96 STRESSES IN A TRANSVERSE BENT 



solved by calculating the stress in 5-6 and substituting it in the diagram, 

 or by substituting an auxiliary member as shown. Compression and 

 tension in the truss and stress diagram in Fig. 53 are indicated by heavy 

 and light lines respectively. 



The stress in each column is equal to one-half the sum of the ver- 

 tical loads, plus the load carried directly by the column. 



Case 2. Wind Load Stresses: Wind Horizontal; Columns 

 Hinged. The wind will be considered as acting at the joints, as shown 

 in Fig. 54. Replace the columns with trusses as indicated by the dotted 

 lines. This makes the bent a two-hinged arch (see Chapter XIV), and 

 the stresses will be statically determinate as soon as the horizontal reac- 

 tions H and H l at the base5 of the columns, have been determined. The 

 usual assumption in mill buildings and portals of bridges is that 

 H H 1 = where W = the horizontal component of the external 

 wind force (see Chapter XII). To calculate V and F 1 graphically, pro- 

 duce the line of resultant wind until it inersects a vertical line through 

 the center of the truss, and connect the intersection A with the bases of 

 the columns B and C. From A lay off H = H 1 = -=-, as shown in 

 Fig. 54, and complete the triangles by drawing vertical lines through 

 the ends of these lines. The vertical closing lines will be V = J 71 , 

 as shown in Fig. 54. 



The stresses are calculated as follows: Beginning with the foot 

 of the column B, lay oft" the dotted line A-B R. At B, lay off the 

 load a-B 2240 Ibs. ; through a draw a line parallel to auxiliary truss 

 member a-b, and through A draw a line parallel to the column b-A, 

 completing the polygon A-B-a-b. 



The line a-b in the stress diagram will be the compression in the 

 auxiliary member a-b, and A-b will be the tension in the column A-b. 

 It should be noted that V is equal to the algebraic sum of the vertical 

 components of the stresses in a-b and A-b. Next lay off x-a = 3200 Ibs. 

 and complete the polygon a-x-c-b by drawing lines through x and b par- 

 allel to the auxiliary truss members x-c and b-c respectively. In like 

 manner determine the stresses at the foot of the knee brace by con- 



