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The beam shown supports a load that varies uniformly from 100 N/m at the left end to 200 N/m at the right end. The lengths of the beam segments are d1 = 12 m, d2 = 8 m, and d3 = 4 m. D B

The beam shown supports a load that varies uniformly from 100 N/m at the left end to 200 N/m at the right end. The lengths of the beam segments are d1 = 12 m, d2 = 8 m, and d3 = 4 m. D B

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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3. Draw a schematic of the standard convention for the meaning of positive shears and bending moments (see Section 8.2). Use your diagram to help you answer 4 and 5

4. Determine the internal shear at a section passing through point D.

5. Determine the internal bending moment at a section passing through point D.

**Description of the Beam System with Varying Load** In this example, we examine a beam subjected to a uniformly varying load. The load intensity increases linearly from 100 N/m at the left end to 200 N/m at the right end. The beam is divided into three segments for analysis, with the following lengths: - \( d1 \) (segment \( AB \)) = 12 meters - \( d2 \) (segment \( DB \)) = 8 meters - \( d3 \) (segment \( D \)) = 4 meters **Diagram Description** The diagram illustrates a simply supported beam with supports at points \( A \) (left end) and \( B \) (right end). Between these supports, the beam is divided as specified. Above the beam, red arrows indicate the direction and variation of the load. The load distribution is shown by a series of arrows with increasing lengths from left to right, representing the increasing load intensity from 100 N/m to 200 N/m. - Point \( A \): Represents the beginning of the beam with initial load intensity of 100 N/m. - Point \( D \): Intermediate point on the beam. - Point \( B \): Represents the end of the beam with a final load intensity of 200 N/m. The load distribution pattern is a trapezoidal load (linear variation), where the load starts at 100 N/m at \( A \) and increases to 200 N/m at \( B \). **Key Points to Note:** - The support at point \( A \) is commonly assumed to be a pin support, which can resist vertical and horizontal forces but allows rotation. - The support at point \( B \) is typically a roller support, which can resist vertical forces but allows horizontal movements and rotation. This type of load distribution is essential in structural analysis and design, as it helps in understanding how varying loads affect beam reactions, shear forces, and bending moments along the length of the beam.
Transcribed Image Text:**Description of the Beam System with Varying Load** In this example, we examine a beam subjected to a uniformly varying load. The load intensity increases linearly from 100 N/m at the left end to 200 N/m at the right end. The beam is divided into three segments for analysis, with the following lengths: - \( d1 \) (segment \( AB \)) = 12 meters - \( d2 \) (segment \( DB \)) = 8 meters - \( d3 \) (segment \( D \)) = 4 meters **Diagram Description** The diagram illustrates a simply supported beam with supports at points \( A \) (left end) and \( B \) (right end). Between these supports, the beam is divided as specified. Above the beam, red arrows indicate the direction and variation of the load. The load distribution is shown by a series of arrows with increasing lengths from left to right, representing the increasing load intensity from 100 N/m to 200 N/m. - Point \( A \): Represents the beginning of the beam with initial load intensity of 100 N/m. - Point \( D \): Intermediate point on the beam. - Point \( B \): Represents the end of the beam with a final load intensity of 200 N/m. The load distribution pattern is a trapezoidal load (linear variation), where the load starts at 100 N/m at \( A \) and increases to 200 N/m at \( B \). **Key Points to Note:** - The support at point \( A \) is commonly assumed to be a pin support, which can resist vertical and horizontal forces but allows rotation. - The support at point \( B \) is typically a roller support, which can resist vertical forces but allows horizontal movements and rotation. This type of load distribution is essential in structural analysis and design, as it helps in understanding how varying loads affect beam reactions, shear forces, and bending moments along the length of the beam.
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