QUESTIONS FOR EXAMINATION.

What is the method adopted for the structures treated of in the preceding chapter? What class of structures are there discussed? What points are illustrated by Fig. 61? What considerations should determine the choice of scales in such a case? Show how to apply the method of moments. In Fig. 63, what apparent difficulty is there and how may it be overcome? How are curved pieces to be treated?

What is the effect and action of wind? Show the application to a roof truss. What two cases may we distinguish? Show how to determine the reactions for each case. Show how to lay off the force polygon and how to form the strain diagram for each case. State and illustrate the method for complete calculation of a roof truss. Show how the method is applied to curved roofs.

EXAMPLES.*

1. If the pole of an equilibrium polygon describe a straight line, show that the corresponding sides of the successive equilibrium polygons will intersect in a straight line which is parallel to the locus of the pole.

2. A system of heavy bars, freely articulated, is suspended from two fixed points; determine the magnitudes and directions of the stresses at the joints. If the bars are all of equal weight and length, show that the tangents of the angles which successive bars make with the horizontal are in arithmetic progression.

3. If an even number of bars of equal length and weight rest in equilibrium in the form of an arch, and a, a, . . . . an, be the respective angles of inclination to the horizon of the 1st, 2nd, . . . . #th bars counting from the top, show that tan an+1 =

2n + I
21 I

tan an.

4. Four bars of equal weight and length, freely articulated at the extremities, form a square ABCD. The system rests in a vertical plane, the joint A being fixed, and the form of the square is preserved by means of a horizontal string connecting the points B and D. If Wbe the weight of each bar, show, 1st, that the W stress at Cis horizontal and = ; 2d. That the stress on BC at B is w√ 5 and makes with the vertical an

4th. That the stress upon AB at A is W; 5th. That the tension of the string is 2 W.

2

5. Five bars of equal length and weight, freely articulated at the extremities, form a regular pentagon ABCDE. The system rests in a vertical plane, the bar CD being fixed in a horizontal position, and the form of the pentagon being preserved by means of a string connecting the joints B and E. If the weight of W each bar be W, show that the tension of the string is (tan 54° + 3 tan 18°), and find magnitudes and 2 directions of the stresses at the joints.

6. Six bars of equal length and weight (= W), freely articulated at the extremities, form a regular hexagon.

First, if the system hang in a vertical plane, the bar AB being fixed in a horizontal position, and the form of the hexagon being preserved by means of a string connecting the middle points of AB and DE, show W that, Ist, the tension of the string is 3W; 2d., the stress at C is and horizontal; 3d., the stress at D 2√3

is w

1

and makes with the vertical an angle tant 2√3. Second, if the system rest in a vertical plane, the bar DE being fixed in a horizontal position, and the form of the hexagon be preserved by means of a string connecting the joints C and F, show that, 1st., the tension of the string is W√√3; 2d., the stress at Cis W31 and makes with CB an angle sin-1,

3

3

3d., the stress at B is Wand makes with CD an angle sin-1 28'

12

;

124

Third, if the system hang in a vertical plane, the joint A being fixed, and the form of the hexagon be preserved by strings connecting A with the joints E, D and C, show that, Ist., the tension of each of the

*The following Examples are taken from "Applied Mechanics," by Henry T. Bovey, Montreal, 1882. It is believed that the intelligent student can solve them by an independent application of preceding principles.