Concept explainers
Three steel plates, each 13 mm thick, are welded together to form a cantilever beam. For the loading shown, determine the normal and shearing stresses at points d and e.
Fig. P8.53 and P8.54
The normal and shearing stress at point a and b.
Answer to Problem 54P
The normal stress at point d is
The shear stress at point d is
The normal stress at point e is
The shear stress at point e is
Explanation of Solution
Given information:
The thickness (t) of the steel plate is
Calculation:
Refer to Figure P8.51 in the textbook.
Forces at H are as follows:
The force in x direction,
The force in y direction,
The force in z direction,
Moments at H are as follows:
Find the moment about x axis as follows:
Find the moment about y axis as follows:
At point A:
Sketch the I section as shown in Figure 1.
Refer to Figure 1.
Find the centroid section
Find the centroid section
Find the area of the section using the relation:
Here, b is the width and d is the depth of the flange and web respectively.
Refer to Figure 1.
Substitute
Find the moment of inertia
Substitute
Find the moment of inertia
Substitute
At point d:
Sketch the I section for point b as shown in Figure 2.
Refer to Figure 2.
Find the area of section (A) as follows:
Substitute
Refer to Figure 2.
The centroid of the
The centroid of the
Find the first moment area
Substitute
Find the first moment area
Substitute
Find the first moment area
The point e is located at edge. Since
The point e is located at edge. Since
Determine the normal stress at point d using the relation:
Here,
Substitute
Thus, the normal stress at point d is
Determine the shear stress at point a due to
Substitute
Sketch the horizontal direction of shear stress as shown in figure 3.
Determine the shear stress at point a due to
Substitute
Sketch the vertical direction of shear stress as shown in figure 4.
Find the shear stress at point d using superposition method.
Thus, the shear stress at point d is
Determine the normal stress at point e using the relation:
Substitute
Thus, the normal stress at point b is
Determine the shear stress at point e using the relation:
The point e is located on edge.
The shear stress at point e is zero.
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Chapter 8 Solutions
Mechanics of Materials, 7th Edition
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