散歩しながら考える構造力学２

Interest of the Tower

　Opening the dictionary, the tower has the following entry.

Tower: 〘name〙 (tower) A tower. Especially, a tower for sightseeing with an observatory. From the Japanese Language Dictionary (Seisen-ban)

　As usual, I always climb towers when I travel. The panoramic view is one thing, but the unique structure of each tower is what catches my attention. I often find myself gazing at the structure without looking at the view. The taller the tower, the better the view. However, the higher the tower, the greater its own weight, which increases seismic forces, and the higher the design wind speed in high winds, which increases wind loads. Towers in various locations have been built to overcome these severe limitations.

　In this issue, three structures with observatory facilities in Japan will be selected, and the innovations that make up the high-rise structures and the characteristics of the structures that ensure various structural performances will be explained.

list of articles (e.g. in a magazine)

Structural Dynamics in a Walking Tour 2

Tokyo Tower

　Around 1955, Tokyo Tower was planned as a support tower to combine antennas of several companies in one place in response to the spread of television broadcasting.

Looking up from an angle

Looking up from the front

Location	Minato Ward, Tokyo
Year Completed	1958
design	Tatyu Naito，Nikken Sekkei
construction	Takenaka Public Works Shop
height	333m
structure	Steel-frame assembled truss structure

　The structural designer, Tanaka Naito, is a major architectural structural engineer who invented the concept of earthquake-resistant walls in building structures, implemented it in buildings he designed, and spread it throughout the world.
　The tower is a 333-meter radio transmission and reception tower with an 80-meter antenna support tower on top of a 253-meter steel tower. The foot of the tower is a rectangle of about 80m x 80m with an aspect ratio of approximately 4.2, ensuring a firm stance at the foot of the tower.

Overall tower configuration

　The structural frame is an assembly of steel shapes (flat and channel steel) and steel plates, which are riveted to each other to form the main truss structure.
　Upon closer inspection, it is interesting to note that the same assembly material has a different configuration of the web part. It is thought that they are probably divided according to the distance between the fulcrums. It is thought that long members are arranged in a lattice-like configuration to suppress out-of-plane deformation during earthquakes, while short members are arranged in a firendial configuration to simplify the joining of the web members.

Assembled member with lattice-like web

Assembly member with web in the form of a firendial

　The primary loads for designing for horizontal forces in above-ground structures are seismic and wind loads. In most buildings in the world, seismic loads are dominant in comparison to wind loads, so the design for wind loads is often omitted. However, wind loads are dominant in the Tokyo Tower, and the horizontal forces are designed for a wind speed of 90 m/s.
　At the time of design, even hand-cranked calculators were not yet widely available, and a slide rule was used to calculate stresses. The Cremona method and the Castigliano Theorem were mainly used to determine the cross-sections of the members. Nowadays, it is convenient to perform structural analysis easily thanks to the widespread use of calculators.
　Below are the results of an analysis in which the Tokyo Tower 1 structure is modeled as a plane surface. For simplicity, static analysis is performed assuming that wind loads are evenly distributed. Shear forces at the top of the tower are transferred to the bottom of the tower by the X-shaped braces. In the lower part of the tower, the shear force transmitted from the upper part is converted to axial force by the arch structure at the ground level and is transferred to the foundation. Since the tower is fundamentally a cantilever structure with the earth as the support point, it is very reasonable for the tower to have a terminal shape at the ground level to handle the incidental bending moments. In addition, since wind loads are dominant, reducing the projected cross-sectional area at the top of the structure by narrowing the top of the tower is considered to contribute effectively to the reduction of stresses.

Left: Axis force diagram during wind load, Right: Transformation diagram during wind load.

References

１）Miyachi Technical Journal No.28 : https://www.miyaji-eng.co.jp/technology/newsletter/media/28/no28-p064-070.pdf

２）Toshiya Tanaka: Tokyo Tower and Eiffel Tower, Architectural Magazine, October 1990, Architectural Institute of Japan, 1990

Kyoto Tower

　Kyoto Tower has a special form of structure with a 100-meter tower on top of a 30-meter-high structure.

