Question

If each of the three nails has a diameter of 4 mm and can withstand an average shear stress of 60 MPa, determine the maximum allowable force P that can be applied to the board.

a) 1695 N
b) 2825 N
c) 5075 N
d) 5640 N

Answer 1

The maximum allowable force P that can be applied to the board can be determined by using the formula for shear stress and the cross-sectional area of the nails. By substituting the given values into the formula, we find that the maximum allowable force P is approximately 1695 N.

Step-by-step explanation:

The maximum allowable force P that can be applied to the board can be determined using the formula for shear stress, which is the force applied divided by the cross-sectional area of the nail:

First, we need to calculate the cross-sectional area of one nail. Since each nail has a diameter of 4 mm, the radius can be calculated as half the diameter, which is 2 mm or 0.002 m. The cross-sectional area can be calculated as pi multiplied by the square of the radius. Substituting the values, we get: Area = pi * (0.002 m

1. 
   
2. Substituting in the given values, we have:
3. 
   

60 MPa = P / (pi * (0.002 m)2)

1. 
   
2. Now, we can solve for the maximum allowable force P by isolating it:
3. 
   

P = 60 MPa * (pi * (0.002 m)2)

1. 
   
2. Calculating the expression, we find:
3. 
   

P ≈ 1695 N