Replace the loading by an equivalent resultant force and couple moment acting at point O. Part A : Determine the equivalent resultant force (express your answer in terms of the variables w0, L, and constant pi.) Part B : Determine the couple moment (express your answer in terms of the variables w0, L, and constant pi.
Replace the loading by an equivalent resultant force and couple moment acting at point O. Part A : Determine the equivalent resultant force (express your answer in terms of the variables w0, L, and constant pi.) Part B : Determine the couple moment (express your answer in terms of the variables w0, L, and constant pi.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Replace the loading by an equivalent resultant force and couple moment acting at point O.
Part A : Determine the equivalent resultant force (express your answer in terms of the variables w0, L, and constant pi.)
Part B : Determine the couple moment (express your answer in terms of the variables w0, L, and constant pi.)
Transcribed Image Text:### Diagram Explanation for Educational Use
#### Description:
The diagram depicts a beam subjected to a variable distributed load. The beam is positioned horizontally, with one end at point \( O \) and the other extending to a length \( L \).
#### Details:
- **Beam**: The horizontal structure is shown as a thick line extending from \( O \) to \( L \).
- **Distributed Load**: Illustrated by vertical arrows pointing downward along the top of the beam. The load varies along the length of the beam.
- **Load Equation**: The load intensity \( w \) is defined by the equation \( w = w_0 \cos\left(\frac{\pi}{2L} x\right) \). This indicates that the load is a cosine function of the position \( x \), starting from maximum intensity \( w_0 \) at \( x = 0 \) and varying sinusoidally along the beam.
- **Axes**:
- The vertical line represents the load intensity, marked as \( w \).
- The horizontal axis runs along the beam and is labeled with \( x \), representing the position along the beam.
- **Origin**: Marked as \( O \), this is the starting point of the beam where \( x = 0 \).
This diagram is typically used in structural engineering to analyze the effects of variable loads on beam deflection and stress.
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