Solution to Problem 592 | Spacing of Rivets or Bolts in Built-Up Beams | Strength of Materials Review at MATHalino

Problem 592
A wide flange section is formed by bolting together three planks, each 80 mm by 200 mm, arranged as shown in Fig. P-592. If each bolt can withstand a shearing force of 8 kN, determine the pitch if the beam is loaded so as to cause a maximum shearing stress of 1.4 MPa.

Solution 592

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$(\,f_v\,)_{max} = \dfrac{VQ_{NA}}{Ib}$

Where

$(\,f_v\,)_{max} = 1.4 \, \text{ MPa}$

$Q_{NA} = 200(80)(140) + 100(80)(50)$

$Q_{NA} = 2\,640\,000 \, \text{ mm}^3$

$I = \dfrac{200(360^3)}{12} - \dfrac{120(200^3)}{12}$

$I = 697\,600\,000 \, \text{ mm}^4$

$b = 80 \, \text{ mm}$

Thus,
$1.4 = \dfrac{V(2\,640\,000)}{697\,600\,000(80)}$

$V = 29\,595.15 \, \text{ N}$

Spacing of bolts
$s = \dfrac{RI}{VQ_{flange}}$

$s = \dfrac{8(1000) \times 697\,600\,000}{29\,595.15 \, [ \, 200(80)(140) \, ]}$

$s = 84.18 \, \text{ mm}$ answer

Solution to Problem 592 | Spacing of Rivets or Bolts in Built-Up Beams

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