The under parts of these members must be stiffened by tie or batten plates, and these plates (44) must be equal in length to the distance between rivet lines. This is 192 inches. They will be made 20 inches long and 23 inches wide. The thickness of these plates (44) must be 0.39 inch (say r inch). The size of the tie-plates will then be 20 in. by a in. by 1 ft. 11 in.
Since the distance between the rivet lines is greater than 15 inches, double latticing must be used (47); and according to Table XXV the lacing must be z inch thick; also, according to (45), it must he 21 inches wide, as the rivets used are inch in diam eter. The lattices will then be 2' by '>-in.
87. The End=Post. Since the minimum section as chosen for the top chord is about 50 per cent in excess of that required by the compression formula, it will be assumed to be sufficient for the section of the end-post, and it will now be investigated to see if it is safe.
In addition to the stress due to direct compression, the end-post is stressed by its own weight, by eccentric loading due to the pin being in the center of the web instead of at the center of gravity of the section, and to a bending moment at the place where the portal brace joins it. This is due to the bending action of the wind on the top chord. These different stresses will now be computed; and since the post is in all cases stressed by a combination of bending and compres-, sive stresses, this fact should be considered in the design. In deter mining the stress in the end-post due to its own weight, the entire weight must not be used in computing the bending action, but only that component of it which is perpendicular to the end-post. The length of the end-post is readily computed, and is as shown in Fig. 186. The general formula for accurately computing stresses due to bending when the member is also subjected to compression, is: My, S Pls , I _ 10 in which, S = Stress in pounds per square inch in the extreme upper fibre of the beam; Exterior moment causing the stress, and is considered positive if it bends the beam downward, and negative if it bends the beam up y,= Distance from the neutral axis to the extreme upper fibre; I = Moment of inertia of the section; P = Direct compressive stress, in pounds; l — Total length, in inches; E = Modulus of elasticity of steel, which is usually taken as 28 000 000 pounds per square inch.
In this case the force causing the bending is that component of the weight perpendicular to the end-post. This is Wi sine, in which
IV is the weight of the steel in tile end-post; and this is computed and is as follows: Cover-plate 1 435 lbs.
Web plates 2 245 " Angles. 1 250 " Flats 1 245 " 6 175 lbs.
Add 25 per cent for details 1 544 " Total. 7 719 lbs.
Substituting in the above formula the various values, there results: In the above equation, the stress in the member is 410500 pounds; the distance is the distance from the neutral axis to the top of the cover-plate, and the coefficient of elasticity of steel is taken as 28 000 000.
In computing the stress due to the eccentric loading, the moment is equal to the product of the total stress in the member by the dis the neutral axis to the center of gravity axis causing a negative moment. Substituting in the above formula for combined stresses, there results: In order to find the compression in the lower fibre, it is only necessary to notice that the stresses are proportional to the distances from the neutral axis. Accordingly (see Fig. 187), the stress in the lower fibre due to the weight is 895 pounds tension, and the stress in the lower fibre due to the eccen tric loading is 302 pounds compression.
Before computing the stress due to the bending moment caused by the wind on the upper chord, it is necessary to in vestigate the post to see if it is fixed or hinged at its lower end. This is very important, since, if the post is found to be hinged, the bending moment will he one-half of that which will occur when the post is not hinged.
An end-post is considered hinged when the product of one-half of the total stress times the distance between the web plates is greater than the product of the wind load acting at the hip, or joint times the length of the end-post. In this case the first value is 410 500 15 = 3 075 000; and the product of the latter (see Article 29) is 12 600 X 36.7 X 12 = 5 550 000. Since the latter is greater than the former, the post is hinged, and the bending moment at the foot of the portal strut, which joins the end-post 28.2 feet from the end, is 6 300 X 28.2 X 12 = 2 130 000 The stress in the extreme fibre due to this bending moment is: • 2 130 000 X 11.5 3 256.3 — 410 500 X (36.7 X 12) 10X 28 000 000 In computing this stress due to the wind moment, care must be taken to take y, equal to one-half the width of the cover-plate, and to take "the moment of inertia as that about the axis perpendicular to the cover-plate.