Section Modulus calculation and optimization

Car Hood

Task

Use the Section from your Hood design and calculate the section modulus using the formula S = I/y

S = Section Modulus

I = Moment of Inertia

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

Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.

Consider Stainless steel AISI 302 – cold-rolled – y = 520 MPa

Software Used

CATIA V5

Section Modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.There are two types of section moduli, the Elastic Section Modulus and the Plastic Section Modulus. For general design, the Elastic Section Modulus is used, applying up to the Yield Point for most metals and other common materials.

It is also often used to determine the Yield Moment (My) such that My = S × σy, where σy is the Yield Strength of the material. (Yield Strength is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. It is used to determine the maximum allowable load in a mechanical component).

Analysis

Case 1

The Inertia Analysis of the Hood Section brings out the following results.

I =2.197e-006 m⁴ = 2197000 mm⁴= 2.19e6 mm⁴

Y= 436mm

Section Modulus S= I/Y = 5022.9= 5023 mm³

Since we are provided with the Yield Strength of Stainless Steel (σ_y= 520 MPa= 520 N/mm²) the material used here, we can also calculate

Yield Moment, My = S × σ_y = 5023 x 520 = 2.61e6 Nmm

Case 2

After increasing the area by modifying the gap between the Inner and Outer Hood, without altering the standard design constraints, we get the following values after Inertia Analysis-

I =2.566e-006 m⁴ = 2556000 mm⁴= 2.55e6 mm⁴

Y= 436mm

Section Modulus S= I/Y = 5862 mm³

And Yield Moment, My = S × σ_y = 5862 x 520 = 3.04e6 Nmm

Conclusion

The Section Modulus in the second case is higher than the first one. Similarly the Yield Moment also increases proportionately, thereby corresponding to greater strength of the Hood. This was achieved due to an increased area by adjusting the position of the Outer Hood, without altering any standard saftey design constraints.