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|15k B 15k とt 33 V M

|15k B 15k とt 33 V M

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Find the reactions. Fill in the blanks and draw the final free body diagram correctly.

### Structural Analysis of a Beam with Distributed and Point Loads #### Beam Diagram The image illustrates a beam subjected to various loads and supports. Below is a detailed explanation: 1. **Beam Specifications**: - The beam spans a total of 29 feet. - It is supported by a pin at point A and a roller at point B. 2. **Distributed Load**: - From point A to point 12 feet away, there is a uniform distributed load (UDL) of 5 kips per foot (k/ft). 3. **Point Loads**: - There is a point load of 15 kips downward located 8 feet from point A. - On the right side of the beam, a point load of 15 kips is acting upward at a distance of 6 feet from the right support. 4. **Sectional Divisions**: The beam is broken into sections for analysis: - 12 feet segment under the distributed load. - 8 feet segment with a point load in between the supports. - 3 segments of 3 feet each and a 6 feet segment on the overhanging portion. #### Find the Reactions - Solve for the reactions at supports A and B. #### Drawing and Labeling V (Shear) and M (Moment) Diagrams - **Shear Force Diagram (V)**: - Indicate how the shear force changes along the length of the beam, with jumps at points where point loads are applied. - **Bending Moment Diagram (M)**: - Show the bending moment variation along the beam, peaking at locations where moments are maximum. #### Equations and Calculation - **Reactions**: \[ Ay = \quad By = \quad \] - **Shear Force Equation**: \[ V(x) = \quad \text{for} \quad 0 \leq x \leq 12 \] - **Boundary Conditions**: \[ V(x=12) = \quad \] - **Maximum Moment**: \[ M_{max} = \quad \] These steps and equations help in determining the internal forces and moments in the beam, essential for designing and ensuring its structural integrity against applied loads.
Transcribed Image Text:### Structural Analysis of a Beam with Distributed and Point Loads #### Beam Diagram The image illustrates a beam subjected to various loads and supports. Below is a detailed explanation: 1. **Beam Specifications**: - The beam spans a total of 29 feet. - It is supported by a pin at point A and a roller at point B. 2. **Distributed Load**: - From point A to point 12 feet away, there is a uniform distributed load (UDL) of 5 kips per foot (k/ft). 3. **Point Loads**: - There is a point load of 15 kips downward located 8 feet from point A. - On the right side of the beam, a point load of 15 kips is acting upward at a distance of 6 feet from the right support. 4. **Sectional Divisions**: The beam is broken into sections for analysis: - 12 feet segment under the distributed load. - 8 feet segment with a point load in between the supports. - 3 segments of 3 feet each and a 6 feet segment on the overhanging portion. #### Find the Reactions - Solve for the reactions at supports A and B. #### Drawing and Labeling V (Shear) and M (Moment) Diagrams - **Shear Force Diagram (V)**: - Indicate how the shear force changes along the length of the beam, with jumps at points where point loads are applied. - **Bending Moment Diagram (M)**: - Show the bending moment variation along the beam, peaking at locations where moments are maximum. #### Equations and Calculation - **Reactions**: \[ Ay = \quad By = \quad \] - **Shear Force Equation**: \[ V(x) = \quad \text{for} \quad 0 \leq x \leq 12 \] - **Boundary Conditions**: \[ V(x=12) = \quad \] - **Maximum Moment**: \[ M_{max} = \quad \] These steps and equations help in determining the internal forces and moments in the beam, essential for designing and ensuring its structural integrity against applied loads.
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