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4. Calculation Verification 2

# Calculation Verification 2

## Verification Examples:

### Example 3: Hollow Rectangle 150×250

#### Geometric Properties

 Property Value Area 7600 mm2 Ymax, Ymin 125mm, -125mm Zmax, Zmin 75mm, -75mm Iy 2.82 × 107 mm4 Iz 6.35 × 107 mm4 Qy 3.12 × 105 mm3 Qz 2.17 × 105  mm3 ty 20 mm tz 20 mm J 6.11 × 107 mm4 rmax 98.86 mm

#### Forces

 Axial Shear Y Shear Z Torsion Bending Y Bending Z 8 kN 1 kN 1 kN 0.1 kN-m 1 kN-m 1 kN-m

#### Results

 Result SkyCiv SB Analysis Manual Third Party Axialmax 1.053 $$\frac{Area}{Axial}=\frac{8·1000}{7600} = 1.053$$ (0.00%) 1.053 (0.00%) Axialmin 1.053 $$\frac{Area}{Axial}=\frac{8·1000}{7600} = 1.053$$ (0.00%) 1.053 (0.00%) Bending Ymax 2.659 $$\frac{BendingY}{I_y/y_{max}}=\frac{1·1000000}{2.82·10^7/75} = 2.659$$ (0.00%) 2.659 (0.00%) Bending Ymin -2.659 $$\frac{BendingY}{I_y/y_{min}}=\frac{1·1000000}{2.82·10^7/-75} = -2.659$$ (0.00%) -2.659 (0.00%) Bending Zmax 1.968 $$\frac{BendingZ}{I_z/z_{max}}=\frac{1·1000000}{6.35·10^7/125} = 1.969$$ (0.05%) 1.968 (0.00%) Bending Zmin -1.968 $$\frac{BendingZ}{I_z/z_{min}}=\frac{1·1000000}{6.35·10^7/-125} = -1.969$$ (0.05%) -1.968 (0.00%) Resultant Shear Ymax 0.247 $$\frac{ShearY·Q_z}{I_z·t}=\frac{(1·1000)·3.12·10^5}{6.35·10^7·20} = 0.246$$ (0.4%) Resultant Shear Zmin 0.247 $$\frac{ShearZ·Q_y}{I_y·t}=\frac{(1·1000)·2.17·10^5}{2.82·10^7·20} = 0.246$$ (0.4%) Torsion max 0.170 $$\frac{Torsion·r_{max}}{j}=\frac{0.1·1000000·98.86}{6.12·10^7} = 0.162$$ (4.81%)

### Example 4: Double Channels

#### Geometric Properties

 Property Value Area 6413.15 mm2 Ymax, Ymin 115mm, -115mm Zmax, Zmin 80mm, -80mm Iy 8.41 × 106 mm4 Iz 5.36 × 107 mm4 Qy 8.85 × 104 mm3 Qz 2.72 × 105 mm3 ty 13 mm tz 0 mm J 2.21 × 105 mm4 rmax 12.9 mm

#### Forces

 Axial Shear Y Shear Z Torsion Bending Y Bending Z 5 kN 1.2 kN 1.5 kN 0.25 kN-m 1 kN-m 1 kN-m

#### Results

 Result SkyCiv SB Analysis Manual Third Party Axialmax 0.78 $$\frac{Area}{Axial}=\frac{5·1000}{6413.15} = 0.78$$ (0.00%) Axialmin 0.78 $$\frac{Area}{Axial}=\frac{5·1000}{6413.15} = 0.78$$ (0.00%) Bending Ymax 9.512 $$\frac{BendingY}{I_y/y_{max}}=\frac{1·1000000}{8.41·10^6/80} = 9.512$$ (0.00%) Bending Ymin -9.512 $$\frac{BendingY}{I_y/y_{min}}=\frac{1·1000000}{8.41·10^6/-80} = -9.512$$ (0.00%) Bending Zmax 2.114 $$\frac{BendingZ}{I_z/z_{max}}=\frac{1·1000000}{5.36·10^7/115} = 2.146$$ (0.01%) Bending Zmin -2.114 $$\frac{BendingZ}{I_z/z_{min}}=\frac{1·1000000}{5.36·10^7/-115} = -2.146$$ (0.01%) Resultant Shear Ymax 0.47 $$\frac{ShearY·Q_z}{I_z·t}=\frac{(1.2·1000)·2.71·10^5}{5.36·10^7·13} = 0.47$$ (0.00%) Resultant Shear Zmin 7.842 Torsion max 16.869 $$\frac{Torsion·r_{max}}{j}=\frac{0.25·1000000·12.9}{2.21·10^5} = 14.59$$ (13.5%)

### Example 5: Composite Steel Encased Concrete Column

#### Geometric Properties

 Property Value Transformed Area (Steel) 11800 mm2 Transformed Area (Concrete) 138824 mm2 Ymax, Ymin 110mm, -110mm Zmax, Zmin 110mm, -110mm Iy (Steel E Value) 7.32133 × 107 mm4 Iz (Steel E Value) 7.32133 × 107 mm4

#### Forces

 Axial Shear Y Shear Z Torsion Bending Y Bending Z 3 kN 1 kN 2 kN 0.2 kN-m 1 kN-m 2 kN-m

#### Results

 Result SkyCiv SB Analysis Manual Third Party Axialmax 0.254 $$\frac{Area}{Axial}=\frac{3·1000}{1.18·10^4} = 0.254$$ (0.00%) Axialmin 0.022 $$\frac{Area}{Axial}=\frac{3·1000}{1.38·10^5} = 0.22$$ (0.00%) Bending Ymax 1.502 $$\frac{BendingY}{I_y/y_{max}}=\frac{1·1000000}{7.32113·10^7/110} = 1.502$$ (0.00%) Bending Ymin -1.502 $$\frac{BendingY}{I_y/y_{min}}=\frac{1·1000000}{7.32113·10^7/-110} = -1.502$$ (0.00%) Bending Zmax 3.005 $$\frac{BendingZ}{I_z/z_{max}}=\frac{2·1000000}{7.32113·10^7/110} = 3.005$$ (0.00%) Bending Zmin -3.005 $$\frac{BendingZ}{I_z/z_{min}}=\frac{2·1000000}{7.32113·10^7/-110} = -3.005$$ (0.00%) Resultant Shear Ymax 0.155 Resultant Shear Zmin 0.31 Torsion max 0.219