There are many kinds of beam bridges, which are also the most commonly used bridge types in highway bridges, and the crossing capacity can range from 20m to 300m.
Commonly used bridge forms of highway bridges are:
According to the structural system, it is divided into simply supported beam, cantilever beam, continuous beam, T-shaped rigid frame and continuous rigid frame.
According to the type of section, it can be divided into: T-beam, box beam (or trough beam) and outrigger beam.
The span size of beam bridge is an important index of technical level, which reflects a country's achievements in industry, transportation, bridge design and construction to some extent.
I. Calculation of Internal Force of Beam Bridge
(A) accuracy and safety analysis
Bridges with considerable width are simplified as a single thin beam to calculate the total internal force. When concentrated force acts on a wide bridge, the bridge deck will bend in two directions, and the work of concentrated force will be dissipated in two directions as deformation energy. For a single infinite thin beam, the work of the same concentrated force only becomes deformation energy in one direction, so the calculated deformation is slightly larger, and the internal force is calculated by deformation, so the internal force is also slightly larger.
(2) The theory of transverse load distribution of beam bridge is only applicable to straight beam bridges with open sections.
For straight beam bridges with open cross-section, the transverse proportion of load distributed to each girder is basically the same as that of bending moment and shear force distributed to the girder, and the torque distributed to the girder can be ignored. For straight box girder bridges and curved box girder bridges with arbitrary cross-sections, the transverse proportion of bending moment and shear force distributed to each girder is completely different, and the torque distributed to the girder must also be considered.
(C) the theory of lateral distribution of internal forces
The box girder bridge with asymmetric section on curved surface is taken as the object (when the thickness of bottom plate is 0, it becomes an open section). The section is divided into several I-beams, and each I-beam is simulated by a thin beam with the same bending, shearing and torsion stiffness, and the plane position of the thin beam is consistent with the centroid position of the I-beam. Cantilever plate, top plate and bottom plate are simulated by fan-shaped unidirectional thick plate, and the lateral bending, shearing and torsion stiffness are the same. This model is called plane plate beam mechanical model. The deflection and torsion angle of each girder can be calculated by applying equal half-wave sine load on each nodal line in turn, and then the bending moment and shear force of each girder can be calculated. Divide the bending moment of each beam by the total bending moment, and get the transverse distribution influence line of bending moment. The shear force is similar. If the total internal torque on the cross section is equal to 1, then each I-beam is distributed to the left and right annular shear flow. For the open section, the smaller torque distributed to each I-beam, such as left and right annular shear flow or smaller torque, can be used as the lateral distribution coefficient of torque. The plane bending internal force caused by temperature change can be decomposed into the axial force of each I-beam. In this way, the internal forces generated by various design loads are all decomposed into bending moment, shear force, left and right circumferential shear flow or torque and axial force of each main beam. The uneven lateral distribution of bending moment reflects the influence of double bending moment to a certain extent, and the left and right annular shear flows reflect the influence of cross-section warping shear to a certain extent. It can be said that the theory of transverse distribution of internal forces not only comprehensively reflects the main mechanical phenomena of box beams and curved beams, but also greatly simplifies their design and calculation. It is a unified algorithm for open, closed section, straight line and curved beam bridges under various design loads, and it is an important development of load lateral distribution theory.
(D) Bearing design of curved beam bridge
Because bridges generally have a large bending stiffness in the horizontal plane, if the bending deformation caused by temperature change is restrained, it will often produce a large horizontal force, which will lead to structural damage in severe cases. The wider the bridge, the smaller the horizontal bending radius, the more obvious this phenomenon is. Generally, only one bearing on the pier of curved beam bridge can be used as a braking bearing; In the horizontal bending radius direction, if the beam is allowed to move slightly, such as using plate rubber bearings or the pier body is thin and elastic, the temperature force along the horizontal bending radius direction can be greatly reduced.
(5) Pre-eccentricity of point-hinged single-column pier improves the bearing capacity of abutment and the internal force of beam.
The preset eccentricity has little effect on the torque envelope diagram of abutment (usually torsion bearing) and torsion or fixed pier.
The torque envelope diagram is an important reference for judging the torsional performance of curved beam bridges. In recent years, the software (including imported software) of curved beam bridges that have accidents has no output torque envelope diagram, so the design is blind. The torque envelope should be calculated correctly. Two points have been ignored by some softwares: 1, the shear center of various shapes of sections must be calculated correctly, and 2, the eccentricity of dead load to the shear center must be calculated correctly (even for sections with left and right symmetry, the dead load is eccentric to the shear center).
