Part no. 1: Triangle
Dimensions:
Height: 27.3636 in
Base: 2.9588 in
Solving for Area:
𝐴=
1
𝑏 × ℎ = 2.9588 in × 27.3636 in
2
𝑨 = 𝟒𝟎. 𝟒𝟖𝟏𝟕 𝒊𝒏𝟐
Solving for Icx and Icz:
𝐼𝐶𝑋
𝐼𝐶𝑋 =
𝑏ℎ3
36
𝐼𝐶𝑧 =
ℎ𝑏 3
48
(2.9588 in) × (27.3636 in )3
=
36
𝑰𝑪𝑿 = 𝟏𝟔𝟖𝟑. 𝟗𝟔𝟒𝟎 𝒊𝒏𝟒
𝐼𝐶𝑍 =
𝐼𝐶𝑧
𝑏3 ℎ
48
(2.9588 𝑖𝑛) 3 × (27.3636 in )
=
48
𝐼𝐶𝑧 =
(17.6564)3 (19.3568)
48
𝑰𝑪𝒛 = 𝟏𝟒. 𝟕𝟔𝟔𝟓𝟒𝒊𝒏𝟒
Solving x and z:
Solving for Ixx and Izz:
𝐼𝑋𝑋 = 𝐼𝐶𝑋 + 𝐴𝑧 2
𝐼𝑋𝑋 = 1683.9640 𝑖𝑛4 + (40.4817 𝑖𝑛2 ) (13.9324 𝑖𝑛)2
𝑰𝑿𝑿 = 𝟗𝟓𝟒𝟏. 𝟗𝟑𝟖𝟒𝟑 𝒊𝒏𝟒
Part no. 5: Semi-Ellipse
Dimensions:
A: 10.7996 in
Base: 4.8969 in
Solving for Area:
𝐴 = 𝜋𝐴𝐵 = 𝜋(10.7996 in)(4.8969 in)
𝑨 = 𝟖𝟑. 𝟎𝟕𝟎𝟗 𝒊𝒏𝟐
Solving for Icx and Icz:
𝐼𝐶𝑋
𝜋𝑎𝑏 3
=
8
𝐼𝐶𝑧 = 𝑎3 𝑏(
𝐼𝐶𝑋 =
𝜋
8
−
)
8 9𝜋
𝜋(10.7996 in)(4.8969 in)3
8
𝑰𝑪𝑿 = 𝟒𝟗𝟖. 𝟎𝟎𝟐𝟐 𝒊𝒏𝟒
𝐼𝐶𝑧 = (10.7996 in)3 (4.8969 in)(
𝜋
8
−
)
8 9𝜋
𝑰𝑪𝒛 = 𝟔𝟕𝟔. 𝟗𝟖𝟎𝟕𝒊𝒏𝟒
Solving x and z:
Solving for Ixx and Izz:
𝐼𝑋𝑋 = 𝐼𝐶𝑋 + 𝐴𝑧 2
𝐼𝑋𝑋 = 498.0022 𝑖𝑛4 + (83.0709 𝑖𝑛2 ) (0)2
𝑰𝑿𝑿 = 𝟒𝟗𝟖. 𝟎𝟎𝟐𝟐 𝒊𝒏𝟒
Part no. 8: Rectangle
Dimensions:
Base: 32.5728 in
Height: 22.4123 in
Solving for Area:
𝐴 = 𝑏 × ℎ = 32.5728 in × 22.4123 in
𝑨 = 𝟕𝟑𝟎. 𝟎𝟑𝟏𝟒 𝒊𝒏𝟐
Solving for Icx and Icz:
𝐼𝐶𝑋
𝑏ℎ3
=
12
𝐼𝐶𝑋 =
𝐼𝐶𝑋
ℎ𝑏 3
12
(32.5728 in)(22.4123 in)3
=
12
𝑰𝑪𝑿 = 𝟑𝟎𝟓𝟓𝟖. 𝟓𝟕𝟕𝟏 𝒊𝒏𝟒
𝐼𝐶𝑧
(32.5728 in)3 (22.4123 in)
=
12
𝑰𝑪𝒛 = 𝟔𝟒𝟓𝟒𝟔. 𝟏𝟔𝟕𝟑 𝒊𝒏𝟒
Solving x and z:
Solving for Ixx and Izz:
𝐼𝑋𝑋 = 𝐼𝐶𝑋 + 𝐴𝑧 2
𝐼𝑋𝑋 = 30558.5771𝑖𝑛4 + 730.0314 𝑖𝑛2 (−4.1291in)2
𝑰𝑿𝑿 = 𝟒𝟑𝟎𝟎𝟓. 𝟐𝟐𝟑𝟐 𝒊𝒏𝟒