Answered: Part A - Free-body diagram of the…

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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Part A - Free-body diagram of the resolved components of the moments

The two externally applied moments can be resolved into their respective y and z components. Determine the moments in each principal direction, My and Mz, and draw the corresponding free-body diagram.

Part B - Moments of inertia of the cross section with respect to the y- and z-axes

To calculate the absolute maximum bending stress in the member using the flexure formula for unsymmetrical bending, the moments of inertia of the cross section must be calculated. Select the correct formulas for these values.

Iy=?

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, αα, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane.

|α| =?

Part D - Absolute maximum stress in cross section ABCD

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

|αmax|=?

Part A - Free-body diagram of the resolved components of the moments
The two externally applied moments can be resolved into their respective y and z components. Determine the moments in each principal direction, M, and Mz, and draw the corresponding
free-body diagram.
Draw the vectors M, and M, that represent the total y and z components of the two externally applied moments. Assume all angles are measured in degrees.
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Learning Goal:
To determine the absolute maximum bending stress in a rectangular cross section that has a circular cutout and is subjected to unsymmetrical bending in the y- and z-directional planes, and to
determine the angles of the neutral axes established by the applied moments.
The rectangular cross section ABCD shown below has a circular cutout of diameter d = 50.0 mm through its center. The member is subjected to two externally applied moments M1= 6.0 kN · m
and M, =17.0 kN - m at angles 0 = 35.0 degrees from the y axis in the yz plane and 0,= 25.0 degrees from the z axis in the yz plane, respectively. The rectangular cross section has a height
of h = 260.0 mm and a width of w = 125.0 mm
h
2
M, 6
M2
D
2

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