Answer:
The question is incomplete. The mass of the board is needed in order to calculate the moment of inertia of the beam. 91.67 * 10⁶mm⁴ is used as the moment of inertia in the calculation below. You can always substitute to get your answer.
The spacing is 95.1mm
Explanation:
Given'
vertical shear V = 1200N
Shearing force = 700N
Thickness of each board = 50mm
The spacing can be calculated using the formula;
F = q * s---------------------------1
but, q = VQ/I---------------------------------2
Therefore, F = VQ/I * s ------------------------------3
where,
s = spacing
v = vertical shear
f = shearing force
I = moment of inertia
Making s subject formula in equation 3, we have
s = FI/VQ-------------------------------4
but Q = YA
A = area = 50 *(150)
Y = 75
therefore, Q = 75 *50*150
Q= 5.625* 10⁶mm⁴
Substituting into equation 4, we have
s = 700 * 91.67 *10⁶) / (1200*5.625* 10⁶)
= 6.42*10¹⁰ /6.75*10⁸
= 95.1mm
