Show all work **6.20** A timber beam \( AB \) of length \( L \) and rectangular cross-section carries a uniformly distributed load \( w \) and is supported as shown. **(a)** Show that the ratio \(\tau_m/\sigma_m\) of the maximum values of the shearing and normal stresses in the beam is equal to \(2h/L\), where \( h \) and \( L \) are, respectively, the depth and the length of the beam.**(b)** Determine the depth \( h \) and the width \( b \) of the beam, knowing that \( L = 5 \, \text{m} \), \( w = 8 \, \text{kN/m} \), \(\tau_m = 1.08 \, \text{MPa}\), and \(\sigma_m = 12 \, \text{MPa}\).---**Diagram Explanation (Fig. P6.20):**- The diagram shows a simply supported beam \( AB \) with a uniformly distributed load \( w \) across its entire length.- The beam is rectangular in cross-section with width \( b \) and depth \( h \).- The beam is supported at two points: \( C \) and \( D \). - The distance between points \( C \) and \( D \) is \( L/2 \), with each support located at a distance \( L/4 \) from the ends of the beam (\( A \) and \( B \)).- The beam bears the load distributed across its entire span, creating bending and shear stresses.

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6.20 A timber beam AB of length L and rectangular cross section carries a uniformly distributed load w and is supported as shown. (a) Show that the ratio T/om of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 5 m, w = 8 kN/m, r, = 1.08 MPa, and o, = 12 MPa. B C D L/2 L/4 L/4 Fig. P6.20

6.20 A timber beam AB of length L and rectangular cross section carries a uniformly distributed load w and is supported as shown. (a) Show that the ratio T/om of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 5 m, w = 8 kN/m, r, = 1.08 MPa, and o, = 12 MPa. B C D L/2 L/4 L/4 Fig. P6.20

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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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

Show all work

**6.20**
A timber beam \( AB \) of length \( L \) and rectangular cross-section carries a uniformly distributed load \( w \) and is supported as shown.

**(a)** Show that the ratio \(\tau_m/\sigma_m\) of the maximum values of the shearing and normal stresses in the beam is equal to \(2h/L\), where \( h \) and \( L \) are, respectively, the depth and the length of the beam.

**(b)** Determine the depth \( h \) and the width \( b \) of the beam, knowing that \( L = 5 \, \text{m} \), \( w = 8 \, \text{kN/m} \), \(\tau_m = 1.08 \, \text{MPa}\), and \(\sigma_m = 12 \, \text{MPa}\).

---

**Diagram Explanation (Fig. P6.20):**

- The diagram shows a simply supported beam \( AB \) with a uniformly distributed load \( w \) across its entire length.
- The beam is rectangular in cross-section with width \( b \) and depth \( h \).
- The beam is supported at two points: \( C \) and \( D \).
- The distance between points \( C \) and \( D \) is \( L/2 \), with each support located at a distance \( L/4 \) from the ends of the beam (\( A \) and \( B \)).
- The beam bears the load distributed across its entire span, creating bending and shear stresses.

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