556 STRUCTURAL MECHANICS. CHAP. XVI. 



Since the vertical components of the reactions are independent of the conditions of the ends 

 of the truss, the vertical components of the reactions in (c) and (d) Fig. 2 are the same. It will 

 be seen that the load PI produces stress in the members of the truss with rollers windward. If 

 the line of action of RZ drops below the joint P$, the lower chord of the truss will be in compression, 

 as will be seen by taking moments about PS. 



STRESSES IN A TRANSVERSE BENT. A transverse bent in a steel mill building 

 consists of a roof truss supported at the ends on columns and braced against longitudinal move- 

 ment by means of knee braces, Fig. 3. The ends of the columns may be fixed at the base or 

 may be free to turn (pin-connected). The stresses in a transverse bent are statically indeterminate 

 and cannot be calculated without taking in account the deformations of the members themselves. 

 The following approximate method, proposed by the author in the first edition of " The De- 

 sign of Steel Mill Buildings," 1903, gives results that are approximately correct, are on the safe 

 side, and is the method now used in practice. 



Dead and Snow Load Stresses. The stresses due to dead and snow loads in trusses of a 

 transverse bent are calculated the same as though the trusses were supported on solid walls. 



Wind Load Stresses. The external wind loads may be taken (i) as horizontal or (2) as normal 

 to the surface. The columns will be assumed to be pin-connected at the tops and to be either pin- 

 connected or fixed at the base. It will be assumed that the horizontal reactions at the foot of 

 the columns are equal to each other, and equal to one-half of the horizontal component of the 

 external wind load. It is also assumed that the truss does not change its length, and that the 

 deflection of the columns at the top of the columns and at the foot of the knee brace are equal. 



It is shown in " The Design of Steel Mill Buildings " that when the columns are fixed at 

 the base the point of contra-flexure comes at a distance of from 5 to f of the distance from the 

 foot of the column to the foot of the knee brace. It is usually assumed that the point of contra- 

 flexure is located at a point in the column one-half the distance from the foot of the column to 

 the foot of the knee brace. If h = height of the column, d = height from the base of the column 

 to the foot of the knee brace, then the distance from the base of the column to the point of contra- 

 flexure will be 



d (d + 2ft) . 



yo = ~ 2 -(2JTJry (4) 







The calculation of the wind stresses in a transverse bent with a monitor ventilator is shown in 

 Fig. 3. The bents are spaced 32 ft. centers and are designed for a horizontal wind load of 20 Ib. per 

 sq. ft., the normal wind load being calculated by Hutton's formula, Fig. 3, Chapter I. The point 

 of contra-flexure is found by substituting in equation (4) to be 





42.5 



The external forces are calculated for the bent above the point of contra-flexure by multiplying 

 the area supported at the point by the intensity of the wind pressure. For example, the load at 

 B is 32' X 6.75' X 20 Ib. = 4320 Ib. 



The line of application and the amount of the external wind load, 1.W, is found by means 

 of a force and an equilibrium polygon. 1>W acts through the intersection of the strings parallel 

 to the rays 0-B and 0-C, and is equal to C-B (line C-B is not drawn in force polygon) in amount. 

 The reactions R and R' may be calculated graphically as follows: Lay off the total wind load 

 2W so that it will be bisected by point A in Fig. 3. Perpendiculars dropped from the ends of 

 load line ~S,W to the dotted lines A B and A C will give V = 12,800 Ib., and V = 700 Ib., respec- 

 tively. Then R and R' are calculated as shown. 



The calculation of stresses is begun at point B in the windward column, and in the stress 

 diagram the stresses at B are found by drawing the force polygon a-B-A-b-a. The remaining 

 stresses are calculated as for a simple truss. In calculating the stresses in the ventilator it was 

 assumed that diagonals 9-10 and 10-12 are tension members, so that 9-10 will not be in action 



