Three boards are nailed together to form the beam shown, which is subjected to a vertical shear. Knowing that the spacing between the nails is s = 75 mm and that the allowable shearing force in each nail is 400 N, determine the allowable shear when w = 120 mm.
Fig. p6.89
The allowable shear in the beam.
Answer to Problem 89RP
The allowable shear in the beam is
Explanation of Solution
Given information:
The spacing between the nails is
The allowable shearing in each nail is
Calculation:
Sketch the cross section as shown in Figure 1.
Refer to Figure 1.
Calculate the moment of inertia (I) as shown below.
Here, b is the breadth of the section, h is the height of the section, A is the area of the beam, and
Calculate the moment of inertia for the whole symmetrical section as shown below.
Calculate the first moment of area (Q) as shown below.
Calculate the horizontal shear per unit length (q) as shown below.
Here, V is the vertical shear.
Substitute
Calculate the allowable shear
Substitute
Therefore, the allowable shear is
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Chapter 6 Solutions
Mechanics of Materials, 7th Edition
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