Questions: The Bank of China Tower in Hong Kong is built in area prone to earthquakes and typhoons. Its architect I. M. Pei and its structural engineer Leslie Robertson applied an innovative approach. For strength, the diagonal braces and the vertical columns were integrated to one frame of a three dimensional space-truss. The diagonal braces are not restricted to the exterior tube of the structure; some penetrate the inner space of that tube. Each member of the space truss shares in supporting the vertical and lateral loads. Bank of China, Hong Kong. Left; the building as it is seen from the ground. Center: Schematics of the space-truss frame of the structure, viewed from the same side as the picture. The four corner columns A, B, C, and D and the center column X are indicated by heavy lines. The two shaded triangles indicate the tops of two quadrants. Right: Floor plans at different heights. The highest suction pressures occur around the tops of the three lower quadrants. As for aesthetics, the diagonal braces are emphasized on the skin of the building rather than being hidden, contributing to a motif that symbolizes the client: a growing bamboo plant. The building consists of four quadrants, each shaped as a triangular prism. The prisms that have truncated tops rise to different heights. Five columns define the edges of the prisms. Four columns rise from the corners of the square base of the building. A fifth column rises at the center of the building from the tip of the lowest prism at the twenty-fifth floor, to the tip of the building at the seventy-sixth floor. The central column serves as an edge to three prisms. Diagonal braces zigzag from the side columns to the center column. The rectangular bases of the prisms, which form the outside walls of the building, are braced with crossed diagonals. In addition, transverse trusses wrap around the building at selected levels. The strongest shear forces in an earthquake-jolt are experienced by the lower part of the building, which supports the weight of the entire building. To provide the necessary shear resistance at the lower parts of the building, the columns are connected at the fourth floor to a system of interior composite walls, consisting of steel plates and concrete slabs surrounded by slurry walls at the perimeter. The columns continue on to the foundations to resist overturning moments. It turned out that the cost of building this tower was significantly less than that of other high rises with comparable floor areas. Windows of high-rise buildings have to withstand suction forces due to strong winds. Estimates of those forces are obtained by a combination of computational methods and model-simulations in wind tunnels. A model of a skyscraper is much smaller than the real thing, and the air speed in the wind tunnel is usually much smaller than that of a hurricane, or a typhoon as it is called in East Asia. Formulas are used to scale up the results obtained from wind tunnel models. In wind tunnel testing of models of the Bank of China Tower in Hong Kong, it was found that suction pressure near the edges of the building are greater than those at the middle of the walls, and suction at certain corners were even higher than at the edges. Assume that for a tunnel wind-speed of 34 mph, the suction pressure at the center of an outer face of the building was 86 Pa and at the tip of one of the quadrants it reached 156 Pa. Estimate the suction pressure at those points for wind speeds of 170 mph, assuming that, but for the different speeds, the flow patterns of the wind are the same for both speeds. (Include units in your answers. More information.) at the center of the outer face at the tip of one quadrant

Transcript text: The Bank of China Tower in Hong Kong (see the figure) is built in area prone to earthquakes and typhoons. Its architect I. M. Pei and its structural engineer Leslie Robertson applied an innovative approach. For strength, the diagonal braces and the vertical columns were integrated to one frame of a three dimensional space-truss. The diagonal braces are not restricted to the exterior tube of the structure; some penetrate the inner space of that tube. Each member of the spacetruss shares in supporting the vertical and lateral loads. Bank of China, Hong Kong. Left; the building as it is seen from the ground. Center: Schematics of the space-truss frame of the structure, viewed from the same side as the picture. The four comer columns A, B, C, and D and the center column X are indicated by heavy lines. The two shaded triangles indicate the tops of two quadrants. Right: Floor plans at different heights. The highest suction pressures occur around the tops of the three lower quadrants. As for aesthetics, the diagonal braces are emphasized on the skin of the building rather than being hidden, contributing to a motif that symbolizes the client: a growing bamboo plant. The building consists of four quadrants, each shaped as a triangular prism. The prisms that have truncated tops rise to different heights. Five columns define the edges of the prisms. Four columns rise from the corners of the square base of the building. A fifth column rises at the center of the building from the tip of the lowest prism at the twenty-fifth floor, to the tip of the building at the seventy-sixth floor. The central column serves as an edge to three prisms. Diagonal braces zigzag from the side columns to the center column. The rectangular bases of the prisms, which form the outside walls of the building, are braced with crossed diagonals. In addition, transverse trusses wrap around the building at selected levels. The strongest shear forces in an earthquake-jolt are experiences by the lower part of the building, which supports the weight of the entire building. To provide the necessary shear resistance at the lower parts of the building, the columns are connected at the fourth floor to a system of interior composite walls, consisting of steel plates and concrete slabs surrounded by slurry walls at the perimeter. The columns continue on to the foundations to resist overturning moments. It turned out that the cost of building this tower was significantly less than that of other high rises with comparable floor areas. Windows of high-rise buildings have to withstand suction forces due to strong winds. Estimates of those forces are obtained by a combination of computational methods and model-simulations in wind tunnels. A model of a skyscraper is much smaller than the real thing, and the air speed in the wind tunnel is usually much smaller than that of a hurricane, or a typhoon as it is called in East Asia. Formulas are used to scale up the results obtained from wind tunnel models. In wind tunnel testing of models of the Bank of China Tower in Hong Kong, it was found that suction pressure near the edges of the building are greater than those at the middle of the walls, and suction at certain corners were even higher than at the edges. Assume that for a tunnel wind-speed of 34 mph , the suction pressure at the center of an outer face of the building was 86 Pa and at the tip of one of the quadrants it reached 156 Pa . Estimate the suction pressure at those points for wind speeds of 170 mph , assuming that, but for the different speeds, the flow patterns of the wind are the same for both speeds. (Include units in your answers. More information.) at the center of the outer face $\square$ at the tip of one quadrant