**Exercise 38** Section 7.2 (Lesson 14) MecMovies M9.1**Given:** A beam with a rectangular cross section is simply supported and loaded at its center with a force \(P\). The dimensions \(b\), \(h\), and \(L\) are shown in the figure.**Find:** Determine (a) the maximum bending stress \(\sigma_{\text{max}}\) and (b) the maximum shear stress \(\tau_{\text{max}}\) in this beam. (c) Then obtain the ratio \(\tau_{\text{max}}/\sigma_{\text{max}}\). *Hint: The maximum stresses occur at different locations in the beam. Be sure to show sufficient work to justify your answers.***Answers:** (a) \(\frac{3PL}{2bh^2}\) (b) \(\frac{3P}{4bh}\) (c) \(\frac{h}{2L}\)**Diagram Explanation:**The figure alongside illustrates a beam with a rectangular cross section. The beam is simply supported at both ends and loaded at the center by a force \(P\). The dimensions of the beam are denoted as: - \(b\): Width of the beam - \(h\): Height of the beam - \(L\): Length of the beamThese dimensions are crucial for calculating the stresses experienced by the beam under the applied force.

Answered: Image /qna-images/answer/54eac2e9-003b-4f69-9f34-27ad165ad5f6.jpg

Abeam with a rectangular cross section is simply supported and loaded at its center with a force P. The dimensions b, h, and L are shown in the figure. b- Determine (a) the maximum bending stress ơ max a Tmax in this beam. (c) Then obtain the ratio Tmax/o occur at different locations in the beam. Be sure to s

Abeam with a rectangular cross section is simply supported and loaded at its center with a force P. The dimensions b, h, and L are shown in the figure. b- Determine (a) the maximum bending stress ơ max a Tmax in this beam. (c) Then obtain the ratio Tmax/o occur at different locations in the beam. Be sure to s

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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**Exercise 38**
Section 7.2 (Lesson 14)
MecMovies M9.1

**Given:**
A beam with a rectangular cross section is simply supported and loaded at its center with a force \(P\). The dimensions \(b\), \(h\), and \(L\) are shown in the figure.

**Find:**
Determine (a) the maximum bending stress \(\sigma_{\text{max}}\) and (b) the maximum shear stress \(\tau_{\text{max}}\) in this beam. (c) Then obtain the ratio \(\tau_{\text{max}}/\sigma_{\text{max}}\). *Hint: The maximum stresses occur at different locations in the beam. Be sure to show sufficient work to justify your answers.*

**Answers:**
(a) \(\frac{3PL}{2bh^2}\)
(b) \(\frac{3P}{4bh}\)
(c) \(\frac{h}{2L}\)

**Diagram Explanation:**

The figure alongside illustrates a beam with a rectangular cross section. The beam is simply supported at both ends and loaded at the center by a force \(P\). The dimensions of the beam are denoted as:
- \(b\): Width of the beam
- \(h\): Height of the beam
- \(L\): Length of the beam

These dimensions are crucial for calculating the stresses experienced by the beam under the applied force.

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