no STRESSES IN PORTALS 



CASE I. STRESSES IN SIMPLE PORTALS: Columns 

 Hinged. The deflections of the columns in the portals shown in Fig. 

 58 are assumed to be equal and 



H = W=. 

 Taking moments about the foot of the windward column 



F 1 = V = ^A 

 s 



Having found the external forces, the stresses in the members 

 may be found by either algebraic or graphic methods. 



Algebraic Solution. Portal (a). To obtain the stress in member 

 G C, (a) Fig. 58, pass a section cutting G F, F and G C, and take 

 moments of the external forces to the right of the section about point F 

 as a center. 



GC= _ _ (46) 



(h d) sin 9 



But H = -^ and (h d) sin 6 = * cos 6. Substituting these 



4 4 



values in (46) we have 



Rh = Fsece (47) 



S COS0 



Resolving at C and F we have, stress in F = o, and also stresses 

 E H' and H H' = o. 



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

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

 point H as a center. 



G D= Mn . - = + Fsec 9 (48) 



(h d) sin 9 



To obtain stress in G F, pass a section cutting G F, E F and G C t 

 and take moments of the external forces to the right of the section 

 about point C as a center/ 



h -d (49) 



