Question

The beam is constructed from three boards. If it is subjected to a shear of V = 5 kip, determine the maximum allowable spacing s of the nails used to hold the top and bottom flanges to the web. Each nail can support a shear force of 500 lb.

Answer 1

Answer / Explanation:

The question is incomplete as the beam was not given. However, kindly find the diagram of the beam below:

Solution:

Referring back to the beam, we have:

I = 1 / 12 ( 1 ) (4)³ + 2 [ 1 / 12 ( 4 ) (1)³ + 4 (1)(2.5)² ]

= 56 cm⁴

τ₁ = vq / it = 5 ( 2.75 )(4)(0.5) / (56)(4) = 1.72mpa

τ₂⁺ = vq / it = 5 (2.5)(4)(1) / (56)(4) = 3.125 mpa

τ₂⁻ = vq / it = 5 (2.5)(4)(1) / (56)(1) = 12.5 mpa

τ₃ = vq / it = 5 (2.5)(4)(1) + (1.75)( 1) (0.5) / (56)(1) = 13.6 mpa

τ₄ = vq / it = 5 (2.5)(4)(1) + (1.5)(1)(1) / (56) (1)

τmax = vq / it = 5 (2.5)(4)(1) + (1.25)(1)(1.5) / (56)(1) = 14.4 mpa