Question

Determine the reactions on the bent rod which is supported by a smooth surface at b and by a collar at a, which is fixed to the rod and is free to slide over the fixed inclined rod?

Answer 1

The reactions on the bent rod can be determined by considering the forces acting at the points of support. At point
`\( b \)`, where the rod is supported by a smooth surface, there will be a vertical reaction force
`(\( V_b \))`. At point
`\( a \)`, where the rod is supported by a collar that is fixed to the rod and free to slide over the fixed inclined rod, there will be both a vertical reaction force
`(\( V_a \))` and a horizontal reaction force
`(\( H_a \)).`

Step-by-step explanation:

To analyze the forces acting on the bent rod, we need to consider the equilibrium of forces at points
`\( a \)` and
`\( b \).` At point \( b \), where the rod is supported by a smooth surface, the only force acting vertically is
`\( V_b \).` At point
`\( a \)`, the collar is free to slide over the inclined rod, so there are both vertical
`(\( V_a \))` and horizontal
`(\( H_a \))` reaction forces.

The vertical equilibrium at point
`\( b \)` gives us
`\( V_b \),` while the horizontal and vertical equilibrium at point
`\( a \)` provides
`\( H_a \)` and
`\( V_a \)` respectively. These reactions are essential for understanding the stability and structural behavior of the bent rod under external loads.

The calculations involve setting up equations based on the equilibrium conditions and solving for the unknown reactions. This process ensures that the forces acting on the bent rod maintain it in a state of static equilibrium, preventing any undesired movement or deformation. The determination of reactions is a fundamental step in structural analysis, enabling engineers to design structures that can safely support applied loads.