COLUMNS FIXED, GRAPHIC SOLUTION 



117 



where W = direct stress in post; 



A = area of base of column in sq. ins. ; 

 M = bending moment = J^ Hd; 

 c = one-half the length of the base plate; 

 7 = moment of inertia of the base plate about an axis at right 



angles to the direction of the wind. 



Graphic Solution. The stresses in the portal in Fig. 62 have been 

 calculated by graphic resolution. This problem is solved in the same 

 manner as the simple portal with hinged columns in Fig. 59. 



'1500 



\ 9 

 \ 



b \ 

 \ 



^ 



-HOOP +3500 R =2000 



^ T 



H30O* -1300 



H 

 1000 



^= -108000 irvlbs- l *.H = IOOO 



Moment Shear 



r- 



Portal 



/ a o 



mT 



.1 



CASE 2 



Columns Fixed 



Stress Diagram 

 o 1000 aooo 3000 



Compression 

 Tension 



FIG. 62. 



STRESSES IN CONTINUOUS PORTALS. The portal 

 with five bays shown in Fig. 63 will be considered. The columns will 

 all be assumed alike and the deformation of the framework will be 

 neglected. The shears in the columns at the base will be equal, and will 



