The beam is fabricated from four boards nailed together as shown. Determine the shear force each nail along the sides C and the top D must resist if the nails are uniformly spaced at s=3 in. The beam is subjected to a shear of V=4.5 kip.

The shear force
The shear force
Answer to Problem 1RP
The shear force
The shear force
Explanation of Solution
Given information:
The shear force is
The uniform nail spacing is 3 in.
Calculation:
Sketch the diagram of the T section as shown in Figure 1.
Refer Figure 1,
The area of the beam is the sum of area of three rectangles 1, 2, and 3.
The dimensions of rectangle 1 as width
The dimensions of rectangle 2 as width
The dimensions of rectangle 2 as width
Find the value of area section 1 as shown below:
Substitute 10 in. for
Find the value of area section 2 as shown below:
Substitute 4 in. for
Find the value of area section 3 as shown below:
Substitute 12 in. for
Calculate the centroid of
Here,
Substitute
Sketch the diagram of
Calculate the moment of inertia of the beam (I) as follows:
Refer to Figure 2:
The value of
The value of
The value of
Substitute 10 in. for
Calculate the first moment area
Here,
Refer to Figure 2.
The value of
Substitute
Calculate the first moment area
Here,
Refer to Figure 2.
The value of
Substitute
Show the formula for shear flow
Here, V is the shear force, I is the moment of inertia, and
Substitute
Show the formula for shear flow
Here, V is the shear force, I is the moment of inertia, and
Substitute
Calculate the shear force
Here, s is the spacing and
Substitute
Hence, the shear force
Calculate the shear force
Here, s is the spacing and
Substitute
Hence, the shear force
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