断面系数公式.doc

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 =
长方形
A = bh
e = h / 2
I = bh3 /12
Z = bh2 /6
i = h / √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 - a12
e = a / 2
I = ( a4 - a14 ) / 12
Z =( a4 - a14 ) / ( 6a )
i = √( ( a2 + a12 ) /12 )
長－角管状
A = bh - b1h1
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
I = π( D4 - d4 ) / 64
Z = π( D4 - d4 ) / 32D
i = √ ( D2 + d2 ) / 4
H ・ C
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-1
H ・ T
相同形状的断面-2
A = BH + bh
e = H / 2
I = ( BH3 + bh3 ) /12
Z = ( BH3 + bh3 ) / ( 6H )
i = √( ( BH3 + bh3 )/ ( 12( BH + bh )))
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 )
上下不相同
A = bt + b1t1
e = ( +  b1t1 (h-)) / A
e1 = h-e
I = bt3/12 + bty2 + b1t13/12 + b1t1y12
Z = I / e 　　：　Z = I /