ISO top hat second moment of area

hi,

Does any one know how to calculate second moment of area and for top hat section? I follow ISO 12215:5 rules, i don’t know what assumptions are made in ISO, my results for standard sections are different than those in table from ISO.

 

Can you give the results you get and the results by the ISO table.

This may help in ascertaining where your error, if any, actually is.

You should also take a standard section Tee from any aluminium catalogue. Run the calc again, and compare with the value given in the catalogue and see if your results are the same. This will indicated where, if any, your errors may be.

 

1. In ISO they use weight of stiffener laminate instead of thickness of stiffener laminate. I would suggest ISO tables assume that 450g of CSM gives 1mm of thickness in structure, but this can be source of difference. Try to compare with tables in Larsson's 'Principles of Yacht Design', they have used thickness there.

2. The approach for steel/alloy beams does not work for real life composite stiffeners (works only with stiffeners built completely of CSM). Composites possess different strength for tension and compression, so effective SM should be obtained by reduction/increase of geometric SM considering tension/compression properties of stretched/compressed parts of stiffener.

 

Alik

When a structural member is in either tension or compression how does one determine this? By calculating the section modulus of the section from its geometry.

You are saying you know in advance whether a section is going to experience tension or compression before you have calculated any values. This does not make sense. Notwhistanding this fact, how do you ascertain the magnitude of the compression....from the section modulus!

The geometry defines how the structure behaves. The "thicknesses" enables one to calculate the section modulus and then finally the material dictates whether the behaviour is within acceptable limits or not.

 

It is easy - check geometrical SM only and estimate neutral axis. This axis defines tension and compression areas. Then, make next approximation assuming tension properties for stretched areas and compression properties for compressed areas.

This is standard approach to calculate hull girder for boats, so we can use it for complex stiffeners. For local strength, most of stiffeners experinece tension at top side, compression at hull plate side.

 

Important thing is that stiffener thickness is given. You can see it on attache pictures. Stiffeneras laminate is mat with glass content equal 30%, tghe same with assosiating plate.

for my calculations:
A1,A2,A3 – areas of square sections, like on Picture.
y1,y2,y3 – distance between reference axis and centre of each square
yn1,yn2,yn3 – distance between neutral axis and centre of each square
I1,I2,I3 – second moment of inertia around axis parallel to reference, and coincidence with centre of each square.

 

apfelsaft

You haven't shifted the calculated "I" (your column X and Y) to the "I" about the neutral axis!
The ISO "I" is about the neutral axis, hence the "Ina" notation.

 

I havaent calcualted "I" around reference axis, results are around neutral axis. I used Parallel Axis Theorem (Ii=I+A*y^2, Ii- second moment of area around i-axis, I - second moment of area between axis considence with centroid, and i-axis, they have to be parallel)

 

2apfelsaft
I just checked couple of numbers in ISO tables using my Excel spreadsheet for top hat beam - results are same. Find mistake in Your calculations.

 

I know that there is mistake between my spreadsheet and ISO, but I don’t know were, I don’t know what is wrong in my understanding of this calculations this is the reason why I started this thread. So it will be useful for if someone could explain me how to do this properly.

 

When you calculate I3 of the web, you should use tw instead of tw/2 as a width of the web. You really don't need that cos-term, this is inaccurate due to the laminate anyway. Check also your calculation of neutral axel, use the outer surface of the plate as a reference.