Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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**Problem Statement:**

The cantilevered round bar in the figure with diameter \( d = 25 \, \text{mm} \), is made from SAE 1020 CD steel. Dimensions are \( a = 500 \, \text{mm} \), \( b = 250 \, \text{mm} \), \( c = 125 \, \text{mm} \). The coordinates of point A are: \( x = 0 \), \( y = d/2 \), \( z = 0 \); and point D: \( x = 0 \), \( y = 0 \), \( z = -d/2 \). The loads are: \( F_x = 0 \, \text{N} \), \( F_y = 0 \), \( F_z = 1400 \, \text{N} \). Do not neglect any stress (due to bending, torque, or shear force) unless the calculation says it is zero.

Calculate:
- The bending stress \(\sigma_x^D\) at point D.
- The shear stress \(\tau^A\) at point A.

Answer tolerance = 2 percent. Be sure to include units and the correct sign with your answer.

**Your Answers:**

\[
\sigma_x^D = \, \square
\]

\[
\tau^A = \, \square
\]

**Figure Explanation:**

The diagram depicts a cantilevered round bar anchored into a wall on the left end, with a force applied at the right end. The force \( F_z \) acts downward. The length dimensions from the wall to the force application point are marked as \( a \), \( b \), and \( c \) respectively, describing the segments of the bar. The bar carries a web width \( w \), thickness \( t \), and a point of reference on the round area is labeled \( R \).

The axes system is denoted with \( x \)-axis running along the length of the bar, \( y \)-axis running vertically, and \( z \)-axis extending perpendicularly. The connection point to the wall is labeled as \( O \) with several divisions marked \( A \), \( B \), and \( D \) near the connection.
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Transcribed Image Text:**Problem Statement:** The cantilevered round bar in the figure with diameter \( d = 25 \, \text{mm} \), is made from SAE 1020 CD steel. Dimensions are \( a = 500 \, \text{mm} \), \( b = 250 \, \text{mm} \), \( c = 125 \, \text{mm} \). The coordinates of point A are: \( x = 0 \), \( y = d/2 \), \( z = 0 \); and point D: \( x = 0 \), \( y = 0 \), \( z = -d/2 \). The loads are: \( F_x = 0 \, \text{N} \), \( F_y = 0 \), \( F_z = 1400 \, \text{N} \). Do not neglect any stress (due to bending, torque, or shear force) unless the calculation says it is zero. Calculate: - The bending stress \(\sigma_x^D\) at point D. - The shear stress \(\tau^A\) at point A. Answer tolerance = 2 percent. Be sure to include units and the correct sign with your answer. **Your Answers:** \[ \sigma_x^D = \, \square \] \[ \tau^A = \, \square \] **Figure Explanation:** The diagram depicts a cantilevered round bar anchored into a wall on the left end, with a force applied at the right end. The force \( F_z \) acts downward. The length dimensions from the wall to the force application point are marked as \( a \), \( b \), and \( c \) respectively, describing the segments of the bar. The bar carries a web width \( w \), thickness \( t \), and a point of reference on the round area is labeled \( R \). The axes system is denoted with \( x \)-axis running along the length of the bar, \( y \)-axis running vertically, and \( z \)-axis extending perpendicularly. The connection point to the wall is labeled as \( O \) with several divisions marked \( A \), \( B \), and \( D \) near the connection.
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