Question 8.12: Determine the proper spacing of the nails used to secure the...
Determine the proper spacing of the nails used to secure the flange boards to the web of the built-up I-beam shown in Figure 8–22. All boards are standard 45 × 190 wood shapes. The nails to be used can safely resist 1000 N of shearing force each. The load on the beam is
shown in Figure 8–16 with P = 2000 N.
Objective Specify a suitable spacing for the nails.
Given Loading in Figure 8–16. P = 2000 N. F_{sd} = 1000 N/nail.
Beam shape and dimensions in Figure 8–22.
Analysis Use the guidelines for specifying the spacing of fasteners.
Results The maximum shearing force on the beam is 2000 N, occurring between each support and the applied loads.
Step 1. The moment of inertia can be computed by subtracting the two open-space rect- angles at the sides of the web from the full rectangle surrounding the I-shape:
I = \frac{190(280)^{3}}{12} – \frac{2(72.5)(190)^{3}}{12} = 2.647 \times 10^{8} mm^{4}
Step 2. At the place where the nails join the boards, Q is evaluated for the area of the top (or bottom) flange board:
Q = A_{p} \bar{y} = (45 mm)(190 mm)(117.5 mm) = 1.00 \times 10^6 mm^3
Step 3. Then the shear flow is
q = \frac{VQ}{I} = \frac{(2000 N)(1.00 \times 10^{6} mm^{3})}{2.647 \times 10^{8} mm^{4}} = 7.56 N/mm
This means that 7.56 N of force must be resisted along each mm of length of the beam at the section between the flange and the web boards.
Step 4. Since each nail can withstand 1000 N, the maximum spacing is
s_{max} = \frac{F_{sd}}{q} = \frac{(1000 N)}{7.56 N/mm} = 132.3 mm
Step 5. A spacing of s = 125 mm would be reasonable.