STRESSES IN TALL BUILDINGS. 77 



ami efficient wind bracing in the ends and sides of the building, it would appear reasonable to 

 usMiinr that in the completed building one-half the wind load will be taken by the intermediate 

 transverse framework, and one-half-will be transferred by means of the floors to the ends of the 

 building and then transferred to the foundations by means of wind bracing in the ends of the 

 building. The author's specifications permit reinforced concrete floors to be considered as assisting 

 in transferring wind loads in finished buildings, but most specifications require that the steel 

 framework be required to carry all the wind loads in the completed structure. 



The transverse intermediate framework usually consists of columns and floor girders, in 

 which the floor girders have brackets or knee braces at the ends to increase the rigidity of the 

 framework. It will be seen that it is not only impossible to calculate the amount of wind load 

 that is taken by each intermediate transverse framework, but that the intermediate transverse 

 framework is itself statically indeterminate. In addition to being statically indeterminate it is 

 not possible to determine the sizes of the columns and floor girders until after the wind stresses 

 are determined. With a given framework in which the sizes of the members and the loads are 

 given the stresses may be calculated by taking into account the deformations of the structure or 

 by the "Theory of Least Work." From the above it can easily be seen that an exact solution of 

 th wind stresses in a tall steel frame building is impracticable and that an approximate practical 

 solution must be used. Three approximate methods for calculating the wind stresses in tall 

 steel frame buildings are described by Mr. R. Fleming in Eng. News, March 13, 1913. The third 

 method described by Mr. Fleming, and known as the " Continuous Portal Method," follows the 

 method of the continuous portal given in the author's " Design of Steel Mill Buildings" and is the 

 method in most common use. This method will now be described and some of its limitations 

 will be shown. 



Problem. A transverse intermediate frame bent consisting of four columns with bracketed 

 floor girders will be taken as in Fig. I. The wind loads are assumed as acting in the planes of the 

 floors as shown. It will be assumed: (i) That the framework is rigid, that is the columns and 

 floor girders do not change their lengths. (2) That each of the four columns takes one-fourth 

 of the shear. (3) That the points of contra-flexure in the columns are midway between the floors. 

 (4) .That the vertical components of the stresses in the columns vary as the distance from the 

 center of the building, or center of gravity of the columns. 



The shear in each column between the 6th floor and the roof will be 1,000 Ib. The shear in 

 each column between the 5th and 6th floors will be 2,500 Ib. The shear in each column between 

 the 4th and 5th floors will be 4,000 Ib. The shears in the other columns are shown in Fig. I. 

 The bending moments at the tops of each column between the 6th floor and the roof is M = 

 + i ,000 Ib. X 6 f t. = + 6,000 ft.-lb. To calculate the vertical stresses in the columns in the top 

 story take moments about a plane cutting the columns in the points of contra-flexure. Then 

 since the stresses vary as the distance from the center of the building, 



Fi X 24 ft. + F 2 X 8 ft. - F, X 8 ft. - F X 24 ft. 

 = 4,000 Ib. X 6 ft. 



= 24,000 ft.-lb. 

 Now 



Fi = - F = 3 F 2 = - 3 F,, 

 and 



F(3 X 24 + 8 + 8 + 3 X 24) ft. = 24,000 ft.-lb 



F, =lb. = i 5 olb. = -F, 



F t = 450 Ib. = - F*. 



The bending moment in the floor girder at the top of column No. i must be M = 6,000 

 ft.-lb., and will be equal to the vertical stress in column No. I multiplied by the distance to the 

 aint of contra-flexure. The point of contra-flexure in floor girder 2-3 will be at the center of 



