Section Modulus calculation and optimization

Section Modulus of a Hood

The section modulus is a direct measure of its strength. Bending a section that has a larger section modulus than another is stronger and more difficult. The section modulus of a cross-section is a geometric property utilized in the design of flexural members. In simple terms, the section modulus is the ratio of bending moment to bending stress. When the section modulus is large, it is harder to bend and can withstand a high moment without bending stress.

It's the point at which the entire cross-section reaches its yield stress. When this point is reached, a plastic hinge is formed, and any load beyond this point will result in theoretically endless plastic deformation.

Section Modulus, S=I/y

Where,

S- Section modulus

I – Area moment of inertia

y – Distance between neutral axis and extreme end of the fiber

Calculating the values for the designed section:

Case I: Initial Hood Design

Y Distance = 485.74

At Neutral axis y=Y/2= 485.74/2 = 242.87

As per the Section inertia calculation through NX CAD

• MOI(Max): 8.233X10⁵ mm⁴
• MOI(Min): 5.072X10³ mm⁴

Section Modulus

• S=I(max)/y = 8.233X10⁵/242.87 = 3.38X10³mm³
• S=I(min)/y = 5.072X10³/242.87= 0.020X10³mm³

The strength of a hood varies from 0.020X10³mm³ to 3.38X10³mm³

As part of the challenge, we now come up with a new cross-section in order to improve the section modulus of the previous section and mention what is the change in strength that has increased

Considering the above challenge, we will be increasing the distance between the inner and the outer panel by 4 and find the change in the strength of the section modulus

Calculating the values for a New designed section:

Case II : New cross-section hood design

Y Distance = 485.74

At Neutral axis y=Y/2= 485.74/2 = 242.87

• MOI(Max): 8.51X10⁵ mm⁴
• MOI(Min): 6.60X10³ mm⁴

Section Modulus

• S=I(max)/y = 8.51X10⁵/242.87 = 3.50X10³mm³
• S=I(min)/y = 6.60X10³/242.87= 0.027X10³mm³

The strength of the new cross-section varies from 0.027X10³mm³ to 3.50X10³mm³

Conclusion

Comparing the values of section modulus of case I and case II it is clear that increasing the distance between the outer and inner panel by 4mm, increases the section modulus by 35%

The moment of inertia is directly related to the strength of a material. As the sectional area of an object increases, so does its overall mass, and hence its strength.