DESIGN OF PLATE GIRDERS 221 



The allowable stress for compression is (16,000 70 /-^r) 1.25. 

 The moment of inertia of a 3" x y%" bar is 0.0135, an d the radius of 

 gyration is o.n inches. The ends of the lacing bars are practically 

 fixed, and it will be assumed that the length c. to c. of rivets will 

 as a result be shortened by one-half. Then l-^-r = 75, the allowable stress 

 will be 13,340 Ibs. and the required area 1 . 10 square inches. The lac- 

 ing bars are therefore sufficient to take either the tension or compression. 

 Lacing bars 2^" x y%' will be found sufficient below the foot of the 

 knee brace. 



The allowable shear on each rivet in the lacing will be (Table XIV) 

 4860 x 1.25 = 6,075 Ibs.; and the allowable bearing will be 6,190 x 

 1.25 = 7,740 Ibs. The stress in the lacing bars below the foot of the 

 knee brace is 5,500 x sec 30 = 6,300 Ibs. ; the ^-rivets are all right 

 for bearing but are not quite large enough for shear, however it is so 

 near, that they will be used. Above the foot of the knee brace it will be 

 necessary to increase the thickness of the lacing bars and put two rivets 

 in each connection as shown in Fig. 102, or use a solid plate. 



In designing the bases of columns hinged at the base, part of the 

 stresses may be assumed to pass directly to the base plate if the abutting 

 surfaces have been milled; but in columns fixed at the base all of the 

 stresses must be transferred by the rivets. The rivets must be designed 

 to take the direct stress and the stress due to bending moment ; the so- 

 lution is similar to that for anchorage (Fig. 61) and will not be given. 



Design of Plate Girders. The maximum moments and shears 

 are found as described in Chapter X. If the plate girder were de- 

 signed by means of its moment of inertia, as in the case of rolled sec- 

 tions, about j of the web would be effective as flange area to take 

 the bending moment ; or deducting rivets about y% would be found ef- 

 fective. It is, however, the common practice to assume that all the 

 moment is taken by the flanges, and that all the shear is taken by the 

 web ; and this assumption will be made in the discussion which follows. 



Flange Stress. The stress, F f in the flanges at any point in a 

 plate girder is 



F = M~h (80) 



