Bolt Group Moment of Inertia

[transmissioneng]

Can anyone give a basic explanation of how to calculate the Moment of Inertia of a Bolt Group?

I need to determine the size of the rebar in an anchor bolt cage that is to be embedded in concrete.

Thank you.

 

[dinjin]

I have seen two different models.
One about the centerline of the bolt pattern
and the other about the furthest bolt in the
bolt pattern.

 

[transmissioneng]

I believe that it is fairly simple to calcuate the stress in one bar using the parallel axis theorum and My/I, though I am not sure how to select the quantity of rebar needed, i.e. the spacing.

Thanks.

 

[asixth]

Ix=y^2
Iy=x^2
Ip=Ix+Iy

For a bolt group, the Ip is the sum of all individual Ip of each bolt that makes up a group.

Ipgroup=sum(Ix)+sum(Iy)

The force due to moment that acts on each bolt then becomes:

Fx=M*y/Ip
Fy=M*x/Ip

Fres=sqrt(Fx^2+Fy^2)

 

[Lion06]

asixth-
I believe what you are showing is for a torsional moment (or an eccentric shear) on a bolt group. I believe the OP was asking a true MOI of the bolt group.

Transmissioneng-
Is that true? Which are you looking for? For the MOI used for calc'ing tension in a bolt, find the sum of Ab*(d^2) for the bolt group about the axis in question. d is the distance from the line of bolts to the centroid of the bolt group. This is the parallel axis theorem that you talk about. The actual I of the bolt is ignored. Do not add Ix and Iy.

 

[miecz]

I believe the solution provided by asixth applies if the moment is about an axis parallel to the axis of a bolt If your bending moments are about an axis perpendicular to the axis of the bolt, find the center of gravity of the bolt group in each direction. Then I=[Σ]Ad[²] in each direction.

 

[transmissioneng]

Basically I am trying to calculate the number of Anchor Bolts required for a steel pole with high overturning moments at the base.

Thanks.