Formulas - Same Section Properties (A , e , I , Z , i )    group 1

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Handbook of Physics Foumulas−Area・Volume Foumulas−Structural Beam .

leabul1e.gif (987 バイト)  Formulas 1-Section Properties     leabul1e.gif (987 バイト)  Formulas 2-Section Properties   leabul1e.gif (987 バイト)  Same Section Properties 2  leabul1e.gif (987 バイト)  Same Section Properties 3 

kousikidanmen49H.jpg (12067 バイト)

Group of the same section properties, cf. following cross section

A:Area (Units2
e:Extreme point(Units)

I:Moment of Inertia(Units4
Z:Section Modulus(Units3) → I/e
i:Radius of Gyration(Units) → √(I/A)

A = BH - bh

e = H / 2

I = ( BH3 - bh3 ) /12

Z = ( BH3 - bh3 ) / ( 6H )

i = √( ( BH3 - bh3 )/ ( 12( BH - bh )))

danmen49H.jpg (25076 バイト)

In the following cross section

When b = B-a and h = H-2t  are all the same,

In a calculation,

it is A: Area, e: Extreme point
I: Moment of Inertia, Z: Section Modulus, i: TRadius of Gyration  becomes all same.

** But, as for the torsion strength, strength may not be the necessarily same because it is different. **

kousikidanmen49a.jpg (17546 バイト) It is the sample as the basic figure.
kousikidanmen49b.jpg (17864 バイト) The positions of the centroid are different in the figure of right and left,

The distance from top and bottom agrees,

The section properties (A,e,I,Z,i) becomes same in a calculation.

kousikidanmen49c.jpg (24100 バイト)  

The number of number of sheets of the rib is how many,

If the total of the thickness of the board long is "a",

The section properties (A,e,I,Z,i) becomes same in a calculation.

kousikidanmen49d.jpg (28570 バイト)

By the way, The section properties (A,e,I,Z,i) becomes same in a calculation.

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leabul1e.gif (987 バイト)  Formulas 1-Section Properties     leabul1e.gif (987 バイト)  Formulas 2-Section Properties   leabul1e.gif (987 バイト)  Same Section Properties 2  leabul1e.gif (987 バイト)  Same Section Properties 3