I'll show you a picture that anyone who's learned structural mechanics can see right away.
It's a free-body diagram.
From the figure above, you can see the element and the boundary condition.
It can also be seen that the time point is horizontally and vertically constrained, and the end point is vertically constrained.
I can express it like this.
Bearing is used to satisfy the boundary conditions in the actual bridge structure.
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Classify |
Elastic Pad |
Pin Type |
Roller Type |
Elastic Bearing |
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Concept |
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Configuration |
Elastic Pad |
Steel |
Stell |
Elastic Pad + Steel |
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Boundary Condition |
vertical, rotational restraint |
vertical, horizontal restraint |
vertical restraint |
vertical restraint |
Assume the boundary condition to be rigid body, but what is it really like?
In practice, the material may deform and not satisfy the assumption of the boundary condition.
The pins and roller supports must be designed to allow circular members to rotate or roll.
All objects are deformed when subjected to a force. Depending on the magnitude of the force, it is accompanied by a deformation of a visible or invisible magnitude.
Then, in the case of a circular member, as the force increases, deformation will occur, and when deformation occurs, will it be impossible to rotate or move as originally assumed?
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Elastic displacement |
Comparison before and after deformation |
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Designing these moving members should find answers in the mechanical field rather than civil engineering.
Let me introduce you to someone you know very well. Heinrich Hertz, a German physicist who is excellent in mechanical, electrical, and electronic fields, is Hertz, who uses how famous he is in terms of frequency.
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Heinrich Hertz |
Contac of a circle |
contact of a cylinder |
The theory is summarized as follows.
The contact surface where the circle meets the circle is a point, the contact surface where the cylinder meets the cylinder is a line, the point is 0 dimensional, and the line is 1 dimensional.
At this time, since the stress is force/area, the force/point (line) is equal to 1/0, so infinite stress acts and yield occurs with any material. As the elastic deformation progresses, the area gradually increases and reaches a certain level, and the contact surface is determined. The stress at this time is called Hertz's contact stress.
Here, is the roller the same as the cylinder and the surface contact? It is the same because the shape of the contact surface is the same line.
The contact stress equation is as follows.
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Assume the stress distribution of the contact surface as an ellipse,
half width of the contact surface
Maximum stress on the contact surface |
Let's design by assuming a support using the equation obtained above.
Reaction force of the point: 200 kN
Material : SS490Y
Permissible stress: 215 MPa
Elastic modulus (E): 200 GPa
Poisson's ratio (ν): 0.30
Roller radius (R): 300 mm
Roller length (L): 1,000 mm
Half width of contact surface (b): 0.637 mm
Maximum stress (pmax): 200 MPa < 215 MPa O.K
Unfortunately, the capacity of the support is not large from the above results. You need to increase the number of rollers or increase the diameter of the rollers to accommodate the large weight. Additional guide structures are needed for the rollers to reciprocate. Maintenance is also not easy. Modern bridge structures do not use roller bearings for reasons of poor economic feasibility and usability.
Therefore, it can be applied to the design of pin members, special bearings, and linkshues and structures attached to bridges with large displacements (such as pedestrian and bicycle road ramps).
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