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Steel Designers Manual - TheBestFriend.org

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This material is copyright - all rights reserved. Reproduced under licence from The <strong>Steel</strong> Construction Institute on 12/2/2007<br />

To buy a hardcopy version of this document call 01344 872775 or go to http://shop.steelbiz.<strong>org</strong>/<br />

<strong>Steel</strong> <strong>Designers</strong>' <strong>Manual</strong> - 6th Edition (2003)<br />

r =<br />

r<br />

I0 for a typical bolt is then ar 2 and it follows that I0 for the whole group becomes<br />

Ixx + Iyy which, if there are m vertical rows and n horizontal rows, is<br />

I = m<br />

where c is the cross centres between the vertical lines. The distance to the extreme<br />

bolt is<br />

r =<br />

The force in the extreme bolt due to the moment is<br />

f<br />

The force in each bolt due to the shear (assumed equally divided between all bolts)<br />

is<br />

f<br />

2<br />

00<br />

v =<br />

È(<br />

n - ) ˘ m<br />

p<br />

c<br />

ÎÍ ˚˙ +<br />

Ï 1 È(<br />

- 1)<br />

˘<br />

Ì<br />

Ó 2 ÎÍ 2 ˚˙<br />

Rxr<br />

I<br />

m = 00<br />

R<br />

mn<br />

2 2<br />

ÈÊ<br />

pˆÊcˆ˘ Í +<br />

Î<br />

Ë ¯ Ë ¯<br />

˙<br />

2 2 ˚<br />

2 2<br />

p c<br />

=<br />

2 2<br />

Ê ˆ Ê ˆ<br />

+<br />

Ë ¯ Ë ¯<br />

J= ( n-1)<br />

J = 0<br />

È(<br />

n-1-2J) ˘<br />

p n<br />

ÎÍ 2 ˚˙ +<br />

2 2<br />

2<br />

¸<br />

˝<br />

˛<br />

J= ( m-1)<br />

 Â<br />

J = 0<br />

È(<br />

m-1-2J) ˘<br />

c<br />

ÎÍ 2 ˚˙<br />

The combined force per bolt is the resultant of these two: see Fig. 23.5.<br />

The resultant bolt force is then checked against the bolt strength in single shear,<br />

double shear or bearing as is appropriate. In the case of bearing, however, it should<br />

be remembered that the full strength cannot be achieved if the end distance meas-<br />

Fig. 23.5 Resultant force<br />

Methods of analysis of bolt groups 679<br />

90°<br />

2<br />

lever arm<br />

to extreme bolt

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