Question

Required Information A 2-in. steel plate and a 1.25-in. gray cast iron plate are compressed with one bolt and nut. The bolt is 12 in-13 UNC. A VN American Standard plain washer is used under the head of the bolt and under the nut. NOTE: This is a multi-part question. Once an answeris submitted, you will be unable to return to this part. Determine the bolt stiffness. The bolt stiffness is Mlb/in.

Answer 1

Given Information :

• 2-in steel plate and 1.25-in gray cast iron plate are compressed with one bolt and nut.
• Bolt is 1/2 in-13UNC.
• Washer used is : 1/2 N American Standard plain washer.

Solution :

Determine the bolt stffness :

Calculating the grip length :

=ts + to

ts
Thickness of steel plate

tc
Thickness of cast iron plate

1= 2+1

For nominal size of 0.5 in finding the height H for hexagonal nut

$H=\frac{7}{16}\ in$

Total length of the bolt :

$L=l+H$

$L=3+0.4375$

Therefore the suitable length of the bolt is :

Finding the threaded length :

Since the suitable length of the bolt is less than 6 in:

$L_T=2*d+\frac{1}{4}$

$L_T=2*0.5+\frac{1}{4}$

Finding the length of unthreaded portion in the grip :

$l_d=L-L_T$

$l_d=3.5-1.25$

Finding the area of unthreaded portion :

$A_d=\frac{\pi d^2}{4}$

$A_d=\frac{\pi* 0.5^2}{4}$

The area of the threaded portion :

Calculating the Fastener stiffness :

$k_b=\frac{A_d*A_t*E}{A_d*l_T+A_t*l_d}$

$k_b=\frac{0.1963*0.1419*30}{0.1963*0.75+0.1419*2.25}$

Therefore the Bolt Stiffness is :