Section Modulus calculation and optimization

SECTION MODULUS ANALYSIS OF HOOD IN NX

Aim:

To analyze the section modulus of the hood design to provide maximum stiffness better than the parent car.

Introduction:

Hood is the part which dissipates the force to other parts like hinges rather than passing it to the passenger cabin during collision. As a hood engineer, we should always ensure a better safety to the passenger with our designs.

Improving the stiffness of the hood better than the parent car is good way of improving the safety mainly during crash.

For improving this kind of stiffness, after designing the hood we have to go for a section modulus analysis.

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such.

Notation:

North American and British/Australian convention reverse the usage of S & Z. Elastic modulus is S in North America, but Z in Britain/Australia, and vice versa for the plastic modulus. Eurocode 3 (EN 1993 - Steel Design) resolves this by using W for both, but distinguishes between them by the use of subscripts - Wel and Wpl.

There are two types of Section Modulus:

• Elastic section modulus and
• Plastic section modulus:

Elastic section modulus

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre.

It is often reported using y = c, where c is the distance from the neutral axis to the most extreme edge of the material. It is also often used to determine the yield moment (M_y) such that M_y = S × σ_y, where σ_y is the yield strength of the material.

Section modulus equations:

Plastic section modulus:

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behaviour is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

the Plastic Section Modulus can also be called the 'First moment of area'

The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, Fy, by Mp=Fy*Z. Plastic section modulus and elastic section modulus are related by a shape factor which can be denoted by 'k', used for an indication of capacity beyond elastic limit of material. This could be shown mathematically with the formula:

Section modulus analysis:

As we have modelled the hood earlier, now we are going to analyse the section modulus in two cases

• As per our design.
• Improving the section area.

Fig. Our hood from inner side

Fig. Our hood from front side

Section modulus analysis as per our design:

Hood design should have a better performance to dissipate the force acting towards the car mainly during frontal crash. So, we have taken the cross section from the front side at an exact center of the hood.

Fig. Intersection curve in hood

This center section is placed using intersection curve option available in curve tab in NX CAD software.

After this we made a sketch from the intersection curve without any void and analyzed the section inertia of the cross section using section inertia analysis option.

The values what we get is:

Maximum moment of inertia: 4.823129387e+06[mm^4]

Minimum moment of inertia: 1.484356973e+04[mm^4]

and the

Section area: 74.304531137[mm^2]

Calculation of section modulus:

Section modulus(S) = I/y

I is moment of inertia, here we take minimum moment of inertia value for I as it starts acting on the part in earlier stage of crash.

y is the distance between the neutral axis to the edge of the cross section.

S=1.484356973e+04[mm^4]/439.3mm

=33.7891412mm^3

Section modulus analysis as per improved cross section:

Then we increased the section area of the cross section up to 0.5mm with respect to inner panel.

After this we offset the sketch from the intersection curve of inner panel, we analyzed the section inertia of the cross section using section inertia analysis option.

The values what we get is:

Maximum moment of inertia: 4.816358746e+06[mm^4]

Minimum moment of inertia: 1.502607964e+04[mm^4]

and the

Section area: 74.268125157[mm^2]

Calculation of section modulus:

Section modulus(S) = I/y

I is moment of inertia, here also we take minimum moment of inertia value for I as it starts acting on the part in earlier stage of crash.

y value will be the same as earlier.

S=1.502607964e+04[mm^4]/439.3mm

=34.2045974mm^3

From this different section modulus values when we have an improved stiffness in hood while we offset the inner panel to an additional 0.5 mm outward. As we get a section modulus of 34.2045974mm^3

Conclusion:

From different values of section modulus of above two cases, we conclude that while offsetting the inner panel to a 0.5mm outside, we get an improved section modulus and this is providing a good stiffness to the hood while comparing to the parent car. So, the section modulus analysis of our hood is analyzed and a better stiffness is achieved comparing to the parent car by offsetting the inner panel to an additional value.