Section Modulus calculation and optimization

Section modulus:

Section Modulus is a geometric property used to calculate the bending stresses in a structural member.

Mathematically,

It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.

S = I / Y

Where

S = Section modulus

I = Moment of Inertia of the section about the bending axis

Y = Distance between the neutral axis and extreme end of the object

Types of Section Modulus

There are two types of section modulus:

• Elastic Section Modulus
• Plastic Section Modulus

Lets Calculate Section Modulus of Hood Which Designed.

Case 1:

Take Section of the of Hood

To Calculate Section Modulus moment of inertia is required so calculating it in Catia v5 .

After creating surface Inertia is Measured

From Software We get

M_{min = 1.558 X 10}^-6 _m⁴

M_{max = 1.637X 10}^-4 _m⁴

From Sketch measured L = 497

M_{min =} 1.558 X 10^-6 m² = 1.558 X 10⁶ mm²

M_{max =} 1.637 X 10^-4 m² = 1.558 X 10⁸ mm²

Y = L / 2 = 497 / 2 = 248.5

S_min = I_min / Y

S = 1.558 X 10⁶ / 248.5

S = 6.269 X 103 mm3

Optimization

offset curve by 0.8 mm and then repeat the process.

Inertia Measured In Catia

M_{min =} 1.66 X 10^-6 m² = 1.66 _X 10⁶ mm²

M_{max =} 1.523 X 10^-4 m² = 1.523 _X 10⁸ mm²

Y = L / 2 = 497 / 2 = 248.5

S = I_min / Y

S_min = 1.66 X 10⁶ / 248.5

Smin = 6.68 X 103 mm3

.

Conclusion

Case	Section	Moment of Inertia	Distance y	Section Modulus
1	Original Section	1.558 X 106 mm4	248.5	6.269 X 103 mm3
2	Depth Increases by 0.8mm	5.600821885e+03	241.6545	6.68 X 103 mm3

The strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is have increase in overall mass of an object ,hence have increase in strength.