SkyCiv Documentation

Your guide to SkyCiv software - tutorials, how-to guides and technical articles

1. Home
2. SkyCiv Section Builder
3. Analysis
4. Calculation Verification

# Calculation Verification

### Example 1

Determine the stresses of a T-section subjected to combined forces.

 Dimensions of section Geometric Properties Forces Area = 3579 mm2 Moment of Inertia Iz = 1.05786·107 mm4 Iy = 6.32306·106 mm4 Distans to Max and Min ymax = 39.3877 mm ymin = -150.6123 mm zmax = 90 mm zmin = -90 mm Shear Properties Qz = 7.93943·104 mm3 Qy = 5.25658·104 mm3 Torsion J = 1.46870·105 mm4 rmax = 13.5357 mm Axial = 10.0 kN Shear Y = 1.0 kN Shear Z = 1.0 kN Torsion = 0.1 kN·m Bending Y = 1 .0 kN·m Bending Z = 1 .0 kN·m

### Comparison of Results

 Result Location SkyCiv SB Analysis Manual Third-Party Primary Stresses (MPa) Axial max 2.794 $$\frac{Area}{Axial}=\frac{10·1000}{3579} = 2.794$$ (0.00%) 2.794 (0.00%) min 2.794 $$\frac{Area}{Axial}=\frac{10·1000}{3579} = 2.794$$ (0.00%) 2.794 (0.00%) Bending Y max 14.234 $$\frac{Bending Y}{I_y/y_{max}}=\frac{1·1000000}{6.32306·10^6/90} =14.234$$ (0.00%) 14.234 (0.00%) min -14.234 $$\frac{Bending Y}{I_y/y_{min}}=\frac{1·1000000}{6.32306·10^6/-90} =-14.234$$ (0.00%) -14.234 (0.00%) Bending Z max 3.723 $$\frac{Bending Z}{I_z/z_{max}}=\frac{1·1000000}{1.05786·10^7/39.3877} =3.723$$ (0.00%) 3.723 (0.00%) min -14.237 $$\frac{Bending Z}{I_z/z_{min}}=\frac{1·1000000}{1.05786·10^7/-150.6123} =-14.237$$ (0.00%) -14.237 (0.00%) Resultant Shear Y max 1.123 $$\frac{Shear Y·Q_z}{I_z·t}=\frac{1·1000·7.93943·10^4}{1.05786·10^7·7} = 1.072$$ (4.54%) 1.120 (0.26%) Resultant Shear Z max 0.698 $$\frac{Shear Z·Q_y}{I_y·t}=\frac{1·1000·5.25658·10^4}{6.32306·10^6·13} = 0.639$$ (8.45%) 0.709 (1.57%) Torsion max 9.956 $$\frac{r_{max}}{J}=\frac{0.1·1000000·13.5357}{1.46870·10^5} = 9.216$$ (7.43%) 9.570 (3.87%)

### Example 2

Determine the stresses of a section subjected to combined forces.

 Dimensions of section Geometric Properties Forces Area = 533.9368 mm2 Moment of Inertia Iz = 3.84955·105 mm4 Iy = 9.59303·104 mm4 α = -0.1562° Izp = 3.84957·105 mm4 Iyp = 9.59281·104 mm4 Distans to Max and Min Pointmax = (-15.7027, 37.2424) mm Pointmin =(14.1016, -42.0526) mm Bending Y Pointmax = (16.0015, -40.1425) mm Bending Y Pointmin = (-15.9392, 30.7351) mm Shear Properties Shear Y Qz = 6533.7159 mm3 Qy = 4.2994 mm3 t=3.9624 mm Shear Z Qz = 929.3201 mm3 Qy = 3337.6401 mm3 t= 2.8145 mm Torsion J = 1513.8 mm4 rmax = 4.6293 mm Axial = 10.0 kN Shear Y = 1.0 kN Shear Z = 1.0 kN Torsion = 0.01 kN·m Bending Y = 1 .0 kN·m Bending Z = 1 .0 kN·m

### Comparison of Results

 Result Location SkyCiv SB Analysis Manual Third-Party Primary Stresses (MPa) Axial max 18.729 $$\frac{Area}{Axial}=\frac{10·1000}{533.9368} = 18.729$$ (0.00%) 18.73 (0.00%) min 18.729 $$\frac{Area}{Axial}=\frac{10·1000}{533.9368} = 18.729$$ (0.00%) 18.793 (0.00%) Bending Y max 166.538 $$\frac{M_y·\cos(\alpha)}{\frac{I_y}{z_{max}}}+\frac{M_y·\sin(\alpha)}{\frac{I_z}{y_{max}}}=\frac{1000000·\cos(-0.1562^\circ)}{\frac{3.84955·10^5}{-42.0526}}+\frac{1000000·\sin(-0.1562^\circ)}{\frac{9.59281·10^4}{14.1016}}=166.694$$ (0.00%) 166.5 (0.00%) min -165.951 $$\frac{M_y·\cos(\alpha)}{\frac{I_y}{z_{min}}}+\frac{M_y·\sin(\alpha)}{\frac{I_z}{y_{min}}}=\frac{1000000·\cos(-0.1562^\circ)}{\frac{3.84955·10^5}{30.7351}}+\frac{1000000·\sin(-0.1562^\circ)}{\frac{9.59281·10^4}{-15.9392}}=166.045$$ (0.00%) -166.0 (0.00%) Bending Z max 97.189 $$\frac{M_z·\cos(\alpha)}{\frac{I_z}{y_{max}}}+\frac{M_z·\sin(\alpha)}{\frac{I_y}{z_{max}}}=\frac{1000000·\cos(-0.1562^\circ)}{\frac{3.84955·10^5}{37.2424}}+\frac{1000000·\sin(-0.1562^\circ)}{\frac{9.59281·10^4}{-15.7027}}=97.19$$ (0.00%) 97.19 (0.00%) min -109.639 $$\frac{M_z·\cos(\alpha)}{\frac{I_z}{y_{min}}}+\frac{M_z·\sin(\alpha)}{\frac{I_y}{z_{min}}}=\frac{1000000·\cos(-0.1562^\circ)}{\frac{3.84955·10^5}{-42.0526}}+\frac{1000000·\sin(-0.1562^\circ)}{\frac{9.59281·10^4}{14.1016}}=-109.64$$ (0.00%) -109.6 (0.00%) Resultant Shear Y max 4.302 $$\frac{ShearY·\cos(\alpha)·Qz}{Izp·t}+\frac{ShearZ·\cos(\alpha)·Qy}{Iyp·t}=\frac{1000·\cos(-0.1562^\circ)·6533.7159}{{3.84955·10^5·3.9624}}+\frac{1000·\sin(-0.1562^\circ)·4.2994}{9.59281·10^4·3.9624}=4.283$$ (0.44%) 4.297 (0.12%) Resultant Shear Z max 16.629 $$\frac{ShearZ·\sin(\alpha)·Qz}{Izp·t}+\frac{ShearZ·\cos(\alpha)·Qy}{Iyp·t}=\frac{1000·\sin(-0.1562^\circ)·929.3201}{{3.84955·10^5·2.8145}}+\frac{1000·\cos(-0.1562^\circ)·3337.6406}{9.59281·10^4·2.8145}=12.36$$ (25.67%) 17.37 (4.46%) Torsion max 30.418 $$\frac{r_{max}}{J}=\frac{0.1·1000000·4.6293}{1513.65} = 30.584$$ (0.55%) 31.98 (5.14%)