Introduction

　We have engineers with backgrounds in various engineering fields such as mechanics, fluid dynamics, physics, mathematics, architecture, and so on, with the common denominator being a love of geometry and mechanics.
　Although there are common theories such as material mechanics, structural mechanics, and vibration engineering as a common language, the objects to be designed in each field differ greatly, and I enjoy learning about the thought process of structures, differences in systems, industry conventions, and technical terms every day.

　Among our engineers, structural engineers with backgrounds in architecture and civil engineering were involved in the structural design of buildings and bridges, which are the largest objects that people use every day without even knowing it.
　In this article, I would like to describe how structural engineers in the architectural and civil engineering fields view structures, using bridges in Tokyo as an example.

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　In this article, I will take the following four bridges in Tokyo as examples and explain their structures.
　All bridges can be reached within 30 minutes from JR Tokyo Station by train.
　Incidentally, our company is located about a 25-minute walk from JR Tokyo Station.

1:Chiyoda Line Arakawa Bridge
2:Hamamatsucho Station Straddling Humanitarian Bridge
3:Bridge Shibuya 21
4:Koshu-kaido Pedestrian Bridge at South Exit of Shinjuku Station

Chiyoda Line Arakawa Bridge：Warren Truss

Year built：1968年
design：不明
structural form：Warren Truss
Span Length：No information
use：railroad bridge

　This bridge is probably a familiar sight to those coming to Tokyo from the Chiba area on the JR Joban Line and Tokyo Metro Chiyoda Line.
　There are four railroad bridges at this location, the JR Joban Line, Tokyo Metro Chiyoda Line, Tobu Isezaki Line, and Tsukuba Express, most of which are "Warren trusses".
　There are various types of truss structures, such as Pratt trusses, Haut trusses, etc. In the case of Warren trusses, the amount of steel frame can be reduced by omitting the vertical members in the middle, which is economical and widely used.

Photo Span Details

　 The following conceptual diagram is a simple representation of the structure.
　This is a structural form in which diagonal latticework is inserted to connect the upper and lower string members.
Since it is necessary for ships to pass under the bridge, rails are installed on the lower stringers to allow trains to pass.

　
　The axial force and bending moment diagrams for this bridge are described below.
　Basically, the upper lattice bears the compressive force and the lower lattice bears the tensile force. For the lattice members in between, there are both compressive and tensile members.
　As for the bending moment, the fixed load around the track and the running load of the train are only applied to the lower string members, and almost no bending moment is generated in the upper string members and lattice members.
　The bending moment diagram assumes that each member is rigidly connected, but the structural form can function without problems even if each member is pin-connected.

Hamamatsucho Station Straddling Humanitarian Bridge：Firendiel truss

Year of construction: 1984
Design: Japan National Railways
Structure: Ferendiel truss
Span length: Approx. 65 m
Use: Pedestrian bridge
Remarks: 1984 JSCE Tanaka Award

　
　This is a humanitarian bridge on the east side of JR Hamamatsucho Station, which you may see when you use the JR Yamanote Line or the Tokyo Monorail when you go to Haneda Airport.
　It is an important bridge that connects the station and the east side of the station across trains and Shinkansen lines.
　
　The following is a conceptual structural drawing of a Ferendiel truss.
　Unlike the Warren truss, the Firendiel truss is composed of only horizontal and vertical members, and has no diagonal members. Unlike the Warren truss shown in the previous section, each member must be rigidly connected to form a structure.

　The axial force and bending moment diagrams are shown below.
　The situation in which compressive and tensile forces act on the upper and lower members, respectively, remains the same. Instead, a large bending moment acts on the vertical members. This is because the vertical members bear the axial forces that were borne by the lattice members in the warren truss.
　In general, it is more efficient for a structural member to bear axial forces than bending moments. Therefore, it is more efficient to use lattice members such as Warren trusses and Pratt trusses, etc. However, the interior of the Hamamatsucho Station Bridge is indoor. It is assumed that the Feulendahl truss was chosen because it does not obstruct the view of the trains from the windows.
　It is interesting to note that structural rationality alone does not determine the structural form.

Bridge Shibuya 21: Trussed Firendiel

Year of construction: 2000
Design: Tokyu Corporation (General Design) + Architect Five (Design Design)
+ Umezawa Architectural & Structural Laboratory Inc.
Structure: Truss type firendir
Span length: 50m
Use: Pedestrian bridge
Remarks: Good Design Award 2001 (Architectural and Environmental Design Category)

　This pedestrian bridge appears as soon as you exit the South South Exit of JR Shibuya Station and go west along the highway. It is located at the foot of Cerulean Tower.
　Incidentally, in episode 94 of the Jutsu Kaisen, Torajo and Fushikuro confront the enemy near this pedestrian bridge and the battle begins.
　This pedestrian bridge is a rarity for a bridge, as it was designed by an architect and a structural engineer. This bridge is a rare example, as architecture and civil engineering do not often cooperate with each other because their aesthetics do not match.
　The bridge gives the impression of floating on the road, avoiding the ruggedness that is often associated with truss structures due to the assembly of members. The size of each member can be smaller than that of a Ferendiel truss.
　

Photo - Partial detail
　
　A conceptual structural diagram is shown below.
　The member arrangement is similar to that of the first Warren truss, but the lattice members are separated from each other and joined to the string members.

　
　The axial force and bending moment diagrams are shown below.
　Depending on the angle of the lattice members, the stress state is between that of a Warren truss and a Fehrendahl truss, with each member bearing the axial force and bending moment in good balance.
　By adjusting the angle of the lattice members, it is possible to control the silhouette of the members by manipulating the stress state of each member.
　The structure is not only aesthetically pleasing but also structurally pleasing.

Shinjuku Station South Exit Koshu-kaido Pedestrian Bridge: Plat + Firendiel Truss

Year of construction: 1998
Design: Kawada Engineering
Structure: Platt truss + Ferendiel truss
Span length: Approx. 54m
Use: Pedestrian bridge

　
　This pedestrian bridge is located on the west side of the South Exit of JR Shinjuku Station. It connects the Odakyu Milord Building and Shinjuku Southern Terrace.
　This bridge is a bit unique, and one wonders how it came to be so.

　A conceptual structural drawing is shown below.
　The bridge is a Fehrendiel truss at the ends and a Pratt truss in the center, and the structural type changes from the middle of the bridge.
　At first glance, one might think that the structural form is appropriately divided according to the stress state, but this is not the case.

　The axial force and bending moment diagrams are shown below.

　Because the shear forces from equally distributed loads are greater at the bridge ends, the shear forces on the vertical members of the Fehrendahl truss are also greater at the ends.
　As mentioned above, it is more efficient to use structural members as shaft members than as bending members, so if lattice members are placed appropriately in terms of stress, it is more efficient to place them at the ends because the axial forces they bear are greater.

　The reason for this configuration may be due to requirements or design reasons, but as far as I could find, I could not find any documents explaining the design.
　This is a hypothesis, but the pedestrian bridge in question has a staircase attached to the side of the Milord Building. The designer may have removed the diagonal latticework because he did not want people using the stairs to hit their heads against the diagonal latticework. If the latticework was removed from only one structure, the design would not be consistent, so I suspect that the latticework at the ends was removed from the entire structure.
　It is very interesting to see how the structure is made not only by optimizing the structural members, but also by taking into account the restrictions imposed by various factors such as people and cars.

Photo - Stair-step area

conclusion

　In this issue, we have toured some of the most characteristic bridges in Tokyo through the eyes of a structural engineer.
　Structures that we see every day can be viewed in a completely different way if we imagine the stress and deformation conditions and the design constraints that lie behind them.
　This year's weather is warmer than usual, so why not take a weekend stroll around the structures in your neighborhood?