w(x) = [2.5x – 0.1x²] kN/m A B 20 m
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![The function \( w(x) = [2.5x - 0.1x^2] \, \text{kN/m} \) describes the distributed loading that acts on the 20 m long green beam AB.
### Function:
\[ w(x) = [2.5x - 0.1x^2] \, \text{kN/m} \]
### Diagram Explanation:
- The diagram shows a green horizontal beam labeled AB, which is 20 meters long.
- A distributed loading is acting downward on the beam. The load intensity starts at zero, increases to a maximum, and then decreases back to zero. This is visualized by uniformly spaced arrows varying in length, forming a parabolic shape above the beam.
- The horizontal axis represents the position \( x \), starting from point A on the left extending to point B on the right.
- The entire span from A to B is 20 meters long.
### Problem Statement:
Determine the magnitude in kilonewtons of the equivalent concentrated force and the location \( \bar{x} \), measured in meters from A, where it acts.
- \( P = \underline{\hspace{3cm}} \, \text{kN} \)
- \( \bar{x} = \underline{\hspace{3cm}} \, \text{m} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf4a0e0b-2125-467b-b1bc-8bc81e995df8%2F84018a5c-ac16-4156-b27b-7a0b8712da99%2Ftr2c8op_processed.png&w=3840&q=75)
Transcribed Image Text:The function \( w(x) = [2.5x - 0.1x^2] \, \text{kN/m} \) describes the distributed loading that acts on the 20 m long green beam AB.
### Function:
\[ w(x) = [2.5x - 0.1x^2] \, \text{kN/m} \]
### Diagram Explanation:
- The diagram shows a green horizontal beam labeled AB, which is 20 meters long.
- A distributed loading is acting downward on the beam. The load intensity starts at zero, increases to a maximum, and then decreases back to zero. This is visualized by uniformly spaced arrows varying in length, forming a parabolic shape above the beam.
- The horizontal axis represents the position \( x \), starting from point A on the left extending to point B on the right.
- The entire span from A to B is 20 meters long.
### Problem Statement:
Determine the magnitude in kilonewtons of the equivalent concentrated force and the location \( \bar{x} \), measured in meters from A, where it acts.
- \( P = \underline{\hspace{3cm}} \, \text{kN} \)
- \( \bar{x} = \underline{\hspace{3cm}} \, \text{m} \)
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