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P8.20. (a) Compute the vertical deflection and slope of the cantilever beam at points B and C in Figure P8.20. Given: El is constant throughout, and E = 4000 kips/in.². What is the minimum required value of I if the deflection of point C is not to exceed 0.4 in.?

P8.20. (a) Compute the vertical deflection and slope of the cantilever beam at points B and C in Figure P8.20. Given: El is constant throughout, and E = 4000 kips/in.². What is the minimum required value of I if the deflection of point C is not to exceed 0.4 in.?

Structural Analysis
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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**P8.20.** (a) Compute the vertical deflection and slope of the cantilever beam at points B and C in Figure P8.20. Given: \(EI\) is constant throughout, and \(E = 4000 \text{ kips/in}^2\). What is the minimum required value of \(I\) if the deflection of point C is not to exceed 0.4 in?
Transcribed Image Text:**P8.20.** (a) Compute the vertical deflection and slope of the cantilever beam at points B and C in Figure P8.20. Given: \(EI\) is constant throughout, and \(E = 4000 \text{ kips/in}^2\). What is the minimum required value of \(I\) if the deflection of point C is not to exceed 0.4 in?
The diagram illustrates a simply supported beam with three distinct sections marked as \( A \), \( B \), and \( C \). The beam is subjected to various loads: 1. **Distributed Load:** - A uniform distributed load of \( w = 1 \text{ kip/ft} \) extends from point \( A \) to point \( B \), covering a span of 6 feet. 2. **Point Load:** - At point \( C \), there is a concentrated point load of \( P = 6 \text{ kips} \). 3. **Moment:** - Also at point \( C \), there is an applied moment of \( 10 \text{ kip} \cdot \text{ft} \). - **Span Lengths:** - The total span of the beam is 12 feet, with each section \( AB \) and \( BC \) being 6 feet long. These loading scenarios are common in structural analysis and are crucial for understanding how different loads affect beams. The distributed load causes bending along the length of the beam, while the point load and moment at \( C \) create additional stress concentrations that must be accounted for in design.
Transcribed Image Text:The diagram illustrates a simply supported beam with three distinct sections marked as \( A \), \( B \), and \( C \). The beam is subjected to various loads: 1. **Distributed Load:** - A uniform distributed load of \( w = 1 \text{ kip/ft} \) extends from point \( A \) to point \( B \), covering a span of 6 feet. 2. **Point Load:** - At point \( C \), there is a concentrated point load of \( P = 6 \text{ kips} \). 3. **Moment:** - Also at point \( C \), there is an applied moment of \( 10 \text{ kip} \cdot \text{ft} \). - **Span Lengths:** - The total span of the beam is 12 feet, with each section \( AB \) and \( BC \) being 6 feet long. These loading scenarios are common in structural analysis and are crucial for understanding how different loads affect beams. The distributed load causes bending along the length of the beam, while the point load and moment at \( C \) create additional stress concentrations that must be accounted for in design.
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