For Problems 9.1 through 9.6, use the virtual work method to determine the deflection of each of the joints indicated. E = 29.000 ksi for all members unless otherwise indicated. The cross section of each member is given as in² unless noted otherwise. P9.1 Find Agx and Ay Bar areas: AB = 7; BC = DE = EC = 2; AD = BE = 4; and DB = 6. (Ans: Ary= 0.753 in. 1. ABx= 0.173 in.) 40 k A D k 20 k BY E 10 k C -20 ft → 20 ft- → 15 ft →→

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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### Problem Description

For **Problems 9.1 through 9.6**, use the virtual work method to determine the deflection of each of the joints indicated. **E = 29,000 ksi** for all members unless otherwise indicated. The cross-section of each member is given as **in²** unless noted otherwise.

#### P9.1

- **Objective:** Find \(\Delta_{BX}\) and \(\Delta_{EY}\).
- **Bar areas**: 
  - AB = 7
  - BC = DE = EC = 2
  - AD = BE = 4
  - DB = 6
- **Forces and Distances:**
  - A 20 k force is applied at joint B.
  - A 40 k force is applied at joint C (15 ft above point).
  - A 10 k force is applied at joint E.
  - The distances from D to B and D to E are each 20 ft.

- **Answers:**
  - \(\Delta_{EY} = 0.753 \, \text{in.}\)
  - \(\Delta_{BX} = 0.173 \, \text{in.} \rightarrow\)

### Diagram Explanation

The diagram is a truss structure with five joints labeled A, B, C, D, and E. 

- **Structure Layout:**
  - Points A, B, and C are aligned horizontally with equal spacing (20 ft apart).
  - Points D and E are directly below points A and B, respectively, each connected by diagonal members.
  - DB and DE are vertical members each 15 ft long.

- **Member Connections:**
  - AB and BE form the top and middle horizontal connections.
  - AD, DB, and ED form the vertical and diagonal connections.
  - BC, DE, and EC form the further connections from B and C.

This description serves to explain the layout and problem requirements for calculating joint deflections using the given parameters.
Transcribed Image Text:### Problem Description For **Problems 9.1 through 9.6**, use the virtual work method to determine the deflection of each of the joints indicated. **E = 29,000 ksi** for all members unless otherwise indicated. The cross-section of each member is given as **in²** unless noted otherwise. #### P9.1 - **Objective:** Find \(\Delta_{BX}\) and \(\Delta_{EY}\). - **Bar areas**: - AB = 7 - BC = DE = EC = 2 - AD = BE = 4 - DB = 6 - **Forces and Distances:** - A 20 k force is applied at joint B. - A 40 k force is applied at joint C (15 ft above point). - A 10 k force is applied at joint E. - The distances from D to B and D to E are each 20 ft. - **Answers:** - \(\Delta_{EY} = 0.753 \, \text{in.}\) - \(\Delta_{BX} = 0.173 \, \text{in.} \rightarrow\) ### Diagram Explanation The diagram is a truss structure with five joints labeled A, B, C, D, and E. - **Structure Layout:** - Points A, B, and C are aligned horizontally with equal spacing (20 ft apart). - Points D and E are directly below points A and B, respectively, each connected by diagonal members. - DB and DE are vertical members each 15 ft long. - **Member Connections:** - AB and BE form the top and middle horizontal connections. - AD, DB, and ED form the vertical and diagonal connections. - BC, DE, and EC form the further connections from B and C. This description serves to explain the layout and problem requirements for calculating joint deflections using the given parameters.
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