Method of sections Method of Sections It is
![Method of sections Method of sections](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-1.jpg)
![Method of Sections • It is based on the principle that if the truss Method of Sections • It is based on the principle that if the truss](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-2.jpg)
![An Important Note If a body is in equilibrium under the action of external An Important Note If a body is in equilibrium under the action of external](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-3.jpg)
![Problem -1 Compute the forces in the members DC, DB and AB of the Problem -1 Compute the forces in the members DC, DB and AB of the](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-4.jpg)
![Support Reactions 3/6/2021 5 Support Reactions 3/6/2021 5](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-5.jpg)
![Calculation of the member forces For convenience, assume tension in all the cut members. Calculation of the member forces For convenience, assume tension in all the cut members.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-6.jpg)
![Calculation of the member forces 3/6/2021 7 Calculation of the member forces 3/6/2021 7](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-7.jpg)
![Member forces 3/6/2021 Member Forces (k. N) Method of Joint Forces (k. N) Method Member forces 3/6/2021 Member Forces (k. N) Method of Joint Forces (k. N) Method](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-8.jpg)
![Example 6: Method of Sections 6 -9 Example 6: Method of Sections 6 -9](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-9.jpg)
![Example 6 (continued): 6 - 10 Example 6 (continued): 6 - 10](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-10.jpg)
![Example 7: Method of Sections 6 - 11 Example 7: Method of Sections 6 - 11](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-11.jpg)
![Example 7 (continued): 6 - 12 Example 7 (continued): 6 - 12](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-12.jpg)
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![Problem For the loaded truss shown in the Figure : 1. Calculate the support Problem For the loaded truss shown in the Figure : 1. Calculate the support](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-19.jpg)
![Solution of Part 1 (Support Reactions at A and F) 40 k. N 2 Solution of Part 1 (Support Reactions at A and F) 40 k. N 2](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-20.jpg)
![Solution of Part 2 (Zero Force Members) 40 k. N 2 m 2 m Solution of Part 2 (Zero Force Members) 40 k. N 2 m 2 m](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-21.jpg)
![Solution of Part 3 (Forces in the members using Method of Joints) 40 k. Solution of Part 3 (Forces in the members using Method of Joints) 40 k.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-22.jpg)
![Solution of Part 4 (Forces in the members using Method of Sections) 40 k. Solution of Part 4 (Forces in the members using Method of Sections) 40 k.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-23.jpg)
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- Slides: 25
![Method of sections Method of sections](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-1.jpg)
Method of sections
![Method of Sections It is based on the principle that if the truss Method of Sections • It is based on the principle that if the truss](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-2.jpg)
Method of Sections • It is based on the principle that if the truss is in equilibrium then any segment of the truss is also in equilibrium. • In this method, a section is passed through the truss to cut it into two parts so that internal forces are exposed at the cut members. • Equations of equilibrium are then applied to the free body diagram of either of the two parts to determine the desired forces. • In choosing a section of the truss, in general, not more than three members whose forces are unknown may be cut, since there are only three available equilibrium equations which are independent. • The method of sections has the basic advantage that the force in almost any desired member may be found directly. March 6, 2021 2
![An Important Note If a body is in equilibrium under the action of external An Important Note If a body is in equilibrium under the action of external](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-3.jpg)
An Important Note If a body is in equilibrium under the action of external forces (including support reactions) then its each and every part is also in equilibrium under the action of external and internal forces. 3/6/2021 3
![Problem 1 Compute the forces in the members DC DB and AB of the Problem -1 Compute the forces in the members DC, DB and AB of the](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-4.jpg)
