Structural Analysis- Properties Of Sections

In summary, the dimensions that you need to solve for are 's', the parallel axis theorem, and the distances 'd' and '\rho'. The parallel axis theorem states that {I_{yy}}_c = \Sigma {I_{yy}}_1 + \Sigma A_1 d^2. You can use this to find s by measuring the distance 'd' from the centroid of the combined section to the y axis, and multiplying that by the yy moment of inertia of the combined section about the y axis.
  • #1
Stacyg
25
0
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 !
 

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  • #2
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.
 
  • #3
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.
 
  • #4
Stacyg said:
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 [tex] {I_{yy}}_c = \Sigma {I_{yy}}_1 + \Sigma A_1 d^2[/tex], where [tex] {I_{yy}}_c[/tex] is the combined section yy moment of inertia about the centroid of the combined section, [tex]{I_{yy}}_1[/tex] is the yy moment of inertia of the individual channel about the centroid of the individual channel, [tex]A_1[/tex] is the individual area of the channel, and [tex]d[/tex] is the distance from the centroid of the individual channel to the centroid of the combined section (that is, in this case, [tex] d = \rho + s/2[/tex]). Try plugging in some numbers and resubmit for further assistance. I've given a lot of hints. And don't forget the summation part!
 

1. What is structural analysis?

Structural analysis is the process of studying and understanding the behavior of structures under various loads and conditions. This includes analyzing the internal forces and stresses, as well as the deflections and deformations of a structure.

2. What are the properties of sections in structural analysis?

The properties of sections in structural analysis refer to the characteristics of a cross-section of a structural member. These include the area, moment of inertia, section modulus, and centroid. These properties are important in determining the strength and stiffness of a structure.

3. How are properties of sections determined in structural analysis?

The properties of sections can be determined using mathematical equations or by using software programs specifically designed for structural analysis. The dimensions and shape of the cross-section are used to calculate the properties, which can then be used in the analysis of the structure.

4. Why are the properties of sections important in structural analysis?

The properties of sections play a crucial role in determining the strength and stability of a structure. They are used to calculate the internal forces and stresses in a structure, which help engineers ensure that the structure can withstand the loads and forces it will be subjected to.

5. How do changes in properties of sections affect the behavior of a structure?

Changes in the properties of sections can have a significant impact on the behavior of a structure. For example, increasing the moment of inertia of a beam can make it stiffer and able to carry more load, while decreasing the section modulus of a column can make it more susceptible to buckling. Therefore, careful consideration and analysis of the properties of sections is necessary to ensure the structural integrity and safety of a building or other structure.

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