COLUMNS HINGED AT THE BASE 85 



stresses V and F 1 . Maximum bending occurs at the foot of the knee 

 brace and is equal to (H W 7 ) d on the windward side, and H 1 d 

 on the leeward side. These bending moments are the same as the bend- 

 ing moments in a simple beam supported at both ends and loaded with 

 a concentrated load at the point of maximum moment. Since the max- 



iw^^v VVv 



(a) 

 External Forces 



(c) 



Leeward Col Beam 



FIG. 51. 



(e) 



Shear Moment 



imum moment occurs at the foot of the knee brace in the leeward 

 column, we will consider only that side. We will assume that the lee- 

 ward column (b), Fig. 51, acts as a simple beam with reactions H 1 and 

 C and a concentrated load B, as in (c) . The reaction C and load B will 

 now be calculated. 



From the fundamental equation of equilibrium, summation hori- 

 zontal forces equal zero, we have 



B = H* + C (25) 



Taking moments about b, we have 



C (h d) = H 1 d 



C= 



(26) 



h d 



The stresses K, U and L can be computed by means of the follow- 

 ing formulas : 



K B cosecant m (27) 



where m = angle knee brace makes with column; 



U = (F 1 K cos m) cosecant n (28) 



where n = angle of pitch of roof; and 



