The moment M acting on the cross section of the tee beam is oriented at an angle of 0 = 64° as shown. Dimensions of the cross section are b₁ = 245 mm, t₁ = 22 mm, d = 279 mm, and tw = 18 mm. The allowable bending stress is 205 MPa. What is the largest bending moment M that can be applied as shown to this cross section? 0 D bf y -tw B d

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Educational Website Text Transcription:**

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**Problem Statement:**

Determine the distance in the y-direction from line DC to the centroid of the area. Then calculate the area moment of inertia about both the x-axis and the y-axis.

**Answer:**

- \( \bar{y} = \) [input box] mm
- \( I_x = \) [input box] mm\(^4\)
- \( I_y = \) [input box] mm\(^4\)

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[Button: Submit Answer]

---

**Part 2:**

The x-component of moment M will cause compression at A and B, and tension at C and D. The y-component of moment M will cause compression at A and D, and tension at B and C. The maximum tensile bending stress will occur at point C. Calculate the magnitude of the largest bending moment that can be applied so that the stress at corner C does not exceed 205 MPa.

**Answer:**

- \( M = \) [input box] kN⋅m

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---

**Part 3:**

The x-component of moment M will cause compression at A and B, and tension at C and D. The y-component of moment M will cause compression at A and D, and tension at B and C. The maximum compressive bending stress will occur at point A. Calculate the magnitude of the largest bending moment that can be applied so that the stress at corner A does not exceed 205 MPa.

**Answer:**

- \( M = \) [input box] kN⋅m

[Button: eTextbook and Media]

[Button: Submit Answer]

---

**Part 4:**

Determine the maximum bending moment that can be applied to this cross section.

**Answer:**

- [Input box]

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[Button: Submit Answer]

--- 

Note: No specific graphs or diagrams are present in the image to describe further.
Transcribed Image Text:**Educational Website Text Transcription:** --- **Problem Statement:** Determine the distance in the y-direction from line DC to the centroid of the area. Then calculate the area moment of inertia about both the x-axis and the y-axis. **Answer:** - \( \bar{y} = \) [input box] mm - \( I_x = \) [input box] mm\(^4\) - \( I_y = \) [input box] mm\(^4\) [Button: eTextbook and Media] [Button: Submit Answer] --- **Part 2:** The x-component of moment M will cause compression at A and B, and tension at C and D. The y-component of moment M will cause compression at A and D, and tension at B and C. The maximum tensile bending stress will occur at point C. Calculate the magnitude of the largest bending moment that can be applied so that the stress at corner C does not exceed 205 MPa. **Answer:** - \( M = \) [input box] kN⋅m [Button: eTextbook and Media] [Button: Submit Answer] --- **Part 3:** The x-component of moment M will cause compression at A and B, and tension at C and D. The y-component of moment M will cause compression at A and D, and tension at B and C. The maximum compressive bending stress will occur at point A. Calculate the magnitude of the largest bending moment that can be applied so that the stress at corner A does not exceed 205 MPa. **Answer:** - \( M = \) [input box] kN⋅m [Button: eTextbook and Media] [Button: Submit Answer] --- **Part 4:** Determine the maximum bending moment that can be applied to this cross section. **Answer:** - [Input box] [Button: eTextbook and Media] [Button: Submit Answer] --- Note: No specific graphs or diagrams are present in the image to describe further.
The moment \( M \) acting on the cross section of the tee beam is oriented at an angle of \( \theta = 64^\circ \) as shown. Dimensions of the cross section are \( b_f = 245 \, \text{mm}, \, t_f = 22 \, \text{mm}, \, d = 279 \, \text{mm}, \, \text{and} \, t_w = 18 \, \text{mm} \). The allowable bending stress is 205 MPa. What is the largest bending moment \( M \) that can be applied as shown to this cross section?

### Diagram Explanation:

- **Diagram Layout**: The diagram depicts a tee beam cross section.
- **Labels**:
  - \( A, B, C, D \): Points on the beam.
  - \( b_f \): Width of the flange.
  - \( t_f \): Thickness of the flange.
  - \( d \): Overall depth of the beam.
  - \( t_w \): Thickness of the web.
  - \( y \): Distance from point \( A \) to the intersection of the web and flange.
  - \( z \): Distance from point \( D \) horizontally to the intersection of the web and point where \( M \) is applied.
  - \( \theta \): Angle at which moment \( M \) is applied.

- **Moment \( M \)**:
  - Illustrated as a vector originating from point \( D \) at an angle \( \theta = 64^\circ \) with respect to the vertical axis.

The objective is to determine the maximum bending moment \( M \) that can be applied to this cross section without exceeding the allowable bending stress of 205 MPa.
Transcribed Image Text:The moment \( M \) acting on the cross section of the tee beam is oriented at an angle of \( \theta = 64^\circ \) as shown. Dimensions of the cross section are \( b_f = 245 \, \text{mm}, \, t_f = 22 \, \text{mm}, \, d = 279 \, \text{mm}, \, \text{and} \, t_w = 18 \, \text{mm} \). The allowable bending stress is 205 MPa. What is the largest bending moment \( M \) that can be applied as shown to this cross section? ### Diagram Explanation: - **Diagram Layout**: The diagram depicts a tee beam cross section. - **Labels**: - \( A, B, C, D \): Points on the beam. - \( b_f \): Width of the flange. - \( t_f \): Thickness of the flange. - \( d \): Overall depth of the beam. - \( t_w \): Thickness of the web. - \( y \): Distance from point \( A \) to the intersection of the web and flange. - \( z \): Distance from point \( D \) horizontally to the intersection of the web and point where \( M \) is applied. - \( \theta \): Angle at which moment \( M \) is applied. - **Moment \( M \)**: - Illustrated as a vector originating from point \( D \) at an angle \( \theta = 64^\circ \) with respect to the vertical axis. The objective is to determine the maximum bending moment \( M \) that can be applied to this cross section without exceeding the allowable bending stress of 205 MPa.
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