Finding Neutral Axis & Second Moment on a T-beam

In summary, the conversation involved a person seeking help with finding the neutral axis and second moment of a T-beam. They provided measurements of the beam and explained their understanding of the process, but were stuck on finding the thickness of the bottom rectangle of the T-beam. Another person provided assistance and explained the use of the parallel axis theorem to find the second moment of area. The conversation ends with the person thanking the helper for their help and expressing their confusion with the calculations.
  • #1
Struggling
52
0
hi I am having trouble with finding the neutral axis and second moment of a T-beam.

here are the measurements of the beam:
http://img354.imageshack.us/img354/8648/beam6xl.jpg [Broken]

i understand to find the neutral axis you divide the beam into 2 rectangles but iam having problem finding the thickness of the bottom rectangle of the t-beam. how can i find the neutral axis if i can't find the width of the bottom rectangle, because i can't find the area of it. iam totally stuck.

also calcutale the second moment of area

for a member with a rectangular cross section bent about the z axis,
Izz =(1/12)bd^3
to determine the second moment of area of a cross section made of a number of different shapes the parallel axis theorem is used.
Iaa = Izz + Ay^2

what i did was:

Izz = (1/12)6.4(38.1)^3
= 29496.72

but it doesn't make sense i was going to insert this into Iaa= Izz + Ay^2 to get the second moment of the vertical.

can someone please help :cry:
 
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  • #2
the bottom thickness is 6.4 just as the vertical is
 
  • #3
how did you get that?
or is it just assumed that it is in my case because both beams are of the same length?
 
  • #4
no i did not assume, it is usually the case that the webs of a beam are the same thickness. In this case since the bottom thickness is not given it should be of the same thickness.
 
  • #5
ARGH :devil: i still can't get it this is what i had
rectangle 1 = 38.1 x 6.4
rectangle 2 = 31.7 x 6.4

from these notes:
http://img400.imageshack.us/img400/8148/neutralaxis9on.jpg [Broken]

i got this:

(Ycent x A) = (sumof)Ai Yi
Rectangle 1
(Ycent x 446.72) = 243.84(3.2)
= 1.746
Rectangle 2
(Ycent x 446.72) = 202.88(19.05)
= 8.651

theyre sposed to be the distances from the arbitary axis to the centroid but common sense tells me its wrong.
please help
 
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  • #6
anyone at all?
 
  • #7
Ok, I'm not sure I understand the method you are using. The way I do it is to consider the distance from the bottom edge of the lowest rectangle to the central axis. Then we have the formula:

[tex]A_1*d_1 + A_2*d_2=A_{1+2}*d_0[/tex]

where A1 is the area of rectangle 1, d1 is the distance from the bottom of the lower rectangle to the centroid of rectangle 1, and d0 is the distance of the central axis.

[tex](38.1*6.4)(3.2)+(31.7*6.4)(22.25)=(38.1*6.4+31.7*6.4)d_0[/tex]

And we find that the neutral axis is 11.85mm above the lowest point, or 5.45mm above the intersection of the two rectangles.

Once you know the location of the neutral axis you should be able to find the second moment of area using the parallel axis theorem.
 
  • #8
thanks for the help but i still am not able to find the second moment of area.

Iaa = Izz + Ay^2

iam lacking a detailed description of how to use the formula.
i understand that

Iaa = parrallel axis
Izz = Centroid Axis
A = Area
y = distance between Iaa and Izz

but i have no clue how to do it. my first attempty went something like this
Neutral axis = 11.85mm from the bottom axis (as kazaa stated above)
Iaa = 11.85+202.88(10.4)^2
Iaa = 21955.35
which obviously isn't the answer so i tried
Izz = (1/2)bd^3
Izz = (1/12)6.4x31.7
Izz = 16.9

Iaa = 16.9 + 202.88(5.05)^2
Iaa = 26145.33

can anyone help me out with what iam supposed to use or direct me to a detailed explanation, i have searched many pages on yahoo etc but still fail to find an explanation i can relate to and the only textbooks i have are very brief on it.
 
  • #9
To use the parallel axis theorem, consider each rectangle seperatly, so we'll call the top one A, and the bottom one B. For each rectangle, calculate the second moment of area about its own neutral axis, and then add to that A*y^2 where y is the distance between the rectangles neutral axis, and the overall neutral axis.

So for rectangle A, the second moment of area is
[tex]\frac{bd^3}{12}[/tex]
And the distance between rectangle A's neutral axis and the overall neutral axis is
[tex]y=6.4+\frac{31.7}{2}-11.85[/tex]
[tex]y=10.4[/tex]

So A's contribution to the total second moment of area is:
[tex]I_A=\frac{bd^3}{12}+(10.4^2)bd[/tex]

And I was about to put all that in my calculator, but I just realized I left it at uni after a physics prac today :cry: :cry: But anyway, you should be able to work it out from there.
 
  • #10
oh alright well wat i ended up doing this morning was:

Izz = (1/12)6.4x31.7^3 = 16989.34
Iaa = (1/12)6.4x38.1^3 = 29496.72

Iaa = Izz +Ay^2
therfore

(Square Root)Iaa-Izz/A = Y
(square root) 29496.72 - 16989.34/ 446.72 = Y
Y = 5.29mm

and i just tried the forumla you gave me and i got and answer of 43363.07?

Ia = (6.4)(31.7)^3/12 + (10.4^2)(38.1)(6.4)
Ia = 16989.34+26373.73
Ia = 43363.07

sooo confused argghhh

ur help is much appreciated kazaa thank you
 

1. What is the neutral axis of a T-beam?

The neutral axis of a T-beam is the line that divides the cross-sectional area of the beam into two equal parts. It is the line where the beam experiences zero stress when subjected to bending.

2. How is the neutral axis of a T-beam determined?

The neutral axis of a T-beam can be determined by using the principle of statics, where the sum of forces and moments acting on the beam must be equal to zero. This can be done by calculating the centroid of the cross-sectional area of the beam.

3. What is the second moment of area on a T-beam?

The second moment of area, also known as the moment of inertia, is a measure of how resistant a beam is to bending. It is calculated by integrating the area of the cross-section with respect to the distance from the neutral axis.

4. Why is it important to find the neutral axis and second moment of area on a T-beam?

Knowing the neutral axis and second moment of area is crucial in designing and analyzing T-beams, as it allows engineers to determine the maximum stress and deflection the beam can withstand. It also helps in selecting the appropriate materials and dimensions for the beam.

5. Are there any simplified methods for finding the neutral axis and second moment of area on a T-beam?

Yes, there are simplified methods such as the parallel axis theorem and the geometric method that can be used to find the neutral axis and second moment of area on a T-beam. However, these methods may not be as accurate as the traditional method of integration.

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