Question

Two steel plates of 15 mm thickness each are clamped together with an M14 x 2 hexagonal head bolt, a nut, and one 14R metric plain washer under the nut.
a) What is a suitable length for the bolt, rounded up to the nearest 5 mm?
b) What is the bolt stiffness?

Answer 1

Answer:

a) 50 mm

b) 808.24 MN/m

Explanation:

Given:

Thickness of each steel plate = 15mm

a) To find suitable length of bolt, we'll use:

Length of bolt = grip length + height of nut

To find the grip length since there is a washer, we'll use:

Grip length = plate thickness + washer thickness

Since we have 2 plates of 15mm thickness,

Plate thickness = 15 + 15 = 30mm

Using the table, a metric plain washer has a thickness of 3.5mm

Grip length = 30 + 3.5 =33.5 mm

Height of nut: Using table A-31, height of hexagonal nut is 12.8 mm

Therefore,

Length of bolt = 33.5 + 12.8 = 46.3

Rounde up to the nearest 5mm, we'll get 50mm

Length of bolt = 50mm

b) Bolt stiffness:

Threaded length for L ≤ 125mm

LT = 2*d + 6

Where d = 14mm, from table(8-7)

= 2*14 + 6

= 34 mm

Area of unthreaded portion:

Ad= $\frac{\pi}{4} d^2 = \frac{pi}{4} * 14^2 = 153.94 mm^2$

Length of unthreaded portion in grip:

Ld = 50 - 34 = 16mm

Length of threaded portion in grip:

Lt = 33.5 - 16 = 17.5mm

Bolt stiffness = $\frac{A_d A_t E}{A_d l_t + A_t l_d}$

$= \frac{153.94 * 115 * 207}{(153.94*17.5)+(115*16)} = 808.24$

Bolt stiffness = 808.24 MN/m