ALLOWABLE STRESSES. 



79 



tin- p.iiu'l, while the point of contra-flexure in floor girder 3-4 will be 13 ft. 4 in. from column 

 N<>. 4. The bending moments at the top of column No. 2 will be M *> + 6,000 ft.-lb.; in the 

 right end of floor girder 1-2 will be Mi-t = 450 Ib. X 2 ft. 8 in. = 1,200 ft.-lb.; in the left 

 end of floor girder 2-3 will be M t -t = 600 Ib. X 8 ft. = 4,800 ft.-lb. It will be seen that 

 the sum of the bending moments equals zero and the point is in equilibrium. The bending 

 niomrnt-i at the tops of columns No. 3 and No. 4 are calculated in the same manner. The direct 

 st iv>s in floor girder 3-4 is 4,500 Ib., in floor girder 2-3 is 3,000 Ib., and in floor girder 1-2 is 1,500 Ib. 



In the plane of the 6th floor the bending moments at the foot of the columns between the 

 6th floor and the roof will be M = -f- 6,000 ft.-lb., while the bending moments in the columns 

 below the 6th floor will be M = 2,500 Ibi X 6 ft. = + 15,000 ft.-lb. The bending moments in the 

 floor girders are calculated as for the roof girders. It will be seen that the sum of the bending 

 moments at each intersection of columns and floor girders equals zero and the structure is in 

 static equilibrium. The remainder of the vertical stresses, horizontal stresses and bending 

 moments are easily calculated in the same manner. 



Limitation of Method. When the transverse framework consists of more than four bays 

 (five columns) the solution above locates the point of contra-flexure of the leeward floor girder 

 in the second panel, and the method fails, as the point of contra-flexure in the girder must not 

 fall outside of the girder. For a wide building the shears cannot be taken equal. 



Distribution of Shears. In the above solution it is assumed that the shear is taken equally 

 by the columns. If the columns do not have the same cross-section this assumption will not be 

 correct. If the columns do not have the same cross-section the condition that the deflection of 

 the points of contra-flexure in each story are equal will require that the shears in the columns 

 be in proportion to the moments of inertia of the cross-sections of the columns. 



For buildings having a greater width than four bays the most consistent method is to calcu- 

 late the shear in the outside columns so that the points of contra-flexure in the floor girders will 

 not fall outside the girder, the remainder of the shear being equally divided among the inside 

 columns. 



ALLOWABLE STRESSES. The allowable stresses in the steel framework of high buildings 

 should be taken the same as for steel frame buildings in Chapter I. It is usual to add 25 per cent 

 to the live load stresses due to cranes and vibrating machinery to provide for impact. 



Comparison of Compression Formulas. The standard formula for the design of compression 

 members adopted by the Am. Ry. Eng. Assoc., is used by the author in his "Specifications for 

 Steel Frame Buildings" in Chapter I, and by the building ordinance of Chicago. The A. R. E. A. 

 formula is 



P = 16,000 70//r (i) 



where P = unit stress in Ib. per sq. in.; / = length and r = least radius of gyration of the column 

 in inches. The maximum value of P is taken as 14,000 Ib. 



The American Bridge Company's Formula. The American Bridge Company has adopted 

 the following formula for the design of compression members. 



Axial compression of gross sections of columns, for 



ratio of l/r up to 120 19,000 ioo//r 



with a maximum of 13,000 



