常用截面几何特性计算公式

V = 1 pr2h 3
A = pr 2 A0 = prl An = pr (r + l )
l = r2 + h2 h
ZG = 4
图
形
(续)
体积 V、底面积 A、侧面积 A0、全面积 An、重心位置 G 的计算公式
h V = 6 (2ab + ab1 + a1b + 2a1b1) A1 = a1b1 A = ab
a2 + b 2 + 4ab H 3 36(a + b)
Wxa
=
H 2 (a 2 + 4ab + b2 ) 12(a + 2b)
Wxb
=
H 2 (a2 + 4ab + b2 ) 12(2a + b)
H ×
3(a + b) a2 + 4ab + b2 2
H (2a + b) 3(a + b)
bH 2
bH 3 36
A0
=
3 2
a
4l 2 − a 2
An = A + A0
h ZG = 4
V
=
hA 3
�
�1 + � �
a1 a
+
� �� �
a1 a
� �� �
2
� � � �
A1
=
33 2
a2
1
A = 3 3 a2 2
A0 = 3g(a1 + a)
An = A + A1 + A0
h(a 2 + 2a1a + 3a 2 )
a2
a4
12
a2 Wx = 6 Wx1 = 0.1179a3
a = 0.289a
12
a ex = 2 ex1 = 0.7071a
a2 −b2
a4 −b4 12
Wx
=
a4 −b4 6a
Wx1
=
0.1179
a4
− b4 a
0.289 a2 + b2
a ex= 2 ex1 = 0.7071a
ab
ab 3
12
第 1 章 常用资料、数据和一般标准
G1 常用几何体的体积、面积及重心位置�表 G1-1�
图
形
表 G1-1 常用几何体的体积、面积及重心位置
体积 V、底面积 A、侧面积 A0、全 面积 An、重心位置 G 的计算公式
图
形
V = a3 A = a2 A0 = 4a2 An = 6a2 d = 3a (d为对角线 )
bH 2 Wxa = 24
bH 2
H = 0.236H
H
32
3
Wxb = 12
4
截面形状
面积 A
惯性矩 I
截面系数W = I e
回转半径 i = I A
(续)
形心距离 e
A = 2.598C2 C=R
I x = 0.5413R4 I y =I x
Wx = 0.625R3 Wy = 0.5413R3
A = pa2
A0 = 2 prh = p(a 2 + h 2 )
An = p(2rh + a 2 ) = p(h 2 + 2a 2 )
ZG
=
h(4r − h) 4(3r − h)
V = 4 pabc 3
重心G在椭球中心
V = 4p r3 3
An = 4p r 2
重心G与球心重合
V = 2p2Rr2 = p2 Dd2 4
a
4
−
3pd
4
� �
6a
� �
16
� �
16a4 − 3pd 4 48(4a2 − pd 2 )
a 2
pd 2 8
Ix = 0.00686d 4
Iy
=
pd 4 128
Wx = 0.0239d 4
Wy
=
pd 3 64
p(D2 − d 2) 8
Ix = 0.00686(D4
A0 = 6ah An = 3 3a2 + 6ah
d = h2 + 4a2 (d为对角线)
ZG
=
h 2
3
G2 常用力学公式
G2.1 常用截面的力学特性(表 G1-2、表 G1-3)
表 G1-2 常用截面的几何及力学特性
截面形状
面积 A
惯性矩 I
截面系数W = I e
回转半径 i = I A
形心距离 e
a ZG = 2
V = abh A = ab A0 = 2h(a + b) An = 2(ab + ah + bh)
d = a2 +b2 + h2 (d为对角线)
h ZG = 2
体积 V、底面积 A、侧面积 A0、全 面积 An、重心位置 G 的计算公式
V = p h(3a 2 + h 2 ) 6
= p h 2 (3r − h) 3
ab 2
b = 0.289b
b
6
12
2
b(H − h)
Ix
=
b(H 3 − h3 ) 12
Iy
=
b3 (H − h) 12
Wx
=ቤተ መጻሕፍቲ ባይዱ
b(H 3 − h3) 6H
Wy
=
b2 (H 6
− h)
ix =
H 2 + Hh + h2 12
i y = 0.289b
H ex = 2
b ey = 2
H (a + b) 2
ix = 0.4566R
ex = 0.866R ey = R
pd 2
pd 4
pd 3
4
64
32
d
d
4
2
p (D2 − d2) 4
p (D4 − d4) 64
p
� �
D4
−
d
4
� �
32
� �
D
� �
D4 + d 4 4
D 2
a2 − pd 2 4
1
� �
a
4
−
3pd 4
� �
12
� �
16
� �
1
� �
A0
=
1 2
[(b1
+
b)
4h2 + (a − a1)2
+ (a1 + a) 4h2 + (b − b1)2 ]
An = A + A1 + A0
ZG
=
h(ab + ab1 + a1b + 3a1b1) 2(2ab + ab1 + a1b + 2a1b1)
V = 1 Ah = 3 a 2 h
3
2
A = 3 3 a2 2
ZG =
1
4(a 2 + a1a + a 2 )
1
( A1为顶面积, g 为斜高)
V = 1 abh 3
A = ab
A0
=
1 2
(b
4h2 + a2
+ a 4h2 + b2 )
An
=
ab +
1 (b 2
4h2 + a2
+ a 4h2 + b2 )
h ZG = 4
V = 3 3 a2h 2
A = 3 3 a2 2
A = p(R2 − r 2 )
A0 = 2ph(R + r)
An = 2p(R + r)(R − r + h)
ZG
=
h 2
V = p h(R2 + r 2 + Rr) 3
A0 = pl(R + r) An = p(R 2 + r 2 ) + A0
l = (R − r)2 + h2
ZG
=
h(R 2 + 2Rr + 3r 2 ) 4(R 2 + Rr + r 2 )
An = 4p2Rr = p2Dd 重心G在圆环中心
V
=
2 p
r3
3
A =p r2
A0 = 2p r 2
An = 3p r 2
ZG
=
3 8
r
V=πr2h A0=2πrh An=2πr(r+h) ZG= h
2
2
图形
体积 V、底面积 A、侧面积 A0、全面积 An、重心位置 G 的计算公式
V = ph(R 2 − r 2 )