Question

A steel plate is fastened to a channel using three identical bolts as shown in the figure. The bolts are made of carbon steel of permissible yield strength in shear as 400 N/mm². The plate is subjected to a force of 12 kN. Neglect the weight of the plate. The magnitude of the resultant shear force (in N) on bolt 2 is ............. (Answer in integer) 

 

Hint:

In problems involving uniform force distribution across identical fasteners, simply divide the total force by the number of fasteners to calculate the force on each.

Answer 1

Correct Answer: 4000

The given problem involves determining the shear force on a specific bolt in a system under an applied force. Here are the steps:

1. Identify Forces: The force acting on the plate is 12 kN, translating to 12000 N.
2. Placement and Symmetry: The bolts are placed symmetrically at distances 50 mm and 100 mm from each other, focusing on Bolt 2.
3. Calculate Lever Arms: Calculate the moments about axis perpendicular to the force. Utilize symmetric placement.
   • Total moment is zero for equilibrium: \(12,000 \times 300 = (F_1 \times 100) + (F_2 \times 0) + (F_3 \times 100)\).
   • For symmetry, assume uniform force distribution: \(F_1 = F_3\).
   • Thus, \(12,000 \times 300 = 2F_1 \times 100\).
   • Therefore, \(F_1 = \frac{12,000 \times 300}{2 \times 100}\).
4. Solve for Forces: Calculate shear force on Bolt 2:
   • \(F_2 = \frac{\text{Total Force}}{\text{Number of Bolts}} = \frac{12,000}{3} = 4000 \, \text{N}\).

Conclusion: The resultant shear force on Bolt 2 is 4000 N, which falls within the expected range of [4000, 4000].