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a) Calculate the deflection at point B, using the unit load method.

a) Calculate the deflection at point B, using the unit load method.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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We are given the structure of Fig. 4a. a) Calculate the deflection at point B, using the unit load method. b) The owner of the structure wants to ensure that point B does not deflect at all (that is, the vertical displacement at B must be zero). To this end, engineers come up with the solution shown in Fig. 4b: to apply an upward force, \( R_B \), at point B, such that the deflection at B is zero. Calculate the value that \( R_B \) must have. **HINT**: You can use the **PRINCIPLE OF SUPERPOSITION**, according to which the total deflection at B (which we want to be zero) is equal to the sum of the deflection at B **due to the distributed load** and of the deflection at B **due to \( R_B \)**. **Diagrams:** - **Fig. 4a** illustrates a beam fixed at point A with a uniformly distributed load of 2 kip/ft over a 10 ft span. The flexural rigidity is given as \( EI = 5.0 \times 10^7 \text{ kip} \cdot \text{in}^2 \). - **Fig. 4b** shows the same beam and load as in Fig. 4a, with the addition of an upward force, \( R_B \), applied at point B. **Figure 4** is referenced for both sub-figures (a) and (b).
Transcribed Image Text:We are given the structure of Fig. 4a. a) Calculate the deflection at point B, using the unit load method. b) The owner of the structure wants to ensure that point B does not deflect at all (that is, the vertical displacement at B must be zero). To this end, engineers come up with the solution shown in Fig. 4b: to apply an upward force, \( R_B \), at point B, such that the deflection at B is zero. Calculate the value that \( R_B \) must have. **HINT**: You can use the **PRINCIPLE OF SUPERPOSITION**, according to which the total deflection at B (which we want to be zero) is equal to the sum of the deflection at B **due to the distributed load** and of the deflection at B **due to \( R_B \)**. **Diagrams:** - **Fig. 4a** illustrates a beam fixed at point A with a uniformly distributed load of 2 kip/ft over a 10 ft span. The flexural rigidity is given as \( EI = 5.0 \times 10^7 \text{ kip} \cdot \text{in}^2 \). - **Fig. 4b** shows the same beam and load as in Fig. 4a, with the addition of an upward force, \( R_B \), applied at point B. **Figure 4** is referenced for both sub-figures (a) and (b).
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