ALGEBRAIC SOLUTION in 



To obtain stress in H G, pass a section cutting H G, H ' and G D, 

 and take moments of the external forces to the left of the section about 

 the point D as a center. 



HG-- , Hd , (50) 



n a 



The stress in the windward post, A F, is zero above and V below 

 the foot of the knee brace C ; the stress in the leeward post is zero above 

 and F 1 below the foot of the knee brace D. 



The shear in the posts is H below the foot of the knee brace, and 

 above the foot of the knee brace is given by the formula 



S = Hd = stress in H G (51) 



h a 



The maximum moment in the posts occurs at the foot of the knee 

 braces C and D and is 



M = Hd (52) 



For the actual stresses, moments and shears in a portal of this 

 type, see Fig. 59. 



Portal (b). The stresses in portal (b) Fig. 58, are found in the 

 same manner as in portal (a). The graphic solution of a similar portal 

 with one more panel is given in Fig. 60, which see. It should be 

 noted that all members are stressed in portals (b) and (d). 



Portal (c). The stresses in portal (c) Fig. 58, may be obtained 

 (i) by separating the portal into two separate portals with simple 

 bracing, the stresses found by calculating the separate simple portals 

 with a load = J^ R being combined algebraically, to give the stresses 

 in the portal; or (2) by assuming that the stresses are all taken by 

 the system of bracing in which the diagonal ties are in tension. The 

 latter method is the one usually employed and is the simpler. 



Maximum moment, shear, and stresses in the columns are given 

 by the same formulas as in (a) Fig. 58. 



Portal 0). In portal (e) Fig. 58, the flanges G F and D C are 

 assumed to take all the bending moment, and the lattice web bracing 



