Which of the following parameters are required for the design of a transition curve for a highway system?
(A) Rate of change of grade
(B) Rate of change of radial acceleration
(C) Rate of change of super elevation
(D) Rate of change of curvature
Choose the most appropriate answer from the options given below:
Step 1: Transition curve design criteria.
Transition curves are introduced in highways to provide gradual change in curvature and superelevation. The key parameters are:
- Rate of change of radial acceleration.
- Rate of change of superelevation.
- Rate of change of curvature.
Step 2: Eliminate unnecessary parameter.
Rate of change of grade (longitudinal slope) is not a governing factor in transition curve design.
Step 3: Conclusion.
Hence, the required parameters are (B), (C), and (D). Therefore, the correct answer is (D).
Match LIST-I with LIST-II (adopting standard notations):\[\begin{array}{|c|c|} \hline \textbf{LIST-I (Parameter)} & \textbf{LIST-II (Formula)} \\ \hline \\ \text{A. Cubic parabola equation} & \text{IV. $\dfrac{X^3}{6RL}$} \\ \\ \hline \\ \text{B. Shift in transition curve} & \text{II. $\dfrac{L^2}{24R}$} \\ \\ \hline \\ \text{C. Length of valley curve} & \text{III. $\dfrac{N S^2}{(1.50 + 0.035S)}$} \\ \\ \hline \\ \text{D. Length of summit curve} & \text{I. $\dfrac{N S^2}{4.4}$} \\ \\ \hline \end{array}\] Choose the most appropriate match from the options given below:
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: