Concept explainers
(a)
The points where the shearing stress is maximum and the values of the stress.
(a)
Answer to Problem 80P
The shearing stress is maximum at the points of
The maximum shear stress along the vertical leg is
The maximum shear stress along the horizontal leg is
The maximum shear stress at the corner of the leg is
Explanation of Solution
Calculation:
Refer to sample problem 6.6 in the text book.
Combined stress along the vertical leg
Combined stress along the horizontal leg
Modify Equation (1).
Calculate the point along the vertical leg differentiate both sides of the equation with respect to y as shown below.
Consider the condition
Hence, the shearing stress is maximum at the points of
Calculate the maximum shear stress along the vertical leg as shown below.
Substitute
Hence, the maximum shear stress along the vertical leg is
Modify Equation (2).
Calculate the point along the horizontal leg differentiate both sides of the equation with respect to z as shown below.
Consider the condition
Hence, the shearing stress is maximum at the points of
Calculate the maximum shear stress along the horizontal leg as shown below.
Substitute
Hence, the maximum shear stress along the horizontal leg is
The corner points of the horizontal and vertical legs are
Calculate the maximum shear stress at the corner point as shown below.
Substitute 0 for y in Equation (1).
Substitute 0 for z in Equation (2).
Therefore, the maximum shear stress at the corner of the leg is
(b)
Show that the points are located on the neutral axis for the loading P.
(b)
Answer to Problem 80P
The points y and z are located on the neutral axis for the loading P.
Explanation of Solution
Calculation:
Sketch the cross section along the neutral axis as shown below.
Refer to Figure 1.
Calculate the moment of inertia as shown below.
Along
Along
Consider the angle
Calculate angle
Substitute
Calculate the angle of the neutral axis from the horizontal as shown below.
Calculate the location of the centroid as shown below.
Along y axis:
Along z axis:
Calculate the neutral axis intersects for vertical leg as shown below.
Substitute
Calculate the neutral axis intersects for horizontal leg as shown below.
Substitute
Therefore, the points y and z are located on the neutral axis for the loading P
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Chapter 6 Solutions
EBK MECHANICS OF MATERIALS
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