First Person - Rethinking Bridge Design: A New Configuration

Figure 1

T.Y. Lin International

It was a spectacular steel cable-stayed bridge, one with both the tower and the girders designed in steel. In China, where the bridge was to be located, a steel girder is usually about twice as expensive as a concrete girder, but a concrete girder is about three times heavier. Changing the girder to concrete would have reduced the cost of the girder, but owing to the increased weight it would also have required a significant increase in the size of the tower, which again would have been unacceptable, both economically and aesthetically. The need to solve that problem led to my development of the concept of a girder bridge that receives some of its support from cables.

Photo composition by Huang He

However, in many instances, especially bridges with short or medium spans, the girder itself possesses a certain amount of capacity. So, I wondered, what if we were to reverse the roles of the two structural elements, employing the girder as the primary member and the cable support as the secondary member? In this way, we would be able to fully utilize the capacity of the girder. This is the concept of a bridge wherein some of the support is provided by cables, an approach that enabled me to use a prestressed-concrete girder in the bridge design and remain within budget.

This is how it works:

In the case of girder bridges with medium span lengths, the rule of thumb is that the appropriate depth of a haunched prestressed-concrete girder at the supports is approximately 1/20 of the span length. For a 100 m span, the girder depth at the supports should be about 5 m. For a girder with constant depth, the span-to-depth ratio may be increased to about 26. For girder bridges with shallower girder depths, the girder will require some additional support. The extradosed bridge is a good example: the girder depth is usually much less than 1/26  of the span and therefore support by external cables is necessary.

For the other three types of bridges in which the girder is supported by cables, the girder depth is not a function of the span length but rather is dictated by constructability and certain other factors. For example, the conventional thinking in the design of a cable-stayed bridge is that the cables carry all of the permanent loads on and of the girder, so under permanent load conditions the girder should have very little bending moment. Most of the live load also is to be carried by the cables. Only because of stiffness compatibility will the girder receive a limited amount of bending under live loads. With such a concept, the girder can be made very slender. In most cases the girders actually are very slender. The ratio of span to girder depth can be as high as 350 in a cable-stayed bridge and can exceed 600 in a suspension bridge. Because the cables are to carry all loads on the girder, the stiffness of the girder is not a major factor in the behavior of the bridge.

A partially cable-supported girder bridge uses cables to impart additional strength to a girder bridge that by itself would not be able to attain a given span length. Depending on the capacity of the girder, this degree of support may vary. The support can be provided by stay cables, by a suspension cable with hangers, or by hangers from an arch. By definition, therefore, there are three different types of partially cable-supported girder bridges: the partially cable-stayed girder bridge, the partially suspended girder bridge, and the partially arch-supported girder bridge. Obviously, there are also many variations within each of the categories. Partial support means that only part of the girder has cable support or that the entire girder is supported by cables that carry only a portion of the loads.

Figure 2

Li Dajiang

Returning to the bridge I mentioned at the beginning of this article—the Taijiang Bridge (see figure 2)—the structure will be situated in the city of Sanming, near Fuzhou, China, and will cross the Sha (Sa) River. Two 110 m adjacent spans will satisfy the local navigation requirement. The owner desires a signature bridge that reflects Chinese design influences. T.Y. Lin International’s Chong-qing office is serving as the design engineer for the project.

The two ends of the bridge are tied into local streets. Hence the elevations at both ends are fixed. The bridge serves a high volume of pedestrian traffic and bicycles, so the grade must be rather modest. Furthermore, the bridge must remain above the high-water level during flooding. These restrictions dictate the allowable depth of the girder. The deck is also very close to the water level, so a deep girder would not be aesthetically pleasing. The bridge in the rendering—as originally designed with a steel box girder—would have satisfied all of the requirements except those relating to cost.

The tower as designed would have been capable of carrying the entire weight of the girder if the girder had been a steel box with an orthotropic deck. (The weight of such a deck should be less than half that of a concrete box girder.) But the cost of the steel box girder would have made the project too expensive. Thus the idea of a bridge that would receive some of its support from cables was born. Instead of the steel box girder, we used a 2.80 m deep prestressed-concrete girder. This yielded a span-to-depth ratio of 39.3. Obviously the 2.80 m depth was not sufficient for a 110 m girder bridge span, although it would have been more than adequate for a cable-stayed bridge. We then decided to have stay cables bear part of the girder load. First we estimated the maximum capacity of the girder and compared it with the total load the girder had to carry. The difference was the amount of support the girder would need in order to function properly. The tower could then be designed based on this requirement. In the final design, the amount of permanent load carried by the tower was approximately 50 percent of the total load. The 2.80 m girder depth was also appropriate for the 60 m long approach spans.

