The body diagram in the figure below is subject to biaxial loading, with stress components given by oxx = 12 kPa, ayy = 20 kPa, and txy = 8 kPa. 12 D m 30° σn 20 12 a. Construct the circle diagram representing this state of stress. Determine, from the diagram, the magnitudes of the principal stresses and the inclination of the major principal stress axis relative to the x reference direction. Determine from the diagram, the normal and shear stress components on and t on the plane EF oriented as shown. b. Determine analytically the magnitudes and orientations of the plane principal stresses and compare them with the values determined graphically in (a) above.

The body diagram in the figure below is subject to biaxial loading, with stress components given by oxx = 12 kPa, ayy = 20 kPa, and txy = 8 kPa. 12 D m 30° σn 20 12 a. Construct the circle diagram representing this state of stress. Determine, from the diagram, the magnitudes of the principal stresses and the inclination of the major principal stress axis relative to the x reference direction. Determine from the diagram, the normal and shear stress components on and t on the plane EF oriented as shown. b. Determine analytically the magnitudes and orientations of the plane principal stresses and compare them with the values determined graphically in (a) above.

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

The body diagram in the figure below is subject to biaxial loading, with stress components given by oxx = 12 kPa, ayy = 20 kPa, and txy = 8
kPa.
12
O
30°
20
on
20
B
12
a. Construct the circle diagram representing this state of stress. Determine, from the diagram, the magnitudes of the principal stresses and the
inclination of the major principal stress axis relative to the x reference direction. Determine from the diagram, the normal and shear stress
components on and t on the plane EF oriented as shown.
b. Determine analytically the magnitudes and orientations of the plane principal stresses and compare them with the values determined
graphically in (a) above.

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