**Learning Goal:**The rectangular cross section \(ABCD\) shown below has a circular cutout of diameter \(d = 50.0 \, \text{mm}\) through its center. The member is subjected to two externally applied moments \(M_1 = 6.0 \, \text{kN} \cdot \text{m}\) and \(M_2 = 17.0 \, \text{kN} \cdot \text{m}\) at angles \(\theta_1 = 35.0\) degrees from the \(y\) axis in the \(yz\) plane and \(\beta_2 = 25.0\) degrees from the \(z\) axis in the \(yz\) plane, respectively. The rectangular cross section has a height of \(h = 290.0 \, \text{mm}\) and a width of \(w = 125.0 \, \text{mm}\).**Diagram Explanation:**The diagram illustrates a 3-dimensional rectangular prism with a circular cutout at its center. The sides of the rectangle are labeled \(ABCD\). The dimensions and placement of forces and angles are depicted as follows:- Two moments, \(M_1\) and \(M_2\), are shown intersecting on the face of the prism.- \(M_1\) is inclined at an angle \(\theta_1 = 35.0\) degrees from the \(y\) axis.- \(M_2\) is angled at \(\beta_2 = 25.0\) degrees from the \(z\) axis.- The circular cutout has a diameter labeled as \(d\).- Horizontal width (\(w/2\)), vertical height (\(h/2\)), and the dimensions of the rectangular section are clearly indicated. **Part C - Neutral-axis angle due to externally applied moments**The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, α, due to the externally applied moments as measured counterclockwise from the positive z-axis in the yz-plane.Express your answer to three significant figures and include the appropriate units.[View Available Hint(s)]\[ \alpha = \boxed{\text{Value}} \quad \text{Units} \][Submit]---**Part D - Absolute maximum stress in cross section ABCD**Determine the absolute maximum stress, |σ_max|, in cross section ABCD due to the two externally applied moments.Express the answer to three significant figures and include the appropriate units.

Answered: Image /qna-images/answer/fcf1ccd3-099f-45fa-ad43-500210e56232.jpg

▼ Part C- Neutral-axis angle due to externally applied moments The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, a, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane. Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) α = Submit Value → Units www. ? Part D- Absolute maximum stress in cross section ABCD Determine the absolute maximum stress, lomax |, in cross section ABCD due to the two externally applied moments. Express the answer to three significant figures and include the appropriate units.

▼ Part C- Neutral-axis angle due to externally applied moments The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, a, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane. Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) α = Submit Value → Units www. ? Part D- Absolute maximum stress in cross section ABCD Determine the absolute maximum stress, lomax |, in cross section ABCD due to the two externally applied moments. Express the answer to three significant figures and include the appropriate units.

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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Question

**Learning Goal:**

The rectangular cross section \(ABCD\) shown below has a circular cutout of diameter \(d = 50.0 \, \text{mm}\) through its center. The member is subjected to two externally applied moments \(M_1 = 6.0 \, \text{kN} \cdot \text{m}\) and \(M_2 = 17.0 \, \text{kN} \cdot \text{m}\) at angles \(\theta_1 = 35.0\) degrees from the \(y\) axis in the \(yz\) plane and \(\beta_2 = 25.0\) degrees from the \(z\) axis in the \(yz\) plane, respectively. The rectangular cross section has a height of \(h = 290.0 \, \text{mm}\) and a width of \(w = 125.0 \, \text{mm}\).

**Diagram Explanation:**

The diagram illustrates a 3-dimensional rectangular prism with a circular cutout at its center. The sides of the rectangle are labeled \(ABCD\). The dimensions and placement of forces and angles are depicted as follows:

- Two moments, \(M_1\) and \(M_2\), are shown intersecting on the face of the prism.
- \(M_1\) is inclined at an angle \(\theta_1 = 35.0\) degrees from the \(y\) axis.
- \(M_2\) is angled at \(\beta_2 = 25.0\) degrees from the \(z\) axis.
- The circular cutout has a diameter labeled as \(d\).
- Horizontal width (\(w/2\)), vertical height (\(h/2\)), and the dimensions of the rectangular section are clearly indicated.

**Part C - Neutral-axis angle due to externally applied moments**

The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, α, due to the externally applied moments as measured counterclockwise from the positive z-axis in the yz-plane.

Express your answer to three significant figures and include the appropriate units.

[View Available Hint(s)]

\[ \alpha = \boxed{\text{Value}} \quad \text{Units} \]

[Submit]

---

**Part D - Absolute maximum stress in cross section ABCD**

Determine the absolute maximum stress, |σ_max|, in cross section ABCD due to the two externally applied moments.

Express the answer to three significant figures and include the appropriate units.

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