This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The apex loads for this case are computed in Example 3, Page 26, to be as represented in Fig. 28. Supposing both ends of the truss to be fastened to the supports, then the reactions (due to the wind alone) are parallel to the wind pressure and the right and left reactions equal 3,600 and 7,200 pounds as explained in Example 2, Page 57.
To draw a clockwise polygon for the loads and reactions, we lay off BC, CF, and FF' to represent the loads at joints (1), (2), and (4) respectively; then since there are no loads at joints (5) and (7) we mark the point F' by C and B' also; then lay off B'A to represent the reaction at the right end. If the lengths are laid off carefully, AB will represent the reaction at the left end and the polygon is BCFF'C'B'AB.
At joint (1) there are four forces, the reaction, the load, and the two stresses. AB and BC represent the first two forces, hence from C draw a line parallel to cd and from A a line parallel to ad and mark their intersection D. Then ABCDA is the polygon for the joint and CD and DA represent the two stresses. The former is 7,750 pounds compression and the latter 9,000 pounds tension.
At joint (2) there are four forces, the stress in cd (7,750 pounds compression), the load, and the stresses in fe and ed. As DC and CF represent the stress 7,750 and the load, from F draw a line parallel to fe and from D a line parallel to de, and mark their intersection E. Then DCFED is the polygon for the joint and FE and ED represent the stresses in fe and ed respectively. The former is 7,750 pounds and the latter 5,400, both compressive.
At joint (3) there are four forces, the stresses in ad (9,000 pounds), de (5,400 pounds), eg and ga. AD and DE represent the first two stresses; hence from E draw a line parallel to eg and from A a line parallel to ag and mark their intersection G. Then ADEGA is the polygon for the joint and EG and GA represent the stresses in eg and ga respectively The former is 5,400 and the latter 3,600 pounds, both tensile.
At joint (4) there are five forces, the stresses in eg (5,400 pounds) and ef (7,750 pounds), the load, and the stresses in f'e' and eg. GE, EF and FF' represent the first three forces; hence draw from F' a line parallel to f'e' and from G a line parallel to e'g and mark their intersection E'. (The first line passes through G, hence E' falls at G). Then the polygon for the joint is GEFF'E'G, and
F'E' (6,250 pounds compression) represents the stress in f'e'. Since E'G = 0, the wind produces no stress in member ge'.
At joint (5) three members are connected together and there is no load. The sides of the polygon for the joint must be parallel to the members joined there. Since two of those members are in the same straight line, two sides of the polygon will be parallel and it follows as a consequence that the third side must be zero. Hence the stress in the member e'd' equals zero and the stresses in f'e' and d'c' are equal. This result may be explained slightly differently: Of the stresses in e'f, e'd', and d'c' we know the first (6,250) and it is represented by E'F'. Hence we draw from F' a line parallel to e'd' and one from E' parallel to d'e and mark their intersection D'. Then the polygon for the joint is E'F C'D'E,' CD' (6,250 pounds compression) representing the stress in c'd'. Since E' and D' refer to the same point, E'D' scales zero and there is no stress in e'd'.
The stress in ad' can be determined in various ways. Since at joint (6) there are but two forces (the stresses in ge' and e'd' being zero), the two forces must be equal and opposite to balance. Hence the stress in d'a is a tension and its value is 3,600 pounds.
2. It is required to analyze the truss represented in Fig. 24 for wind pressure, the distance between trusses being 15 feet.
The length equalsor
= 24.4 feet.
Hence the area sustaining the wind pressure to be borne by one truss equals 24.4 X 15 = 366 square feet.
The tangent of the angle which the roof makes with the horizontal equals 14 20 = 0.7; hence the angle is practically 35 degrees. According to Art. 19, the wind pressures for slopes of 30 and 40 degrees are 32 and 36 pounds per square foot; hence for 35 degrees it is 34 pounds per square foot. The total wind pressure equals, therefore, 366 X 34 = 12,444, or practically 12,400 pounds.
The apex load for joint (2) is ½ of 12,400, or 6,200 pounds, and for joints (1) and (3), ¼ of 12,400, or 3,100 pounds (see Fig. 29).
When the wind blows from the right the load for joint (5) is 6,200 pounds, and for joints (3) and (6) 3,100 pounds.
If the left end of the truss is fastened to its support and the right rests on rollers*, when the wind blows on the left side the right and left reactions equal 3,780 and 9,550 pounds respectively and act as shown. When the wind blows on the right side, the right and left reactions equal 6,380 and 8,050 pounds and act as shown. The computation of these reactions is shown in Example 1, Page 58.
For the wind on the left side, OA, AB, and BC (Fig. 295) represent the apex loads at joints (1), (2) and (3) respectively and CE and EO represent the right and left reactions; then the polygon (clockwise) for the loads and reactions is OABCDPEO. The point C is also marked D and P because there are no loads at joints (5) and (6).
The polygon for joint (1) is EOAFE, AF and FE representing the stresses in of and .fe respectively. The values are recorded in the adjoining table. The polygon for joint (2) is FABGF, BG and GF representing the stresses in bg and fg. The polygon for joint (3) is GBCIIG, CH and HG representing the stresses in ch and hg respectively. At joint (5) there is no load and two of the members connected there are in the same line; hence there is no wind stress in the third member and the stresses in the other two members are equal. The point H is therefore also marked I to make HI equal to zero. The polygon for joint (5) is HCDIH.