Structural Analysis- Properties Of Sections

[Stacyg]

The two steel channels shown are arranged to form a compound section in which Ixx=Iyy.
Determine the value of the dimension 's' that will satisfy this condition.

We have been working on radius of gyration, section modulus, second moment of area, the parallel axis theorem, polar second moment. But all the questions we have done in class are using universal beams and none ask to determine the dimension of anything. Please Help !

 

[PhanthomJay]

The dimensions you need are given, except for 's' , which you are asked to find. The properties of one channel are also noted. The I_xx of the combined section is independent of the channel spacing, so you should be able to easily calculate it. Once you know I_xx of the combined section, you are asked to make the
I-yy of the combined section equal to it. This can be done using the parallel axis theorem, about the y axis. Note that in using this theorem, the unknown distance 'd' to use in your 'Ad^2" calculations is measured from the cg of the channel to the y axis. Please show your attempt.

 

[Stacyg]

So would the combined Ixx of both channels be 2 times the Ixxof 1 channel. And sorry, but I'm not sure on how to calculate s using the parallel axis theorem. i haven't been taught much about it just given a bunch of formulas. Thanks For any help.

 

[PhanthomJay]

So would the combined Ixx of both channels be 2 times the Ixxof 1 channel.

Yes, correct.

And sorry, but I'm not sure on how to calculate s using the parallel axis theorem. i haven't been taught much about it just given a bunch of formulas. Thanks For any help.

Have you been given the parallel axis theorem formula $${I_{yy}}_c = \Sigma {I_{yy}}_1 + \Sigma A_1 d^2$$, where $${I_{yy}}_c$$ is the combined section yy moment of inertia about the centroid of the combined section, $${I_{yy}}_1$$ is the yy moment of inertia of the individual channel about the centroid of the individual channel, $$A_1$$ is the individual area of the channel, and $$d$$ is the distance from the centroid of the individual channel to the centroid of the combined section (that is, in this case, $$d = \rho + s/2$$). Try plugging in some numbers and resubmit for further assistance. I've given a lot of hints. And don't forget the summation part!