32 NOTES ON PLATE-GIRDER DESK A 



The two values of p given from (9) correspond to the 

 mum and minimum values and occur on cither OP 

 or 01' 



For an extended treat men! of the subject of combined 

 stresses see Wood's Analytical Mechanics, Chapter V. 



If either or all of the quantities p*, p y or q have a 

 ion opposite to that shown in FMJJ. <W they should 

 be entered in the formulas with a minus sign. 



The planes of maximum shear make angles of 45 with 

 the lines of maximum direct stress. 



The amount of p w is small, except for large concen 

 trated loads, with reference to p r and 7. If p u he neglected, 

 at the end of the beam where p x = the angle = 45 

 and p = q, that is the direct stresses are equal to the shears 

 in intensity and make an angle of 45 with them. 



If p y be neglected, at all points on the neutral axis 

 where p f is zero, p=q and makes an angle of 45 with the 



In determining the location of the plane on which p, 

 the principal stress intensity, is a maximum note, the values 

 of the component stresses and inspection will show about 

 the direction the resultant must have. If difficulty occurs 

 in applying formula (9) it will be better to derive a special 

 formula for the case at hand. 



PROBLEM 



6a. A plate girder of 14' effective length carries a total load of 

 10,000 Ibs. per linear foot of length, tin- lo.-i.l bring applied to the top 

 flang?. Consider the structure to be solid and of a cross section com- 

 posed of 4 angles 4"X4"Xi" and 1 plate 24X*", a* shown in the 

 >ketrli, determine the maximum stress intensity and the direction of 



