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15.4 Determine the force in each member of the truss, state if the members are in tension of compression. 600 N 400 N E D \45° 45% \45° 45% A B 2 m Fn =-778 N, F =-500 N, FR = 70.7 N, F = 450 N 2 m DE EB BA

15.4 Determine the force in each member of the truss, state if the members are in tension of compression. 600 N 400 N E D \45° 45% \45° 45% A B 2 m Fn =-778 N, F =-500 N, FR = 70.7 N, F = 450 N 2 m DE EB BA

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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**Section 15.4: Analysis of Forces in a Truss Structure** In this section, we examine the forces acting on each member of a truss and determine whether each member experiences tension or compression. The diagram provided illustrates a truss with external forces and dimensions. **Truss Description:** - The truss is supported at points A and C. - An external force of 400 N is applied downward at point E. - An external force of 600 N is applied downward at point D. - The truss spans a total length of 4 meters, with sections AE, EB, and BD, DC each measuring 2 meters. - Angles at A, B, and C are 45 degrees, indicating symmetry in the structure. **Forces in Truss Members:** 1. **\( F_{CD} = -778 \, \text{N} \)**: This member is in compression. 2. **\( F_{DE} = -500 \, \text{N} \)**: This member is in compression. 3. **\( F_{EB} = 70.7 \, \text{N} \)**: This member is in tension. 4. **\( F_{BA} = 450 \, \text{N} \)**: This member is in tension. **Understanding Force States:** - **Compression**: Negative force values indicate that the member is being compressed, with forces pushing inward towards each other. - **Tension**: Positive force values indicate that the member is being stretched, with forces pulling outward away from each other. **Conclusion:** By analyzing the forces in each member of the truss, engineers can ensure that the structure is safe and efficient. This analysis helps in understanding how the forces are distributed and allows for the design of trusses that can withstand specified loads without failure.
Transcribed Image Text:**Section 15.4: Analysis of Forces in a Truss Structure** In this section, we examine the forces acting on each member of a truss and determine whether each member experiences tension or compression. The diagram provided illustrates a truss with external forces and dimensions. **Truss Description:** - The truss is supported at points A and C. - An external force of 400 N is applied downward at point E. - An external force of 600 N is applied downward at point D. - The truss spans a total length of 4 meters, with sections AE, EB, and BD, DC each measuring 2 meters. - Angles at A, B, and C are 45 degrees, indicating symmetry in the structure. **Forces in Truss Members:** 1. **\( F_{CD} = -778 \, \text{N} \)**: This member is in compression. 2. **\( F_{DE} = -500 \, \text{N} \)**: This member is in compression. 3. **\( F_{EB} = 70.7 \, \text{N} \)**: This member is in tension. 4. **\( F_{BA} = 450 \, \text{N} \)**: This member is in tension. **Understanding Force States:** - **Compression**: Negative force values indicate that the member is being compressed, with forces pushing inward towards each other. - **Tension**: Positive force values indicate that the member is being stretched, with forces pulling outward away from each other. **Conclusion:** By analyzing the forces in each member of the truss, engineers can ensure that the structure is safe and efficient. This analysis helps in understanding how the forces are distributed and allows for the design of trusses that can withstand specified loads without failure.
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