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Re: Bolt Pre-Tensioning

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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  |    |



If you could follow all the bad graphics, it shows that the direct loading
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"