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Anchor Bolt Tension in Circular Pattern (For Vessels) 1

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techiestruc

Structural
Nov 23, 2011
37
Hi!

In ASCE Wind Loads and Anchor Bolt Design for Petrochemical Facilities, the anchor bolt maximum tension is calculated by the formula below:

Tension = 4*M / (N*BC) - W / N

Where:
M = maximum moment on vessel
N = number of anchor bolts
BC = bolt circle diameter
W = minimum weight of vessel

It is stated there that it was calculated by assuming an elastic distribution of forces and moments, which is based on the moment inertia of the bolt group.

I'm just curious on how did they arrive on this formula. How was it derived?
Can anyone show me the formulas used? Thanks :)
 
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For a thin cylindrical beam, bending stress is equal to Mc/I +/- P/A.
Set c = R, I is pi*R^3*t, and A is 2*pi*R*t, where t is the thickness, R is the radius.
Then stress is equal to M/(pi*R^2*t) +/- P/A.
This is a varying stress, but the equivalent axial load that would give that same stress is A*stress or
(M/(pi*R^2*t) +/- P/A) * 2pi*R*t = 2M/R +/- P
And, assuming this total force is divided amongst N bolt, the load per bolt is 2M/(RN) +/- P/N or 4M/(ND) +/- P/N

There may be more elegant ways to show that, but it's still based on the Mc/I +/- P/A.

People have tried to complicate this by considering the composite steel/concrete area in the foundation. However, the stress in the cylindrical shell is assumed to be of this load distribution, so there's not much motivation to assume a different load distribution above the concrete surface than below.
 
Thanks for your fast response. Your answer did enlighten me. :)
 
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