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# 物理代考|理论力学代考THEORETICAL MECHANICS代考|PHY4310 Hinged or pinned support

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## 物理代考|理论力学代考THEORETICAL MECHANICS代考|Hinged or pinned support

If a rod is fixed by the ground, and it can also slightly rotate at this point, this kind of constraint is called hinged or pinned support, as shown in Fig. 3.8. In fact, there are two holes on the ground and the bar, respectively, which are matched by a cylindrical pin. However, in the process of analysis, the pin can be thought to be fixed on the ground or on the bar, and we only consider the match of the two objects, i.e., the ground (or the other bar) and the selected bar. As the bar can rotate with respect to the hinged point $O$, it will endure the reactive force from the ground. It is clear that this is a problem of contact surface, where the reactive force is normal to the tangential line of the contact surface. However, the bar can rotate at any angle at the hinged point, and the direction of the reactive force can’t be a determined one. Therefore, we decompose the reactive force in two directions, i.e., $\boldsymbol{X}{O}$ and $\boldsymbol{Y}{O}$, respectively.
The similar case can happen when two bars are hinged together by a cylindrical pin, as schematized in Fig. 3.9. Each bar can rotate with respect to the hinged point, and therefore the direction of the reactive for each bar is not a determined one, then it can be expressed by the two components along the $x$ – and $y$-coordinate axes, respectively.

## 物理代考|理论力学代考THEORETICAL MECHANICS代考|Roller support

Another special constraint is the roller support, which is shown at point $B$ in Fig. 3.10. The constraint is similar to a small car, which can roll in the horizontal direction, but it can’t move in the vertical direction. As a result, the constraint can only provide one component reactive force $Y_{O}$, which is shown in Fig. 3.10. This structure can be also expressed in two other formats, which are shown in Fig. 3.11. The roller support is especially important in engineering. For example, if we design a bridge, which can be modeled as a beam with two hinged ends, then one end should be designed as a roller support. If both ends are fixed as hinged constraints, then the temperature can induce elongation or compression, and the bridge can’t match this deformation. The roller support can make the bridge slightly move in the horizontal direction, and can overcome the influence of temperature.

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