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Problem 2: At a point in an elastic material, there are two mutually perpendicular planes, one of which carries a direct (normal) tensile stress of 50 N/mm²2 and a shear stress of 40 N/mm². The other plane is subjected to a direct (normal) compressive stress of 35 N/mm² and a complementary shear stress of 40 N/mm². (a) Draw a figure showing the given state of stress. (b) Calculate the values of the normal and shear stresses on a plane that is rotated by 45° counterclockwise with respect to the original plane. Do this using force equilibrium directly (do not use the 2D stress transformation equations). (c) Determine the principal stresses and the maximum shear stress, and the orientation of the planes on which they act (i.e., state the angles that these planes make with respect to the original plane). You may use the 2D principal stress equations. (d) Determine the orientation of the planes where there is no normal stress. What happens to the shear stress on the planes where there is no normal stress? Find these values of shear stress.

Problem 2: At a point in an elastic material, there are two mutually perpendicular planes, one of which carries a direct (normal) tensile stress of 50 N/mm²2 and a shear stress of 40 N/mm². The other plane is subjected to a direct (normal) compressive stress of 35 N/mm² and a complementary shear stress of 40 N/mm². (a) Draw a figure showing the given state of stress. (b) Calculate the values of the normal and shear stresses on a plane that is rotated by 45° counterclockwise with respect to the original plane. Do this using force equilibrium directly (do not use the 2D stress transformation equations). (c) Determine the principal stresses and the maximum shear stress, and the orientation of the planes on which they act (i.e., state the angles that these planes make with respect to the original plane). You may use the 2D principal stress equations. (d) Determine the orientation of the planes where there is no normal stress. What happens to the shear stress on the planes where there is no normal stress? Find these values of shear stress.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 2: At a point in an elastic material, there are two mutually perpendicular planes, one of which carries a direct (normal) tensile stress of 50 N/mm²2 and a shear stress of 40 N/mm². The other plane is subjected to a direct (normal) compressive stress of 35 N/mm² and a complementary shear stress of 40 N/mm². (a) Draw a figure showing the given state of stress. (b) Calculate the values of the normal and shear stresses on a plane that is rotated by 45° counterclockwise with respect to the original plane. Do this using force equilibrium directly (do not use the 2D stress transformation equations). (c) Determine the principal stresses and the maximum shear stress, and the orientation of the planes on which they act (i.e., state the angles that these planes make with respect to the original plane). You may use the 2D principal stress equations. (d) Determine the orientation of the planes where there is no normal stress. What happens to the shear stress on the planes where there is no normal stress? Find these values of shear stress.
Transcribed Image Text:Problem 2: At a point in an elastic material, there are two mutually perpendicular planes, one of which carries a direct (normal) tensile stress of 50 N/mm²2 and a shear stress of 40 N/mm². The other plane is subjected to a direct (normal) compressive stress of 35 N/mm² and a complementary shear stress of 40 N/mm². (a) Draw a figure showing the given state of stress. (b) Calculate the values of the normal and shear stresses on a plane that is rotated by 45° counterclockwise with respect to the original plane. Do this using force equilibrium directly (do not use the 2D stress transformation equations). (c) Determine the principal stresses and the maximum shear stress, and the orientation of the planes on which they act (i.e., state the angles that these planes make with respect to the original plane). You may use the 2D principal stress equations. (d) Determine the orientation of the planes where there is no normal stress. What happens to the shear stress on the planes where there is no normal stress? Find these values of shear stress.
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