Formulas - Same Section Properties (A , e , I , Z , i )  group 3

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

kousikidanmen51T.jpg (9631 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 - b ( e2 + h )

e1 = (aH2 + bt2) / ( 2(aH + bt))

e2 = H - e1

I = ( Be13 - bh3 + ae23 ) / 3

Z = I / e1  : Z = I / e2

i = √( I / A )

danmen51T.jpg (24001 バイト)

In the following cross section

When b = B-a and h = e1-t  are all the same,

In a calculation,

it is A: Area ,  e1 and e2: 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. **

kousikidanmen51a.jpg (16789 バイト) It is the sample as the basic figure.
kousikidanmen51b.jpg (23468 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.

 

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.

kousikidanmen51c.jpg (12429 バイト) By the way,

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

.

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