress on the original 
figure. But when the pressure or stress on a plane figure is uniform, the 
centre of pressure or centre of stress is at its centroid. Therefore the 
centroid of the figure a’nCDma is the centre of pressure or centre of 
stress of the original figure. 
Exercises Va. 
The following exercises may be worked graphically, or by calculation, or by a 
combination of these methods. 
1. ABCD is a square of 6} feet side. A force P=5 tons acts from A to D, and 
a force Q=3} tons acts from Bto ©. Determine the moment (in foot-tons) of 
the resultant of P and Q about a point within the square and 4 feet from AD. 
la. Same as preceding exercise, except that the force P acts from D to A 
instead of from A to D. 
ib. ABC is a triangle, AB=1}4 inches, BC=24 inches, and CA=2 inches. 
A force P has a moment of ~12 inch-lbs. about A, a moment of —30 inch-lbs. 
about B, and a moment of +20 inch-lbs, about C. Determine the magnitude 
and line of action of the force P. 
2. Six parallel forces, having the same sense, act at the angular points A, B, 
O, D, E, and F of a regular hexagon of 2 inches side. The magnitudes of the 
forces, taking them in the order A, B, C, etc., are 2, 14, 24, 3, 1,and 14. Find 
the centre of these parallel forces. : 
3. ABC isa right-angled triangle having the right angle at C. AB=2} inches, 
AC=lI} inches. Determine the centroid of the three squares described on the 
three sides of this triangle. 
, 3a. Determine the centroid of the three equilateral triangles described on 
the sides of the triangle given in the preceding exercise. 
4. A wire is bent into the zig-zag form ABCD shown at Ex. 4, Fig. 47, and 
Cc 
A Cc | | 
aS IEX7. \ 
2% R 
B are D x *, 
x5 Ex.6. B < 
B A % ! A 
~ B A Vv 
x. X 
Exlli\| | — 
Cc Ex.9. \ Ex 
L| l 
Cc A Cc oc 
Fria. 47. 
In reproducing the above diagrams the sides of the small 
squares are to be taken equal to half an inch. 
- is suspended by a string attached to the wire at the point A. Draw the direc- 
tion of the string. 
5. Determine the centroid of the figure shown at Ex. 5, Fig. 47. 
6. Determine the centroid of the figure shown at Ex. 6, Fig. 47. 
7. The intensity of the load at any point of the beam AB, Ex. 7, Fig. 47, is 
peoeeers! to the height of the diagram above the beam at that point. The 
ength of AB is 16 feet. Determine the position of the resultant load. 
8. Determine the centroid of the figure shown at Ex. 8, Fig. 47. 
9. Determine the centroid of the figure shown at Ex. 9, Fig. 47. 
D 
