500.141 Perspectives on the Evolution of Structures
The objectives of this structural study are to (1) discover how the John Hancock Building in Chicago resists wind and gravity loads, (2) how to combine the structural effects of wind and gravity loads, and (3) learn how calculate and interpret a structural factor of safety.
Project Influences John Hancock Insurance commissioned the design of a Chicago skyscraper in 1966. Their vision was a grand commercial and residential structure serving in harmony with the existing skyline on Michigan Avenue. Their mixed-use criterion was not easily accommodated with traditional high-rise building forms, and therefore presented a unique structural and aesthetic challenge. Structural engineer Fazlur Khan led the creative design effort of this new building with architect Bruce Graham while employed by the architecture and engineering firm Skidmore, Owings, and Merrill. Their solution, the John Hancock Tower (figure 1), combines a unique external structural form with a strong skyward elegance. In addition to the roughly 827,000 sq. ft. of office space, the Tower contains 711 apartments that have attracted such famous tenants as the late Chris Farley (Saturday Night Live, Tommy Boy) and Oprah Winfrey. When completed in 1969, the Tower was the second tallest building in the world.
Structural Characteristics The Hancock Tower is a 100-story, 1127 ft. tall skyscraper. The building is designed to resist wind and gravity loads using an interior reinforced concrete core and an exterior steel frame incorporated into the facade. By shifting a large portion of the supporting structure to the outside skin of the building, interior columns are eliminated (figure 2). This allows maximum usability of the floor space at each story, one of the main criteria for a building accommodating both residential and commercial tenants. An example of a building built in the old style, with many interior columns is the Empire State Building.
The concrete core and steel frame work together as a column to transmit the weight of the individual floors to the ground. The steel frame behaves as a cantilever under the action of wind. Its network of vertical columns, horizontal beams, and diagonal struts stiffen the building and prevent excessive side sway at the higher stories.
Simplifying the Structure In this study, we will concentrate our efforts on understanding the behavior of the most visible part of the structural system, the exterior steel frame. Two assumptions will be made that allow us to analyze the steel frame as its own structure, separate from the core. The first assumption is that fifty percent of the building’s gravity load is carried by the external steel frame, and the other fifty percent is carried by the concrete core. The second assumption is that the steel frame resists the entire wind load applied to the structure. The second assumption is valid because of the immense stiffness imparted to the trussed tube by x-bracing specified by Khan.
Design Loads The three dominant loads acting on the Hancock Tower are its self weight, the live or occupancy load, and wind. The total downward force from the self weight of the Tower is approximately 462,000 kips and for live load is approximately 140,000 kips (figure 3).
The horizontal wind pressure is highest at the top of the Hancock Tower, and decreases near the ground. The geometry of the Tower reflects an opposing trend, where its width (and wind bearing area) is smallest at the top and increases near the ground. If we assume that the highest pressure at the top of building produces the same force as the lowest pressure on base of the building, then the wind pressure can be approximated in two dimensions as a continuous line of equal horizontal point loads (figure 4). In this study, we will apply the wind pressure to the widest face of the building (figure 1).
Analysis We will begin our analysis by determining the axial forces in the vertical steel columns due to the combination of self weight and live load. These loads accumulate, story by story, until they are transferred to the ground at the foundation (figure 3). We will assume that these vertical loads are distributed equally to the steel columns around the perimeter of the building (24 columns in total). A general equation for the axial force per column due to self weight and live load is provided (figure 5). In the below expressions, FG is the column force due to gravity, and PSW and PLL are the total force due to self-weight and live load.
Next, we will calculate the axial forces in the columns due to the horizontal wind pressure. As the wind blows, internal forces develop to resist the tendency of the Tower to tip over on its side. These resisting internal forces can be characterized as a moment. We will assume that only the columns in the two building faces perpendicular to the wind pressure (7 columns per face) will be active to resist the wind’s overturning moment. This is a reasonable assumption since these columns are the farthest from the centerline of the building, and so will do the most to resist the wind load. A general equation for the axial force per column due to wind is provided (figure 6), where P is the total wind force, M is the moment due to wind, C and T are the total tension and compression forces to counteract this moment, W is the width of the building, and FW is the force per column.
Finally, we can calculate a factor of safety for columns of interest by comparing their demand loads to the capacity of a column. The factor of safety gives us a measure of the efficiency of the structure since it describes how close the calculated force is to the allowable force per column. The allowable force is calculated by combining the allowable stress with the column area. A general equation for the factor of safety is provided (figure 7). Note particularly in the below expressions that on one face of the building the wind adds to the compressive force due to gravity, and on the other it subtracts from it.
A sample calculation is provided which determines the maximum and minimum column forces due to the combination of self weight, live load, and wind at h=600 ft. (figure 8). The calculation then determines the minimum and maximum factors of safety for the columns at this building height.
Designer’s Thoughts The following quotations give us some insight into the motivations of the designers.
“It was as essential to us to expose the structure [the Hancock Tower] of this mammoth as it is to perceive the structure of the Eiffel Tower, for Chicago, honesty of structure has become a tradition."