3) A beam of square cross section of the dimensions shown below is subjected to a shear force of V=8 kN. (a) Calculate the average shear stress at the neutral axis ( y² = 0), (b) at y' = 0.01 m and (c) at y'= -0.02 m. (d) Calculate the normal stress at the neutral axis. 0.04 m 0.06 m y Z
3) A beam of square cross section of the dimensions shown below is subjected to a shear force of V=8 kN. (a) Calculate the average shear stress at the neutral axis ( y² = 0), (b) at y' = 0.01 m and (c) at y'= -0.02 m. (d) Calculate the normal stress at the neutral axis. 0.04 m 0.06 m y Z
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Problem Statement
3) A beam of square cross-section of the dimensions shown below is subjected to a shear force of \( V = 8 \, \text{kN} \).
(a) Calculate the average **shear** stress at the neutral axis (\( y' = 0 \)).
(b) Calculate the average **shear** stress at \( y' = 0.01 \, \text{m} \).
(c) Calculate the average **shear** stress at \( y' = -0.02 \, \text{m} \).
(d) Calculate the **normal** stress at the neutral axis.
### Diagram Explanation
The diagram illustrates a rectangular beam with the following dimensions:
- Width: \( 0.04 \, \text{m} \)
- Height: \( 0.06 \, \text{m} \)
The coordinate system is defined with:
- The \( y \)-axis along the height of the rectangle.
- The \( z \)-axis running horizontally through the middle of the rectangle.
The origin of the coordinate system is at the center of the beam. The coordinates \( y' = 0 \), \( y' = 0.01 \, \text{m} \), and \( y' = -0.02 \, \text{m} \) refer to positions along the height of the beam where shear stress calculations are to be performed.
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