(a) Sketch a free-body diagram showing the forces and reactions imposed on the rigid I-beam in Fig. (a). (b) How many unknown reactions are there in this problem? Is the beam statically determinate or indeterminate? (c) In Fig. (b), the connection to the rigid wall at point A in Fig. (a) is replaced by a torsional spring with stiffness kt. The roller support at point C in Fig. (a) is replaced by a linear spring with stiffness k, oriented vertically, as shown. Sketch the free-body diagram showing the forces and reactions acting on the rigid I-beam in Fig (b). (d) Compute the reactions at points A and C, expressed in terms of F, FH, L, k, kt, etc. Y A B (a) D X A B (b) 1/12 FH
(a) Sketch a free-body diagram showing the forces and reactions imposed on the rigid I-beam in Fig. (a). (b) How many unknown reactions are there in this problem? Is the beam statically determinate or indeterminate? (c) In Fig. (b), the connection to the rigid wall at point A in Fig. (a) is replaced by a torsional spring with stiffness kt. The roller support at point C in Fig. (a) is replaced by a linear spring with stiffness k, oriented vertically, as shown. Sketch the free-body diagram showing the forces and reactions acting on the rigid I-beam in Fig (b). (d) Compute the reactions at points A and C, expressed in terms of F, FH, L, k, kt, etc. Y A B (a) D X A B (b) 1/12 FH
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Problem 1.1MA
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Transcribed Image Text:(a) Sketch a free-body diagram showing the forces and reactions imposed on the **rigid I-beam** in Fig. (a). (b) How many unknown reactions are there in this problem? Is the beam statically determinate or indeterminate? (c) In Fig. (b), the connection to the rigid wall at point A in Fig. (a) is replaced by a torsional spring with stiffness \( k_t \). The roller support at point C in Fig. (a) is replaced by a linear spring with stiffness \( k \), oriented vertically, as shown. Sketch the free-body diagram showing the forces and reactions acting on the **rigid I-beam** in Fig. (b). (d) Compute the reactions at points A and C, expressed in terms of \( F, F_H, L, k, k_t, \) etc.
**Diagrams:**
- **Figure (a):** Illustrates a rigid I-beam between points A and C, with point A fixed to a rigid wall, and point C supported by a roller. A downward force \( F \) is applied at point B, located at the midpoint of the beam, with a horizontal reaction \( F_H \) at point D.
- **Figure (b):** Shows a similar configuration; however, point A is now attached with a torsional spring (stiffness \( k_t \)) instead of a rigid wall. Point C has a linear spring oriented vertically with stiffness \( k \). The force \( F \) and reaction \( F_H \) remain in the same positions as in Fig. (a).
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