断面系数公式

断面图形

A：断面積（cm2）

e：到图心的距离（cm）

I：断面二次力矩（cm4）

Z：断面系数（cm3）→I/e

i：断面二次半径（cm）→ √（I/A）正方形 A = a2

e = a/2

I = a4 /12

Z = a3 /6

i = a / √12 =

正方形 A = a2

e = a / √2

I = a4 /12

Z = a3 / ( 6√2 )

i = a / √12 =

長方形斜着 A A = bh

e = bh / √( b2 + h2 )

I = b3 h3 / ( 6 ( b2 + h2 ) )

Z = b2 h2 /( 6 √( b2 + h2 ) )

i = b h /√( 6 ( b2 + h2 ) )

長方形斜着B

A = bh

e = ( h・cosθ + b・sinθ) / 2

I = b h ( h2・cos2θ + b2・sin2θ) /

12

Z = b h ( h2・cos2θ + b2・sin2θ) /

( 6 ( h・cosθ + b・sinθ ) )

i = √( ( h2・cos2θ + b2・sin2θ) /

12 )

正－角管状 A = a2 - a

12

e = a / 2

Z =( a4 - a14 ) / ( 6a )

i = √( ( a2 + a12 ) /12 )

長－角管状 A = bh - b

1h1

e = h / 2

I = ( bh3 - b1h13 ) / 12

Z = ( bh3 - b1h13 ) / ( 6h )

i = √(( bh3 - b1h13 )/ ( 12(bh -

b1h1 )))

圆 A = π d2/ 4 =πR2

e = d / 2

I = πd4 / 64 = πR4 / 4

Z = πd3/ 32 = πR3 / 4

i = d / 4 = R / 2

圆管状 A = π ( D2 - d2 ) / 4

e = D / 2

Z = π( D4 - d4 ) / 32D

i = √ ( D2 + d2 ) / 4

H ・ C

相同形状的断面-1

A = BH - bh

e = H / 2

I = ( BH3 - bh3 ) /12

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

i = √( ( BH3- bh3)/ ( 12( BH - bh )))

H ・ T

A = BH + bh

e = H / 2

I = ( BH3 + bh3 ) /12

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

i = √( ( BH3+ bh3 )/ ( 12( BH + bh)))

相同形状的断面-2

L ・ U

相同形状的断面-3

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 )

H

A = b1h1 + b2h2 + b3h3

e1 = h2 - e2

e2 = (b2h22 + b3h32 + b1h1( 2h2 - h1))

/ ( 2 (b1h1 + b2h2 + b3h3 ))

I = ( b4e13 - b1h53 + b5e23 - b3h43) / 3

Z = I / e1：Z = I / e2

i = √( I / A )

e1 = h-e i = √( I / A )

上下相同 A = b ( h - h

1 )

e = h / 2

I = b ( h3 - h13 ) / 12

Z = b ( h3 - h13 ) / ( 6h )

i = √(( h3 - h13 )/ ( 12(h - h1 )))

正六角形

A = 3/2 ・ h2tan30°

A = 3√3・R2 / 2

e = ＝R

I = 5√3・R4 /16

Z = 5√3・R3 /16

i = √(5/24)・R =

三角形

A = bh / 2

e = 2h / 3

I = b h3 / 36

Z = b h2 / 24

i = √( h / 18 ) = h

半圆－竖着

A = π R2 / 2

e = R

I = π R4 / 8

Z = π R3 / 8

i = R / 2

椭圆－实心

A = π b h / 4

e = h / 2

I = π b h3 / 64

Z = π b h2 / 32

i = h / 4

半圆－管状

A = π ( D2 - d2 ) / 8

e = 2 ( D3 - d3 )/(3π( D2 - d2 ))

I = (D4 - d4) /

- D2 d2 (D-d) /

( (D+d) )

Z = I / e

i = √ ( I/A )

椭圆－管状

A = π ( BH - bh ) / 4

e = H / 2

I = π( BH3 - bh3 ) / 64

Z = π( BH3 - bh3 ) / ( 32H )

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