E1 = H2 n/2m

E2 = H1 n/2 - W1 (n/4 - m/2 ) /m

Bending moment at b = Mb, = Hl n/2 - W1 (n/4 - m/2)

Bending moment at b' Mb= H2- n/2.

For the truss-bent of Fig. 45, when the columns are fixed at the base, the stresses are the same as if the columns were shortened by an amount n ÷ 2, as above mentioned. The bent would then appear as in Fig. 49, and the values of the various stresses and the quantities, together with their points of application, are:

W = 18 X 16\ =9 650 pounds, as before.

W1, = 13 X 16 X 20 = 4 160 pounds.

H1 = H2 = 4 160 + 4 320 /2 = 4 240 pounds.

Sab = + 4240 X 13 - 4 160 X 6.5 / 5 = +5 616 pounds.

Sa'b'= + 4 240 X 13/ 5 = - 11 024 pounds.

sb'c' = 4160X7 + 4320X20.5-8650X45/60 = - 4 526 pounds.

Sb'c'= 4 160X7 + 4320X20.5+8 650X15/60= - 4 124 pounds.

Et = 4 240 X 7 /6 = 4 947 pounds.

4 240 X 7 - 4160 X 0.5

E2 = 4 240 X 7 - 4160 X 0.5 / 6 = 4 600 pounds.

Mb = 4 240 X 7 - 4 160 X 0.5 = 27 600 pound-feet. Mb= 4 210 X 7 = 29 680 pound-feet.

The stresses in the bent are then computed in a manner similar to that used when the columns are fixed, E1 E2, and the stresses in the knee-braces being attached to the truss as concentrated loads.

Since in this case, E1 E2, and the stresses in the knee-braces are less than they are when the columns are free at the base, the wind stresses throughout the truss will be less when the columns are fixed than when they are free.

On account of the difficulty of fixing the ends rigidly, it is advisable always to consider the ends free and to compute the stresses accordingly.

The student is advised not to take the trouble of determining the wind stresses in trusses of steel truss-bents by the method given above, but to use the 40 pounds per square foot of horizontal projection and to correct the stresses as previously mentioned (see Fig. 39).

The formulas of this article giving the stresses in the knee-bracing and the bending moment in the columns, should be used in all cases, and the posts and knee-braces designed according to the stresses so determined.

In cases where the 40 pounds per square foot is used, the direct stress in each column is:

S = 40 X a X l / 2 ; and the column should be designed for this stress, together with the stress due to the bending at the point where the knee-brace joins the column. See "Strength of Materials," pp. 85 and 86.

In case a crane is attached to either the truss or the column, the stresses due to its action must be considered in the design.

11. Suspended Loads. Under this head come any loads which may be suspended from the lower chord of the truss. The load may not be actually suspended from the underneath part, but may be placed above, and the connections so arranged as to bring the weight on the lower chord. This weight should preferably be concentrated at a panel point. In case it cannot be brought directly to the panel point, it may be distributed over a portion or all of the panel. In this case the portions distributed to the adjacent panel points are computed, and they are, for purposes of computation, considered as concentrated loads at the panel points. The sections of the chord over which these loads are distributed are in the condition of direct tension and bending, and must be designed for such stresses (see ••Strength of Materials," pp. So and S6).

Fig. 48. Notation for Formulas, Ends Fixed.

Fig. 49. Position, Direction, and Intensit}' of Wind Forces, Ends Fixed.

The suspended loads may consist of small hand cranes; shafting for transmission of power; heating apparatus, such as steam or hot-air pipes; water or compressed-air tanks; or platforms on which stand the operators for the cranes or hydraulic lifts. Figs. 50 and 51 show trusses with various forms of suspended loads attached.

12. Details of Roof Trusses. The spans of triangular roof trusses of the Fink type are usually less than 100 feet, and the spans of roof trusses with chords nearly horizontal are seldom greater than 50 feet. For trusses of such spans the details are almost standard. Since these spans and trusses constitute a large majority of those built, only the details of such trusses will be considered in this text. "Where trusses rest on masonry walls or on light columns in masonry walls, provision is made for expansion due to temperature. For trusses up to 75 or SO feet, slotted holes are placed in the end-bearing, and the bearings rest directly upon another plate. Bolts are fastened to the masonry, and extend upward through the slotted holes and have nuts on their ends. The nuts hold the truss securely to the wall, while the slotted holes allow the bearing to move backward and forward when the temperature falls or rises. The slotted holes should be 1/8 inch in length for every ten feet of span. The bolts should not be less than \ inch in diameter, and should be buried in the masonry at least 6 inches. Fig. 52 shows details of an expansion bearing of this character. In case the span of the truss is greater than 75 or 80 feet, a roller or a rocker bearing is used. Figs. 53 and 54 show details of this class of bearings.

Fig. 50.

Fig.51. Various Kinds of Suspended Loads.

For convenience in references to the common Fink truss, the following notation will be used: the points in the upper chord are given the letter U, with a subscript corresponding to the number of the joint from the left end. The lower chord and interior joints are given the letter L, with a subscript corresponding to the number of the joint from the left end (see Figs. 24 to 38). The advantage of this system of notation is that it enables one to refer to any particular joint by the use of the letter and its subscript, and its position will at once be apparent to the mind without the use of a figure.