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# Frequency of Tall Steel Tanks

• To: <seaint(--nospam--at)seaint.org>
• Subject: Frequency of Tall Steel Tanks
• From: "Jim Lutz" <Jim.Lutz(--nospam--at)bhcconsultants.com>
• Date: Mon, 9 Oct 2006 08:47:21 -0700

Title: Frequency of Tall Steel Tanks

I would treat this as a cantilever beam of uniformly distributed mass and check it both empty and dry, since the full tank will have a much lower frequency than the empty one due to the difference in mass.

Just for illustration, I took a look at your tank (8 dia x 66 ft high) and assumed a .25 inch shell.  The mass is about 8 slugs/ft for the dry tank and about 105 slugs/ft for the full tank.

The natural frequency of a cantilever beam of uniformly distributed mass is

Omega = (lambda^2)*(sqrt(EI/rho)/L^2

Where omega is the natural frequency in radians per second, lambda^2 is a modal constant (3.52 for the first mode), E is the modulus of elasticity of the tank material, I is the moment of inertia of the tank cross section, L is the length of the beam, and rho is the unit mass per length of the beam. You have to make sure to use consistent units.

For this tank, you end up for the dry tank with an omega of 37.86 radians per second, which is 6.03 Hz or a period of about 0.17 second. For the full tank, the frequency is about 1.66 Hz or a period of 0.60 seconds. The wind provisions dont require you to consider flexibility for the gust factor until the period is 1.0 seconds or higher.

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