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# Re: Bolt Pre-Tensioning

• To: <seaint(--nospam--at)seaint.org>
• Subject: Re: Bolt Pre-Tensioning
• From: "Glenn Otto" <glenn.liberty.engineering(--nospam--at)worldnet.att.net>
• Date: Wed, 22 Jul 1998 14:49:12 -0400

```Dan,

Consider a bolt that is torqued to its proof load and clamps two plates:
FBD on plates:

Co                          Co
||<-------                        |----->  ||
||<-------          To           |----->  ||
||         ---------> <--------- |         ||
||<-------                        |----->  ||
||<-------                        | -----> ||

To = initial bolt tension
Co = initial clamping force compressing plates

As an external load, P, is applied, the tension in the bolt and the
clamping
force become T and C, respectively

P/2           C                          C                 P/2
<----     ||<-------                        |----->  ||   ---->
||<-------          T            |----->  ||
||         ---------> <--------- |         ||
||<-------                        |----->  ||
<----     ||<-------                        | -----> ||  ---->
P/2                                                             P/2

Therefore:

T = C + P

While the plates remained clamped, the elongation of the bolt is equal to
the increase in thickness of the connected plates: (using a strain
equation)

Delta_bolt = Delta_plate

T - To                Co - C
_______      =    _______
A_b E_b            A_p E_p

|           P                   |
|  ________________  |
T =  To  +  |          |  A_p E_p  |    |
|  1  +  | ________  |    |
|          |  A_b E_b  |    |

has to overcome the initial tensioning via decompressing the plates.  If,
for example, the
plate's lateral dimensions were 3 times bolt diameter, computing the
respective areas, and plugging into the equation, it would show that

T ~  To  +  ( 0.088 P )

So,

To = .77 Fu
P  < or = .33Fu

Tmax = (.77 + (.088 x .33)) Fu = .80 Fu

The purpose of this is to keep the plates together, slip
critical....another discussion.

Hope it helps,

Glenn Otto

Disclaimer:  "My opinions don't necessarily reflect those of the corporate
entity"

```