### Vertical Curve Calculation**Given:**- Velocity (\( V \)) = 50 mph- Length of the sag curve (\( L \)) = 510 ft**Find:**- \( H_1 \) for \( V \) = 55 mph**Solution:**1. **From Table 3.2**: - Design speed (\( K_{design} \)) for 50 mph = 962. **Calculate \( L \)**: \[ L = K \times A \quad \text{where} \quad A = \frac{L}{K} \] Using given values: \[ A = \frac{L}{K} = \frac{510}{96} = 5.3 \]3. **Assume \( S \leq L \)**4. **From Table 3.1**: - Stopping sight distance (\( S \)) for 55 mph = 495 ft Since \( 495 \, ft \leq 510 \, ft \), the assumption is valid.5. **Calculate \( L \)**: \[ L = \frac{AS^2}{800\left(\frac{H_c + \frac{H_2}{2}}{2}\right)} \] Substituting the values: \[ H_c = 16.5, \quad H_2 = 2 \quad \text{(as per design standard)} \] Therefore: \[ \frac{495^2}{800 \left(\frac{16.5 + 2}{2}\right)} = 510 = 5.3 \times \frac{495^2}{800(16.5 - \frac{H_1 + 2}{2})} \]6. **Solving for \( H_1 \)**: \[ H_1 = 24.6 \, ft \]In this solution, the calculations involve determining the required sight distance and solving for the height \( H_1 \) given the design parameters from standard tables. This method ensures the safety and efficiency of the design for the given speed and curve. **Design Parameters and Calculation for Sag Curves**---### Problem Statement 1A 490 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If all the other design inputs are standard, what must the driver’s eye height be (in the van) for the student’s claim to be valid?### Example ProblemA 510 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If all the other design inputs are standard, what must the driver’s eye height be (in the van) for the student’s claim to be valid?---### Explanation of Diagrams and GraphsWhile there are no specific diagrams or graphs shown in the provided text, here is how one might explain pertinent concepts typically related to sag curves:**Sag Curve Diagram**: A sag curve is typically depicted in road design charts as a smooth, concave curve connecting two sloped sections of road. Parameters such as curve length, vehicle speed, headlight height, and driver eye height are annotated.1. **Curve Length (L)**: This is typically the total distance over which the curve extends, measured in feet (ft). 2. **Design Speed (V)**: The speed at which the curve is designed, which impacts the minimum radius of curvature and other safety parameters. 3. **Headlight Height (h1)** and **Driver Eye Height (h2)**: These heights affect how far ahead a driver can see. For a van, the assumption is that h1 > h2 compared to a regular car. 4. **Sight Distance (S)**: The distance over which a driver should be able to see an object on the road surface ahead of them.### Formula for Eye Height CalculationThe student's claim hinges on matching eye height (h2) with higher travel speed while maintaining adequate stopping sight distance. The curve's stopping sight distance (SSD), using standard parameters and the new travel speed, must be equated to ensure safety. Relevant equations typically employed include:\[ SSD = \frac{V^2}{2g(f + G)} \]where \(V\) is speed, \(g\

Given;V = 50 mphL = 490 ft. equal-tangent sag cureFind;H1 FOR V = 55 mph

A 490 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If the all other design inputs are standard, what must the driver's eye height be (in the van) for the student's claim to be valid?

A 490 ft equal-tangent sag curve is currently designed for 50 mph. A CE 321 student thinks that traveling at 55 mph on the curve is safe for a van since the van will have a higher headlight height. If the all other design inputs are standard, what must the driver's eye height be (in the van) for the student's claim to be valid?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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