The state of stress on an element relative to the xy-axis is presented above. The element is to be reoriented as shown.a) What are the components that describe its original state of stress (??, ??, ???) and what is the angle of rotation (?)? Make sure your signs are correct.b) Using the equations of stress transformation, determine ??′, ??′, and ??′?′ and draw these components of stress on the rotated element.c) What are the principal stresses and angles of the principal planes? What is the shear stress associated with this orientation?d) What is the maximum in-plane shear stress and the angle of its associated plane? What are the associated normal stresses in this orientation?e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress act upon? 90 MPa55 MPa70 MPay70 MPa55 MPa-90 MPa65°LThe state of stress on an element relative to the xy-axis is presented above. The element is to bereoriented as shown.a) What are the components that describe its original state of stress (x, y, Txy) and what is theangle of rotation (0)? Make sure your signs are correct.b) Using the equations of stress transformation, determine x', σy', and 'y' and draw thesecomponents of stress on the rotated element.c) What are the principal stresses and angles of the principal planes? What is the shear stressassociated with this orientation?d) What is the maximum in-plane shear stress and the angle of its associated plane? What arethe associated normal stresses in this orientation?e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress actupon?

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Answered: 90 MPa 55 MPa 70 MPa y 70 MPa 55 MPa…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The state of stress on an element relative to the xy-axis is presented above. The element is to be reoriented as shown.

a) What are the components that describe its original state of stress (?_?, ?_?, ?_??) and what is the angle of rotation (?)? Make sure your signs are correct.

b) Using the equations of stress transformation, determine ?_?′, ?_?′, and ?_?′?′ and draw these components of stress on the rotated element.

c) What are the principal stresses and angles of the principal planes? What is the shear stress associated with this orientation?

d) What is the maximum in-plane shear stress and the angle of its associated plane? What are the associated normal stresses in this orientation?

e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress act upon?

90 MPa
55 MPa
70 MPa
y
70 MPa
55 MPa
-90 MPa
65°
L
The state of stress on an element relative to the xy-axis is presented above. The element is to be
reoriented as shown.
a) What are the components that describe its original state of stress (x, y, Txy) and what is the
angle of rotation (0)? Make sure your signs are correct.
b) Using the equations of stress transformation, determine x', σy', and 'y' and draw these
components of stress on the rotated element.
c) What are the principal stresses and angles of the principal planes? What is the shear stress
associated with this orientation?
d) What is the maximum in-plane shear stress and the angle of its associated plane? What are
the associated normal stresses in this orientation?
e) What is the absolute maximum shear stress and what plane (xy, xz, or yz) does this stress act
upon?

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