Second, the reinforced concrete curved beam reinforcement calculation
There are some shortcomings in the provisions of "Torsional Members" in Highway Bridge Code: 1, and there is no definition and classification of pure shear, pure torsion and shear-torsion members; 2. There is no mention of the strength reduction of shear-torsion members; 3. It seems unscientific that the suitable reinforcement range of shear-torsion members simply follows the reinforcement range of pure shear members; 4. The torsion member refers to a rectangular section, which is not convenient for bridge application. China's Code for Design of Concrete Structures is a summary of more than ten years' experimental research by many scientific research institutions in China, which has a high level. Its stipulation on "torsion member" has many advantages: 1, which classifies members into pure torsion members when the torque they receive is less than a certain value, pure torsion members when the shear force they receive is less than a certain value, and shear torsion members when the combined action of shear force and torque is greater than a certain value, which is very scientific; 2. Each component is divided into four categories according to its stress; 3. The strength reduction factor of shear-torsion members is specified in detail; 4. The torsion member is an I-shaped section, and the concept of torsional plastic resistance moment is introduced to redistribute the torque of the I-shaped section, which is convenient for bridge application.
The formulas in the design codes of concrete structures in various countries are summarized from a large number of tests. Concrete is a heterogeneous brittle material, and the experimental results of small components and large components will be very different. It is difficult to grasp the error when applying the standard formula obtained from small components to large components such as bridges. The theory of lateral distribution of internal forces put forward by the author has a strict mechanical basis and strict verification in every step. When the internal force is decomposed into each I-shaped section, it will be decomposed into each small rectangular section, and then the standard formula will be applied, which is very reassuring.
3. Prestress calculation of curved beam bridge
(1) Difference in prestress calculation between curved beam bridge and straight beam bridge
1, calculation of friction loss of curved beam bridge
Spatial rotation angle = the sum of the square of the vertical offset angle increment and the square of the horizontal offset angle increment of each micro-section of the cable relative to the previous section;
Friction coefficient: take the recommended value of highway bridge code;
Local deviation coefficient: slightly larger than the recommended value of highway and bridge regulations; If the plane bending radius of steel strand and corrugated pipe is about 70M, the local deviation coefficient can be taken as 0.0035 (the recommended value in highway bridge code is 0.003).
2. In general, the prestress of each main girder of continuous curved beam bridge is not equal to the pretension of steel cables.
If the curved beam deforms freely in the plane, it will not only shorten the axial direction, but also bend under the action of prestress, and the plane bending radius will become smaller. However, the constraint of pier and abutment generally does not allow the radius to become smaller, so the outer main beam of the curved beam is subjected to extra pressure and the inner main beam is subjected to extra tension, so that the pre-stress of each main beam is generally not equal to the pre-tension of its inner steel cable. This phenomenon requires that the plane bending deformation of curved beam bridge under prestress must be calculated, and the prestress of each main beam and each section must be calculated. This phenomenon brings convenience to the prestress of curved beams: although the bending moment of the outer main beam is greater than that of the inner main beam, in many cases, the cables of the inner and outer main beams can be designed as much as the same, and even the vertical coordinates of the cables of the inner and outer main beams are designed exactly the same.
3. The linear transformation theorem is not applicable to curved beam bridges.
As long as the longitudinal coordinates of prestressed cables in curved beam bridges change, the prestress effect must be recalculated.
(2) Reasonable calculation method of stress loss of concrete in creep, shrinkage and batch tension.
Except for the programs purely used for scientific research, all domestic and foreign prestressed structural analysis programs convert cables into equivalent force before calculating structural deformation. Before converting into equivalent effect, all prestress losses must be deducted. Some losses are related to structural deformation and time, and only when the deformation with time is known can these losses be deducted correctly. Therefore, the reasonable algorithm for calculating the creep shrinkage and tensile stress loss of concrete in batches is to adopt the cyclic iterative algorithm, that is, the cable is approximately converted into equivalent force to calculate the structural deformation, then the cable is converted into equivalent force again, and then the structural deformation is calculated. After repeating the cycle (generally three times), accurate results can be obtained. Other algorithms must be approximate.
At least before 1989, the design method of prestressed curved beam bridge abroad is to regard the whole bridge as a beam and divide the cables into bending and torsion types according to their functions. In order to make the upper and lower edge stresses meet the requirements, the arrangement of curved cables is the same as that of straight beam bridges. Torsion cable is a cable with opposite bending directions arranged on the top and bottom plates (or left and right webs), which is specially used to balance the torque generated by dead load and bending cable. In fact, twisting the cable is redundant. Using pressure line and pressure line forbidden zone method, as long as the bending stress of each beam meets the requirements, the torque can also meet the requirements. Of course, the influence of torque should be calculated in detail.
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