Formulas 2 - Section Properties(Area , Section Modulus , Moment of Inertia , Radius of Gyration)

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Handbook of Physics Foumulas−Area・Volume Foumulas−Structural Beam .
Formuras 1 . Formuras 1-Section Properties Same Section Properties

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)

Regular Hexagon

kousikidanmen14seirokkaku.jpg (11608 バイト)

A = 3/2 ・ h2 tan30°

A = 3√3 ・ R2 / 2

e = h/2

I =  5√3 ・ R4 /16

Z = 5 R3 /8

i = √(5/24) ・R = 0.457R

danmen14rokkaku.jpg (24413 バイト)

Regular Hexagon

kousikidanmen15seirokkaku.jpg (12068 バイト)

A = 3/2 ・ h2 tan30°

A = 3√3 ・ R2 / 2

e = 0.577h = R

I = 5√3 ・ R4 /16

Z = 5√3 ・ R3 /16

i =  √(5/24) ・ R = 0.457R

danmen15rokkaku.jpg (27114 バイト)

Trapezoid

kousikidanmen20daikei.jpg (11487 バイト)

A = h ・ ( a + b ) / 2

e = h・( a + 2b ) / ( 3 ( a + b ) )

I = h3 ( a2 + 4 ab + b2 )/ ( 36 ( a + b ) )

Z = h2 ( a2 + 4 ab + b2 )/ ( 12 ( a + 2b ) )

i = √(h2 (a2 + 4ab + b2)/ (18 (a + b)2 ) )

danmen20daikei.jpg (33503 バイト)

Triangle

kousikidanmen23sankaku.jpg (11002 バイト)

A = bh / 2

e = 2h / 3

I = b h3 / 36

Z = b h2 / 24

i = √( h / 18 )    = 0.236 h  

danmen23sankaku.jpg (20205 バイト)

Half Round

kousikidanmen26hanen.jpg (11784 バイト)

A = π D2 / 8

e = D (3π- 4) / ( 6π)

I = D4 ・( 9π2 - 64) / ( 1152π)

Z = D3 ・( 9π2 - 64) / ( 192 (3π-4))

i = √( D2 ( 9π2 - 64) / (144π) )   

danmen26hanen.jpg (39533 バイト)

Half Round−Stand

kousikidanmen27hanentate.jpg (11090 バイト)

A = π R2 / 2

e = R

I = π R4 / 8

Z = π R3 / 8

i = R / 2

danmen27hanentate.jpg (16451 バイト)

Oval

kousikidanmen28daen.jpg (11129 バイト)

A = π b h / 4

e = h / 2

I = π b h3  / 64

Z = π b h2  / 32

i = h / 4

danmen28daen.jpg (16185 バイト)

Half Round Tube / Pipe

kousikidanmen30hanenpipe.jpg (11929 バイト)

A = π ( D2 - d2 ) / 8

e = 2 ( D3 - d3 )/(3π( D2 - d2 ))

I = (D4 - d4) / 145.7
     -  D2 d2 (D-d) / ( 56.5 (D+d) )

Z = I / e

i = √ ( I/A )

danmen30haenpipe.jpg (27152 バイト)

Oval Tube / Pipe

kousikidanmen31daenpipe.jpg (14536 バイト)

A = π ( BH - bh ) / 4

e = H / 2

I = π( BH3 - bh3 ) / 64

Z = π( BH3 - bh3 ) / ( 32H )

i = √( (BH3 - bh3 ) / (16( BH - bh) ) )

danmen31daenpipe.jpg (23933 バイト)

Square and Round Hole

kousikidanmen46sikakuana.jpg (11326 バイト)

A = a2 - πd2 / 4

e = a / 2

I = ( a4 - 3πd4 / 16) / 12

Z = ( a4 - 3πd4 / 16) / ( 6a )

i = √ ( I/A )

danmen46sikakuana.jpg (19771 バイト)

Top page Handbook of Mathematics Collection−Mathematics Formulas Structural Calculation Program Take a break
Handbook of Physics Foumulas−Area・Volume Foumulas−Structural Beam .
Formuras 1 . Formuras 1-Section Properties Same Section Properties

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