Panoramic daytime view

Panoramic night view

Year Completed	1964
design	guardian of Yamada
Structural Design	Ryo Tsukihashi
construction	Obayashi Corporation
Height	131m	Structure
Structure	Lower part: Steel Rahmen Structure Upper part: Steel Monocoque Structure
Location	Shimogyo-ku, Kyoto City, Kyoto Prefecture

　The structural form of this building is significantly different between the building and tower sections. The lower structure is a steel frame rame structure, while the upper tower structure is a monocoque structure (stress outer skin membrane structure). The monocoque structure is made of steel plates of 12 to 22 mm in thickness, and rib plates are placed inside to prevent local buckling. As can be easily seen in the night view photo above, the steel plates are cut into rings at a height of 2.7 m for transportation and divided into four sections in the circumferential direction. These parts were welded together on site.

　It is fun to visit the observatory to see the structural framework near the internal staircase. Incidentally, there seems to be an event twice a year where visitors climb the internal stairs to the observation deck. If you are physically fit, you should definitely try it.

塔Inner rib: from Shohei Furuichi

　The upper monocoque structure and the lower ramen structure are connected by eight connecting diagonal columns. Furthermore, the connected diagonal columns are rigidly connected by four ring beams to form a rigid-frame structure. Since it was anticipated that the stress state would be complicated due to the connection of structures of different types, a 1/120-scale photoelastic experiment was conducted in the design stage to confirm the stress state.

Overall structural configuration

References

１）Ryo Tanahashi: Kyoto Tower Building Vibration Experiment, Transactions of the Architectural Institute of Japan, September 1965, 1965.

２）R. Tanahashi: Static Loading Poetic Decision Result of the Steel Model of Kyoto Tower, Transactions of the Architectural Institute of Japan, September 1965, 1965

Umeda Sky Building

　The Umeda Sky Building is a skyscraper located northwest of JR Osaka Station with an observation deck on the top floor and roof.

©Kakidai(Licensed under CC BY 4.0)

*looking up＊

Year of Completion	1993
Hara Hiroshi	TOSHIHIKO KIMURA
Structural Design	KIMURA Toshihiko
Construction	Takenaka Public Works, Ohayashi Group, Kashima Construction, Aoki Construction JV
TAKANAKA Kobayashi, Kashima Kobayashi, Aoki Kobayashi JV - - Construction
Constructions	Iron Bone Construction
Location	Osaka City, Osaka Kita-ku

　Each building consists of two wings separated by 54 m, the east wing measuring 27 m wide by 54 m deep, the west wing measuring 33 m wide by 54 m deep, and a hanging garden connecting the two wings at the top.

　The aspect ratio of each building is about 5.2 to 6.4, and there is a concern that the buildings may cause vibration problems for office use, where people are always in residence. By connecting the two buildings rigidly with each other by the roof garden, the two buildings resist external forces as a whole, and the bending back effect of the roof garden structure significantly improves the generated stresses and deformations. The following figure shows an analysis of the concentrated load applied to the apex of a gabled girder structure, which is modeled after the Umeda Sky Building. The cross-sectional performance of the top spanner is varied, and you can see the increase or decrease in bending moment and horizontal displacement as the cross-sectional performance is increased or decreased.

Left: Bending moment diagram, Right: Displacement diagram

　The original plan called for the construction of a 54m x 54m hanging garden, with half of the members from each building being taken out from the top and joined together in the center. However, this method requires a lot of work in the air and special construction equipment, such as suspended scaffolding, is needed. Under these circumstances, the lift-up method was proposed to rationalize the construction. In this method, the hanging garden components are assembled on the ground and then fished up to a predetermined position. On the day of the lift-up, the hanging garden was raised to the specified height and connected to the east and west wings in about 7 hours. The speed was overwhelmingly fast.

*Lifting status from 1)

参考文献

１）Shinkenchiku-sha: Japan Contemporary Architects Series⑰ Toshihiko Kimura, 1996

Summary.

　In this issue, we have introduced buildings with observation facilities in Japan. As structures become taller and taller, the load increases and the response increases, leaving designers with no choice but to do something about it. However, it is very interesting to see how the structural devices used to meet these restrictions have resulted in a unique form, which is an advantage as an urban landmark.

　Why don't you climb up to one of the observatories on your next vacation? If possible, I hope you will not only enjoy the view, but also contemplate the structural structure behind it.