The resulting bridge is a beautiful structure that is economical and aesthetically pleasing. It is neither a girder bridge nor a conventional cable-stayed bridge. Rather, it is a girder bridge that receives some of its support from cables.

The advantage of this concept can be explained as follows: The bending moment of a girder bridge determines the required depth or the cross section of the girder. The bending moment, M, in any point of the girder can be expressed as

where p is the load applied on the bridge, L is the span length, and   is a coefficient related to the location of the point under consideration, the type of loading, and the structural system of the bridge. Thus, if we can have a cable system that carries 50 percent of the load, the bending moment will be reduced by 50 percent. In other words, for the same girder depth, the span can be extended by a factor of    (1/0.5) = 1.414. Consequently, the ratio of span to girder depth can be increased to 1.414 × 26 = 36.8. This is certainly oversimplified, but the rationale offers a rather good approximation. The actual benefit is greater because stay cables also introduce a large compression force into the girder, which is very beneficial to a concrete girder. The same is true of a self-anchored suspension system.

Certainly, when we provide partial cable support to a girder bridge, both the girder and the cable system will be affected by all applied loads. However, while the amount of live load each will carry is strictly based on its relative stiffness, the cable forces under permanent loads can be adjusted to any rational value we desire. For a bridge of medium span, the permanent load of a concrete girder is usually much higher than the live load. Once the permanent load condition is established, the effect of live load is not as significant. In the Taijiang Bridge, the live-load stress in the cables is generally less than 8 percent of the maximum stress.

Furthermore, it is not necessary to assign a fixed percentage of load to every cable. Each individual cable force can be selected to offer the maximum effect. As a result, some may carry 100 percent of the local load while others may carry only 10 percent.

Figure 4

Li Dajiang

Part of the girder in deck arch and half-through arch bridges is supported by spandrels. The spandrel can be open with columns or it can be closed, in which case it takes the form of double walls. The spandrels act in the same way as cable hangers except that spandrels are in compression rather than in tension. Therefore, for simplicity, we assume that it is understood that when we mention cable supports spandrels are included.

The extradosed bridge can be viewed as a special instance of this concept. But an extradosed bridge has particular definitions, for example, the inclination of the cables and the location of the cables. If we increase the tower height of an extradosed bridge to make the cables more effective, the structure can no longer be defined as an extradosed bridge. We can also use cables to support the middle portion of the span. In that case the structure becomes a girder bridge that receives some of its support from cables, that is, a partially cable-stayed girder bridge.

T.Y. Lin International is working on a number of bridges in China. This has afforded me the opportunity to apply the concept to several other bridges with good results given the success attained in the design of the Taijiang Bridge. The Sanhao Bridge (see figure 3), in Shenyang, is another example of how a girder bridge that receives some of its support from cables has made a special bridge project possible. Shenyang is the capital of Liaoning, a province in northern China. The owner fell in love with the beauty of the bridge scheme when it was proposed. However, the cost of the bridge that was originally proposed, which featured a steel box girder and steel towers, was prohibitive. It was to be a fully cable-stayed bridge in which the entire weight of the steel box girder was to be carried by the cables to the tower. Consequently, in order to stay within budget I modified the design to a partially cable-stayed bridge with steel towers and a prestressed-concrete girder.

The prestressed-concrete girder is 2.6 m deep, and the two adjacent main spans are each 100 m long. The ratio of span to girder depth is 38.5. A study shows that this girder is capable of carrying about 60 percent of the total load. Therefore, the towers are required to carry only about 40 percent of the total load.

Taking advantage of the shallow water, the prestressed-concrete girder will be constructed on falsework. Once the girder is complete, we will assemble the tower arches, which will lie flat, on top of the deck. A temporary tower will be erected between these two arches, and the arch ribs will be raised by winches from the temporary tower to their final position before the final cables are installed.

