reaction force/lenght for seismic and wind

[inammanj123]

Hi,

In tank design calculation we provided foundation data like done in the attached file. The issue is that our client has commented on the formula of reaction due to seismic and wind. That comment can be seen in the attachment.We used the formula of M/pi* D^2, which we came up using following derivation:

With seismic moment action at the end, following will is derivation for reaction force:
Reaction force x diameter= seismic moment(Ms)
Reaction force= seismic moment/ diameter(Ms/D)
Reaction due to seismic= reaction force/circumference = (Ms/D)/(PI*D)= Ms/(PI*D2)


the formula which client is asking for will be possible if moment is located in the center.



Regards,
Inam

 

[MAshok]

The Client’s comment is correct.
The derivation is:
Section modulus of shell z = (PI() * D^2 * t) / 4.
Stress on shell due to moment = M/z = 4 * M / (PI() * D^2 * t)
Force per unit circumference = F = stress * thickness
= (+/-) 4 * M / (PI() * D^2) KN/M
(This load varies from (+) F (upward force) at one side of the shell to (–) F (downward force) on the opposite side.)

 

[inammanj123]

Thanks

Mashok can you please give me some reference of these formulation.

 

[inammanj123]

Force per unit circumference = F = stress * thickness

Can any one tell how this formula has come.

 

[MAshok]

Total Force applied = F.
Total area of shell transferring the load to foundation = PI() * D * t .
Assuming the force is uniformly distributed around shell circumference:
Force per unit circumference = F / (PI()*D) ;
But,
Stress = Force / area = F/(PI() * D * t)
= F/(PI() * D ) * ( 1/t)
Stress * t = F/(PI() * D ) * ( 1/t) * t = F/(PI() * D ) = Force per unit circumference.
The above equation is true even if the force is not uniformly distributed as in the case of stress due to moment. The maximum force per unit circumference will be equal to the maximum stress * thickness, where the maximum stress due to bending is (M/Z)
Hope this answers your query.

 

[inammanj123]

thanks mashok for clearing confusion

regards,
inam