90 MPa 55 MPa 70 MPa 55 MPa 90 MPa 65° TE 70 MPa 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 (σx, Øy, Txy) and what is the angle of rotation (0)? Make sure your signs are correct. b) Using the equations of stress transformation, determine d', dyr, and Tx'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?

90 MPa 55 MPa 70 MPa 55 MPa 90 MPa 65° TE 70 MPa 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 (σx, Øy, Txy) and what is the angle of rotation (0)? Make sure your signs are correct. b) Using the equations of stress transformation, determine d', dyr, and Tx'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?

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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Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

90 MPa
55 MPa
70 MPa
70 MPa
55 MPa
-90 MPa
65°
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, y, and Txy 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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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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