Problem -1 Compute the forces in the members DC, DB and AB of the truss, shown here, using method of sections. 3/6/2021 4
![Support Reactions 362021 5 Support Reactions 3/6/2021 5](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-5.jpg)
Support Reactions 3/6/2021 5
![Calculation of the member forces For convenience assume tension in all the cut members Calculation of the member forces For convenience, assume tension in all the cut members.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-6.jpg)
Calculation of the member forces For convenience, assume tension in all the cut members. 3/6/2021 6
![Calculation of the member forces 362021 7 Calculation of the member forces 3/6/2021 7](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-7.jpg)
Calculation of the member forces 3/6/2021 7
![Member forces 362021 Member Forces k N Method of Joint Forces k N Method Member forces 3/6/2021 Member Forces (k. N) Method of Joint Forces (k. N) Method](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-8.jpg)
Member forces 3/6/2021 Member Forces (k. N) Method of Joint Forces (k. N) Method of section Nature AB 2. 0 Tension DC 2. 0 Tension DB -2. 5 Compression 8
![Example 6 Method of Sections 6 9 Example 6: Method of Sections 6 -9](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-9.jpg)
Example 6: Method of Sections 6 -9
![Example 6 continued 6 10 Example 6 (continued): 6 - 10](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-10.jpg)
Example 6 (continued): 6 - 10
![Example 7 Method of Sections 6 11 Example 7: Method of Sections 6 - 11](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-11.jpg)
Example 7: Method of Sections 6 - 11
![Example 7 continued 6 12 Example 7 (continued): 6 - 12](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-12.jpg)
Example 7 (continued): 6 - 12
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![Problem For the loaded truss shown in the Figure 1 Calculate the support Problem For the loaded truss shown in the Figure : 1. Calculate the support](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-19.jpg)
Problem For the loaded truss shown in the Figure : 1. Calculate the support reactions at A and F. 50 k. N 40 k. N 2 m 2 m 2. Identify the zero force members. 2 m D E 3. Determine the force in the member FE and FG using Method of Joints. 4. Calculate the force in the members ED, EH and GH using Method of Sections. Assume the supports at A and F as pin and roller respectively. March 6, 2021 F G H I C B 1. 5 m 30 k. N 1. 5 m 40 k. N 1. 5 m A 19
![Solution of Part 1 Support Reactions at A and F 40 k N 2 Solution of Part 1 (Support Reactions at A and F) 40 k. N 2](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-20.jpg)
Solution of Part 1 (Support Reactions at A and F) 40 k. N 2 m 2 m 50 k. N 2 m D E F G C H Ax 30 k. N 1. 5 m B I Fy 1. 5 m A 40 k. N 1. 5 m Ay 3/6/2021 20
![Solution of Part 2 Zero Force Members 40 k N 2 m 2 m Solution of Part 2 (Zero Force Members) 40 k. N 2 m 2 m](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-21.jpg)
Solution of Part 2 (Zero Force Members) 40 k. N 2 m 2 m Only member GE is a zero force member as members FG and GH are collinear and there is no external force acting at joint G. 50 k. N 2 m D E G F C H Ax 30 k. N 1. 5 m B I Fy 1. 5 m A 40 k. N 1. 5 m Ay 3/6/2021 21
![Solution of Part 3 Forces in the members using Method of Joints 40 k Solution of Part 3 (Forces in the members using Method of Joints) 40 k.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-22.jpg)
Solution of Part 3 (Forces in the members using Method of Joints) 40 k. N 2 m 2 m FFE F θ 2 m D E FFG Fy= 57. 5 k. N 50 k. N G F C H Ax 30 k. N 1. 5 m B I Fy 1. 5 m A 40 k. N 1. 5 m Ay 3/6/2021 22
![Solution of Part 4 Forces in the members using Method of Sections 40 k Solution of Part 4 (Forces in the members using Method of Sections) 40 k.](https://slidetodoc.com/presentation_image_h/2881ae5f7faefe2e6eddf76e1da22c4a/image-23.jpg)
Solution of Part 4 (Forces in the members using Method of Sections) 40 k. N 2 m 2 m E F G D H 40 k. N 2 m 2 m FED FGH 50 k. N 2 m D E 1. 5 m θ FEH G F Fy = 57. 5 k. N C H Ax 30 k. N 1. 5 m B I Fy 1. 5 m A 40 k. N 1. 5 m Ay 3/6/2021 23
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Method of sections example
Method of sections example
Method of sections
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Volume of solids with known cross sections
Think on these things
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Ctd ich
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Sectional plane are represented by
Sections of solids
Cutaways and cross sections definition
Revolved section
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Parabolas in the real world
Rotating conic sections
Lesson 1 exploring conic sections
Aristotle anatomy
Volumes with known cross sections
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Anatomy terms
Cross slice