Another example is the Jiayue Bridge (see figure 4), which crosses the Jialing River in the city of Chongqing. The bridge deck is about 70 m above water level amidst a picturesque and serene landscape. Navigation dictates that the main span be at least 230 m at this location. A haunched prestressed-concrete girder would be too bulky for such a landscape, whereas a conventional cable-stayed bridge with tall towers over the already very deep gorge would not be acceptable from an aesthetic point of view. Therefore we decided to reduce the height of the tower to an acceptable level and increase the capacity of the girder to carry a large portion of the loads. This resulted in a bridge that will receive some of its support from cables. It is not a true extradosed bridge, even though it looks like one; the towers are taller and therefore the cables are more efficient than the cables in a conventional extradosed bridge. In this case, the cables are designed to meet the same specifications as those in a regular cable-stayed bridge.

A girder that receives some of its support from cables may assume various forms. Aside from the stay cables, the partial support can come from a suspension system or an arch system. Like fully cable-stayed bridges, both suspension bridges and arch bridges are usually designed in such a way that the entire load of the girder is carried by the suspension cable or the arch. This may not be economical in the case of bridges with short or medium spans because the capacity of the girder itself is not being fully utilized. When we utilize the girder capacity to the fullest possible extent, savings can be realized in the supporting cables and towers or arch ribs.

Figure 5

T.Y. Lin International, both

The graph in figure 6 can be used to estimate the effectiveness of various partial supports. For example, the blue curve shows that if we apply a uniform load on the middle third of the girder span, the fixed-end moment will be equivalent to about 50 percent of the fixed-end moment resulting from a uniform load along the entire span. Consequently, by applying the partial cable force selectively, we can achieve greater efficiency.

The percentage of load carried by the girder and the cable support should be determined by the condition of the bridge in question. The most efficient design is the one that uses both capacities fully. If the girder is very flexible, the cable support will take up most of the load, so the bridge will approximate a conventional cable-supported bridge. If the support is very small, the structure will behave more like a girder bridge.

The advantage of a partially cable-supported girder bridge is that the capacity of each of the two load-carrying systems—the girder itself and the cable supports—can be fully utilized. This makes the structure more efficient economically. This advantage is especially significant in bridges with spans of no more than 250 m. Because considerations of constructability usually dictate a minimum girder depth of 2 to 3.5 m, such a girder is inherently able to carry a certain portion of the loading. This capacity has not been fully utilized until now.

Constructing a bridge that receives some of its support from cables imposes no special requirements. There are always many ways to build a bridge. We carry out construction engineering analyses to find the most efficient way to build a given structure. Each project is unique. We must consider such factors as the capacity of the structure in each construction stage, the site conditions, the available equipment, the labor force, and the transport of materials.

Figure 6                                                                           

For example, most engineers define an extradosed bridge as one in which the girder can be constructed first without any cable support. Many even expect the cables to be effective only for live loads. But these restrictions are unnecessary and they confer no practical benefit to the construction process or the final structure. There is no reason why the cables cannot be installed and stressed as the girder is constructed if this will simplify or expedite construction or increase safety. We should not impose such restrictions on the construction of partially cable-supported bridges.

Of the three examples described above, the Sanhao Bridge and the Taijiang Bridge will be built on falsework because this will simplify construction and can easily be done during the low-water season. This method of construction is very efficient. We expect to see more of it in the future.

Falsework support is obviously out of the question in the case of the Jiayue Bridge because of the height of the girder above the water level. The contractor will construct the girder by using the free cantilever method. But the cables will be installed and stressed shortly after the cantilever segment has been completed and the traveler has been advanced to allow cable installation without interference. This will also shorten the construction schedule.

The engineers who participated in the development and design of the three bridges partially supported by cables described in this article—all of which are currently under construction—include Yang Lianzhang, Jiang Zhonggui, Yin Delan, Ren Guolei, Yang Chun, Ma Zhengdong, Xi Jianshan, Liu Anshang, and Liu Xueshan, all of whom work for T.Y. Lin International in Chongqing. In many areas where prestressed-concrete girders are much less expensive than steel box girders, it can be anticipated that more bridges utilizing this concept will be built. However, the concept is not restricted to the use of concrete girders. Even with steel, designing a bridge based on this concept can achieve savings by fully utilizing the capacity of the steel girder.

China is about the size of the United States but is much more mountainous. Many of its smaller cities are bisected by rivers. These cities need bridges with medium spans. For the bridges in these cities, girder bridges that receive some of their support from cables can offer great advantages both economically and aesthetically.