Seismosoft | Earthquake Engineering Solutions

Hi:

I'm new using seismostruct. I have a basic questions regarding the formulas that appears in the verification example 2, to calculate the constant G (shear modulus) and J (Polar moment of inertia. Can any body tell me the formula for both, G and J? I have use several ones but I'm not getting the same results.

Hi nrojas.

I suspect that the problem lies in the definition of J.

G is easy enough. It is given by:

G = E/(2(1+n)) where n is Poisson's ratio.

J, however, is often confused with the polar moment of inertia.

I suspect you have taken J as the polar moment of inertia, J = I1+I2.

In SeismoStruct, J is the torsional constant, not the polar moment of inertia. The torsional constant is equal to the polar moment of inertia for circular sections and circular sections only. For other sections, it is some fraction of the polar moment of inertia. For thin-plate I-sections, it is typically a small fraction of the polar moment of inertia.

One common means of estimating the torsional constant for I-shaped members is:

Torsional Constant = Sum of bt^3/3 for all plates in the section. b is the plate width and t is the thickness. Note that in computing the torsional constant, you are always cubing the smaller dimension. Hence, it's small value relative to I1 and I2 for an I-shape.

So, while it is not explicitly stated in the problem, I can peruse my steel manual and find that the section having A=31.2, I1 = 933, and I2 = 301 is a W12X106. My steel manual also gives me the torsional constant for a W12X106, J = 9.13.

G = 29000/(2(1+0.3)) = 11,154
GJ = 11,154(9.13) = 101,835 as given in the problem.

If I use the approximate method described above, I'll get J = 8.73. So you can see, it's best to take the number from a manual of steel construction when available, because it is based on a more rigorous means of calculation J. The estimate isn't bad, though, is it?

Best of luck nrojas.

Thanks huffte for your explanation:

However, I believe we are talking about two different problems. I'm talking about the verification problem 2 of chapter 2 of the verification problems (page 11 of the pdf document). This problem use an area of 144 in2; E = 3600 ksi; I = 1728 in4 (Its a square 12 in by 12 in section). I looked for an equation for the torsional constant J for square or rectangular section. I found this one:
J = 0.80295 Io; where Io = b^4/6
With this equation I got J = 2,774.96 in^4

I calculated G = E/2.3 (using 0.15 for concrete Poisson's ration

And thus G = 1565.22 ksi;

GJ = 4343315.71 kip-in^2

In this example, GJ = 4380845 kip-in^2. It can be appreciated that both numbers are very close. However I want to know what specific equation does seismosoft use for the computation of J for square and rectangular sections.

Thanks in advance.

Perhaps we are using different versions of SeismoStruct, nrojas. Because Example 2 of Chapter 2 is the problem I previously discussed in my last post. Example 1 of Chapter 2 is the problem you have most recently described.

Roarke's Formulas for Stress and Strain gives the following:

Square: J = 2.25(a/2)^4 = 0.84375a^4/6 to compare with your value.

Rectangle: J = (a/2)(b/2)^3[16/3-3.36(b/a)(1-(b/a)^4/12)]

"a" is the long side; "b" is the short side.

This is the reference I have used. I an not certain what is used in SeismoStruct.

Also note that SeismoStruct uses 0.2 for Poisson's ratio for concrete. See the notes to the Help Section entitled "Materials".

Using these parameters I get GJ = 4,374,000 k-in^2. This is 0.16% lower than the number reported in the Verification Manual.

If I use Poisson's ratio of 1.2 and back out J to give the GJ reported by SeismoSoft, I get the following formula for J, which may or may not be more accurate than the ones we have used:

J = 2.2535(a/2)^4

Best of luck nrojas.