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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 × 10 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
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