Concept explainers
(a)
The strains for an element oriented at
(a)
Answer to Problem 7.7.18P
The normal strain in x direction is
The normal strain along y direction is
The shear strain is
Explanation of Solution
Given:
Stress along x direction is
Write the Equation for strain along x axis
Here, the normal strain along x direction is
Write the Equation for strain along y axis
Here, the normal strain along the y direction is
Write the expression for the shear strain ix-y plane
Here, modulus of rigidity is
Write the expression for strain along x direction
Write the expression for strain along y direction
Write the expression for shear strain
Here, the shear strain along x-y plane is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
In below figure the normal strains are shown
:
Figure (1)
Conclusion:
The normal strain along x direction is
The normal strain along y direction is
The shear strain along x-y plane is
(b)
The principal strains.
(b)
Answer to Problem 7.7.18P
The maximum principal strain is
Explanation of Solution
Write expression for the principal strains.
Here, the maximum principal strain is
Write the expression for the principal angle.
Here,
Calculation:
Substitute
While taking positive sign you get maximum principal strain:
While taking negative sign you get minimum principal strain.
Substitute
In below figure principal strains and principal angle are shown:
Figure (2)
Conclusion:
The maximum principal strain is
(c)
The maximum shear strain.
(c)
Answer to Problem 7.7.18P
The maximum shear strain is
Explanation of Solution
Write the expression for maximum shear strain,
Here,
Write expression for first shear angle
Here,
Write expression for second shear angle
Here,
Write the Equation for average strain
Write expression for maximum shear strain.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
In below figure average minimum strain and shear angle are shown:
Figure (3)
Conclusion:
The maximum shear strain is
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Chapter 7 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning