R,' X 14 -I- R," X 20- 3,100 X 24.4-6,200 X 12.2 - R2 X 20 = 0.
As in (b) we find from the first two equations the values of R," and R2. These values substituted in the third equation change it to x 14 + 6,373 X 20 - 3,100 X 24.4 - 6,200 X 12.2 - 3,782 X 20 = 0 or - 373 x 20 + 3,100 X 24.4 -I- 6,200 x 12.2 + 3,782 x 20 = ' 14 = 7,104.* (d) When using the fourth set of conditions we always determine the reaction at the roller end from the moment equa tion. Then, knowing the value of this reaction, draw the force polygon for all the loads and reactions and thus determine the magnitude and direction of the other reaction.
Taking moments about the left end, we find as in (a),(b), and (e) that R2 = 3,782. Then draw AB, BC and CD (Fig. 36) to represent the wind.loads, and DE to represent R2. Since the force polygon for all the forces must close, EA represents the magni tude and direction of the left reaction; it scales 9,550 pounds.
2. It is required to determine the reactions on the truss of the preceding illustration when the wind blows from the right.
The methods employed in the preceding illustration might be used here, but we explain another which is very simple. The truss and its loads are represented in Fig. 37. Evidently the resultant of the three wind loads equals 12,400 pounds and acts in the same line with the 6,200-pound load. If we imagine this
resultant to replace the three loads we may regard the truss acted upon by three forces, the 12,400-pound force and the reactions, and these three forces as in equilibrium. Now when three forces are in equilibrium they must be concurrent or parallel, and since the resultant load (12,400 pounds) and 112 intersect at 0, the line of action of must also pass through 0. Hence the left reaction acts through the left support and 0 as shown. We are now ready to determine the values of It and 112. Lay off AB to represent the resultant load, then from A and B draw lines parallel to and and mark their intersection C. Then BC and CA represent the magnitude and directions of and B, respectively; they scale 6,380 and 8,050 pounds.
1. Determine the reactions on the truss represented in Fig. 26 due to wind pressure, the distance between trusses being 15 feet, supposing that both ends of the truss are fastened to the supports.
Reaction at windward end is 6,6821 pounds.
Reaction at leeward end is 3,037i pounds.