Question

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are $S_x = 280$ MPa, $S_y = 55$ MPa, and $S_{xy} = 65$ MPa. Assume $\beta = 70^\circ$ For Mohr's circle, all angular measures are doubled; therefore, point n (which represents the state of stress on the n plane) on Mohr's circle is rotated $2\beta$ counterclockwise from point x. From the Mohr's circle that you constructed on a piece of paper, determine the central angle $\beta$ between point n and the principal stress $\sigma_{pl}$. Answer: $\beta = -9.98^\circ$ Use the center of the circle C, the circle radius R, and the angle $\beta$ determined in Part 8 to compute: (a) the normal stress $\sigma_n$. Give the stress value including sign if any. (b) the shear stress $\tau_{nt}$. Give the stress value including sign if any. Answers: (a) $\sigma_n = $ MPa, (b) $\tau_{nt} = $ MPa. Calculate the absolute maximum shear stress magnitude. Answer: $\tau_{abs\ max} = $ MPa.

          Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal
and vertical planes at the point are $S_x = 280$ MPa, $S_y = 55$ MPa, and $S_{xy} = 65$ MPa. Assume $\beta = 70^\circ$

For Mohr's circle, all angular measures are doubled; therefore, point n (which represents the state of stress on the n plane) on
Mohr's circle is rotated $2\beta$ counterclockwise from point x. From the Mohr's circle that you constructed on a piece of paper,
determine the central angle $\beta$ between point n and the principal stress $\sigma_{pl}$.
Answer: $\beta = -9.98^\circ$

Use the center of the circle C, the circle radius R, and the angle $\beta$ determined in Part 8 to compute:
(a) the normal stress $\sigma_n$. Give the stress value including sign if any.
(b) the shear stress $\tau_{nt}$. Give the stress value including sign if any.
Answers:
(a) $\sigma_n = $ MPa,
(b) $\tau_{nt} = $ MPa.

Calculate the absolute maximum shear stress magnitude.
Answer: $\tau_{abs\ max} = $ MPa.

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal
and vertical planes at the point are Sx = 280 MPa, Sy = 55 MPa, and Sxy = 65 MPa. Assume β = 70^∘

For Mohr's circle, all angular measures are doubled; therefore, point n (which represents the state of stress on the n plane) on
Mohr's circle is rotated 2β counterclockwise from point x. From the Mohr's circle that you constructed on a piece of paper,
determine the central angle β between point n and the principal stress σpl.
Answer: β = -9.98^∘

Use the center of the circle C, the circle radius R, and the angle β determined in Part 8 to compute:
(a) the normal stress . Give the stress value including sign if any.
(b) the shear stress τnt. Give the stress value including sign if any.
Answers:
(a) = MPa,
(b) τnt = MPa.

Calculate the absolute maximum shear stress magnitude.
Answer: τabs max = MPa.

Added by Nathan R.

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