Concept explainers
Three forces are applied to the bar shown. Determine the normal and shearing stresses at (a) point a, (b) point b, (c) point c.
Fig. P8.47
(a)
The normal and shearing stress at point a.
Answer to Problem 47P
The normal stress at point a is
The shear stress at point a is
Explanation of Solution
Given information:
The centric force p is
Calculation:
At point A:
Find the area of cross section
Here, b is the width of the bar and h is the height of the bar.
Substitute
Find the moment of inertia
Substitute
Find the moment of inertia
Substitute
Sketch the side view of bar as shown in Figure 1.
At the section containing point a, b, and c.
Refer to Figure 1.
Find the moment about z axis as follows:
Sketch the side view of bar as shown in Figure 2.
Find the moment about y axis as follows:
Find the normal stress
Here, P is the centric force, A is the area of rectangular cross section,
Substitute
Thus, the normal stress at point a is
Sketch the cross section at point a as shown in figure 3.
Determine the first moment area (Q) as follows:
Here,
Refer to Figure 2.
Substitute
Find the shear stress
Here,
Substitute
Thus, the shear stress at point a is
(b)
The normal and shearing stresses at point b.
Answer to Problem 47P
The normal stress at point b is
The shear stress at point b is
Explanation of Solution
Calculation:
At point b:
Find the normal stress
Substitute
Thus, the normal stress at point b is
Sketch the cross section at point b as shown in figure 4.
Determine the first moment area (Q) as follows:
Here,
Refer to Figure 2.
Substitute
Find the shear stress
Here,
Substitute
Thus, the shear stress at point b is
(c)
The normal and shearing stresses at point c.
Answer to Problem 47P
The normal stress at point c is
The shear stress at point c is
Explanation of Solution
Calculation:
Find the normal stress
Substitute
Thus, the normal stress at point c is
Find the shear stress
The point c is edge on the cross section. Since Q is zero.
Substitute
Thus, the shear stress at point c is
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Chapter 8 Solutions
Mechanics of Materials, 7th Edition
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