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ENGR 213001 Sp17 / HW CH 12

*P12.081 GO Multipart

*Part 1

Correct

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 = 330 MPa, Sy = 105 MPa,

and Sxy = 65 MPa. Assume .

Construct Mohr’s circle for this state of stress on paper and use the results to answer the questions

in the subsequent parts of this GO exercise.

For this Mohr’s circle, point x, which represents the state of stress on the x face of the stress element, should appear:

*Part 2

Correct

For the given state of stress at a point in a structural member, determine the center C and the radius R of Mohr’s circle.

Answers: C = MPa, R = MPa.

Below and to the right of the circle center.

Above and to the left of the circle center.

Above and to the right of the circle center.

Below and to the left of the circle center.

217.5 129

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Answer *1: the tolerance is +/2% Answer *2: the tolerance is +/2%

*Part 3

Correct

Determine the principal stresses ( ) for this state of stress.

Answers: MPa, MPa.

Answer *1: the tolerance is +/2% Answer *2: the tolerance is +/2%

*Part 4

Incorrect

Use the coordinates of point x and the center C of the circle to determine the acute central angle. The other central angle is 180° minus the acute angle.

For this Mohr’s circle, determine the magnitude of the central angle between:

(a) point x and the point representing the principal stress .

(b) point x and the point representing the principal stress .

Answers:

(a) Angle = °,

(b) Angle = °.

Answer *1: the tolerance is +/2% Answer *2: the tolerance is +/2%

Part 5

Correct

Angles measured in Mohr’s circle are double angles . The orientation of the principal planes in

the x–y coordinate system is defined by an angle . If the acute angle determined in Part 4 is

used for , which sketch correctly defines the orientation of the principal planes?

88.5 346.5

4.09 *1

175.91 *2

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*Part 6 (a) Determine the magnitude of the maximum inplane shear stress.

(b) Determine the normal stress that acts on planes of maximum inplane shear stress. Give the

stress value including sign if any.

Answers:

(a) MPa.

(b) MPa.

Answer *1: the tolerance is +/2% Answer *2: the tolerance is +/2%

*Part 7 To determine the normal and shear stresses on the indicated plane, we must first determine the

orientation of the inclined plane relative to the x face of the stress element. Determine the

magnitude of the counterclockwise angle between the x face and the inclined plane. Assume Sx

= 330 MPa, Sy = 105 MPa, Sxy = 65 MPa, and .

Answer: °.

the tolerance is +/2%

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*Part 8 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 counterclockwise from point x. From the

Mohr’s circle that you constructed on a piece of paper, determine the central angle between

point n and the principal stress .

Answer: °.

the tolerance is +/2%

*Part 9

Use the center of the circle C, the circle radius R, and the angle determined in Part 8 to

compute:

(a) the normal stress . Give the stress value including sign if any.

(b) the shear stress . Give the stress value including sign if any.

Answers:

(a) MPa,

(b) MPa.

Answer *1: the tolerance is +/2% Answer *2: the tolerance is +/2%

*Part 10 Calculate the absolute maximum shear stress magnitude.

Answer: MPa.

the tolerance is +/2%