First, the beam bridge
Beam bridge is a bridge with curved main girder as the main load-bearing component.
According to the static diagram of the main girder, the beam bridge can be divided into three types: simply supported beam bridge, continuous beam bridge and outrigger beam bridge.
The first two kinds of beam bridges are not uncommon from ancient times to today. At present, the main span of the world's largest steel truss bridge has reached 549 m, and people are not familiar with the cantilever beam bridge. There is a graphic introduction on the 92nd surface of the standard experimental textbook Physics I (Compulsory) published by Shandong Science and Technology Publishing House, which makes people clear at a glance, so I won't repeat it here (this textbook is one of the many new textbooks in the curriculum standard, hereinafter referred to as Shankeben).
Materials with different hardness have their own uses. Concrete is hard, but it lacks elasticity, so it is easy to break in tension, while steel bars are tensile, so steel bars are used to strengthen the tensile part of concrete precast bridge deck. Proper placement of steel bars can make the bridge stronger. As shown in figure 1, the correct position of bridge reinforcement is ().
When the object is pressed on the bridge, the upper surface of the bridge deck inside the pier is under pressure and the lower surface is under tension. The upper surface of the bridge deck outside the pier bears tension and the lower surface bears pressure. In order to make the steel bar under tension, the placement of the steel bar should be as shown in figure 1(a).
The key to comment is to know whether all parts of the bridge are in compression or tension.
A similar problem is also explained on page 68 of Shankben.
Second, the arch bridge
Arch bridge is a bridge with the arch (called main arch ring) bearing axial pressure as its main load-bearing component. Many arch bridges with exquisite structures were built by craftsmen in ancient China, such as Zhao Zhouqiao, which is a classic of early arch bridges. There is a graphic introduction on the 87th face of Shankeben, briefly describing the mechanics principle. At present, the largest steel arch bridge in the world is Shanghai Lupu Bridge, with a main span of 550 meters ... Other long-span arch bridges have been built, including Chongqing Wanzhou Yangtze River Bridge (a concrete arch bridge with a main span of 420 meters) and Hunan Phoenix Wuchaohe stone arch bridge with a main span of 120m. ..
The completion of the light rail "Pearl Line" eased the traffic congestion in Xujiahui area. Please draw the stress diagram of the arched beam at point A in Figure 2. The advantage of this arch bridge is that.
According to the principle of force decomposition, the stress direction of the arch beam at A should be tangential (as shown by the arrow in Figure 2). Its advantage is that the force on the beam is transmitted tangentially and finally to the pier, and a larger span space is formed at the same time.
This comment is one of the examination questions for Shanghai's spring enrollment in 2002. Technically, this kind of arch bridge with deck under arch rib belongs to through arch bridge. Because the two arch feet are connected by a longitudinal horizontal tie bar called tie bar at the arch foot (not shown in Figure 2, its function is to reduce the horizontal thrust of arch rib on pier), the through arch bridge is also called tie bar arch bridge.
Third, cable-stayed bridges.
The typical schematic diagram is shown in Figure 3, which consists of a main girder, a steel cable that obliquely tightens the main girder and a pylon that supports the steel cable. The Laasola of the cable-stayed bridge is in a straight line, which forms a stable triangular structure with the bridge tower and bridge deck (main beam); Compared with multi-pier continuous beam bridge, (a pair of) stay cables are (elastic) fulcrums instead of piers, so the performance of the main beam is similar to that of a continuous beam supported on elastic supports, and its stiffness is greater than that of a suspension bridge, while the span of the main beam is generally between the beam bridge and the suspension bridge.
At present, the largest cable-stayed bridge in the world has a main span of 890 m. In China, there are the Second Nanjing Yangtze River Bridge (with a main span of 628m), Shanghai Yangpu Bridge (with a main span of 602m) and Shanghai Xupu Bridge (with a main span of 590 m). Prestressed concrete cable-stayed bridges include Chongqing Second Yangtze River Bridge (main span 444m), Tongling Second Yangtze River Bridge (main span 432m), Yunyang Hanjiang Bridge (main span 4 14m) and Wuhan Yangtze River Bridge (main span 400m). Cable-stayed bridge is the most widely used bridge in recent years.
Example 3 As shown in Figure 4, when the uniform suspension bridge with gravity g is in a horizontal position, the bridge deck forms three parallel steel cables.
30. The distance between two points AB = BC = CD = DO. If each steel cable bears the same force, the force on each steel cable is ().
If the zero point is taken as the rotation axis (assuming the Zhang Liwei f of each cable), the moment balance relationship can be expressed as follows.
The solution is f = 2/3g, so choose option D.
Comments: Compared with Figure 3, Figure 4 is equivalent to a part of one side of pylon of cable-stayed bridge.
The actual cable-stayed bridge is very complicated. It's just that cables are distributed in various forms, such as single-sided or double-sided cables, dense cables or few cables, parallel or radial cables, etc. Therefore, the stress calculation of stay cables in the design should be processed by a large computer after synthesizing many factors, and the control and adjustment of cable force in the construction is also extremely accurate. This problem is only the most simplified model (this problem is a national middle school student mechanics competition).
Fourth, suspension bridge
It is a bridge with steel cables or chain cables (both called main cables) bearing tension as the main load-bearing components. It consists of main cable, bridge tower, anchorage, sling (or suspender), bridge deck and other parts. The basic schematic diagram is shown in Figure 5. The main cable mainly bears tensile force, and generally adopts steel with high tensile strength, which can make full use of the strength of the material and has the characteristics of material saving and light weight, so it has the largest spanning capacity in all kinds of bridges (the span can reach more than 1000 m). The main disadvantage of suspension bridge is its low stiffness.
1999 10, the first super-large suspension bridge with a span over 1000 meters in China was officially opened to traffic in Jiangyin. The main span of the bridge is 1385 m, the total length of the bridge is 307 1 m, the navigation height under the bridge is 50m, and the tower heights on both sides are 196 m. Two main cables across the north and south banks of the Yangtze River are wound on the saddle at the top of the bridge and fixed by the north and south anchors. The weight of the whole bridge deck and the main cable is 48,000 tons, which is hung on these two main cables. For the convenience of calculation, the overall structure can be simplified as shown in Figure 6, and the tension of each main cable is about ().
24,000 tons
C.65438+200,000 tons D.24 tons
It is analyzed that the bridge in Figure 6 bears the total gravity of the whole deck and the main cable and the tension of four sections of steel cables. The resultant force of these forces is zero, and the bridge is in a static equilibrium state. These forces can be equivalent to a plane point force system. Let its extension line intersect at point O, and its stress diagram is as shown in Figure 7. Let the total gravity be G(4.8× 108N) and the tension of each section of the four-section steel cable be f, then the similar triangles relation.
The solution is f = 5.8× 108n. So choose option B.
It is very complicated to comment on the actual calculation of suspension bridges. If this problem is simplified, students can estimate according to the knowledge of middle school physics.