Section Modulus calculation and optimization

Introduction

Hoods are those part of the automobiles that take huge loads during frontal crashes. So it is primary concern of the design engineer to design a hood with greater strength. Since hoods need to withstand greater bending loads during frontal crash, it is important to design hoods with greater section modulus.

Image showing deformation mode of hood during frontal crash

Image showing cross section of the hood

Section Modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. The section modulus of the cross-sectional shape is of significant importance in designing hood. It is a direct measure of the strength of the hood. A hood that has a larger section modulus than another will be stronger and capable of supporting greater loads.

Mathematically,

`S= I/y`

Where, S = Section modulus,

I = Moment of Inertia,

y = Distance from neutral axis to extreme fiber

Moment of Inertia

The tendency of a body to resist angular acceleration, expressed as the sum of the products of the mass of each particle in the body and the square of its perpendicular distance from the axis of rotation. In other words, moment of inertia of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.

`I=m ×r^2`

Where, m= Mass,

r = Distance from the axis of rotation

Section modulus calculation

Create a datum plane exactly at the middle of the hood.

Use the command ‘Intersection Curves’ to get the cross section of the hood. This will be a 3D sketch. We need to convert this 3D sketch into 2D sketch to edit the sketch. In sketcher work bench, use ‘Project Curve’ command to get the 2D sketch.

To perform section inertia analysis, the outer boundaries in the sketch should be closed. Use ‘Studio Spline’ command to fill the gaps in the sketch.

Images below shows the results of ‘Section Inertia Analysis’ of the car hood

Section modulus can be calculated as shown below. MOI (Min) value should be used to get the section modulus.

MOI (Max) = 4.876 × 10⁶ mm⁴

MOI (Min) = 1.468 × 10⁴ mm⁴

Y = 438.3 mm

S_max = 11124.8 mm³

S_min = 33.5 mm³

Section modulus improvement

Section modulus is proportional to cross sectional area. So increasing cross sectional area will improve section modulus. I have offset the outer fiber of inner and outer hood panel to 1mm to increase the cross sectional area. Results are shown below

MOI (Max) = 4.917 × 10⁶ mm⁴

MOI (Min) = 1.520 × 10⁴ mm⁴

Y = 438.3 mm

S_max = 11218.34 mm³

S_min = 34.68 mm³

Conclusion

The section modulus of the designed hood panel is calculated. Sectional modulus for two different cases is compared. It is found that, there is 3.6% increase in the sectional modulus when there is increase in cross sectional area.