Section Modulus calculation and optimization

AIM: To Calculate and Compare the section modulus of the Hood Design and to conclude which one has more strength.

INTRODUCTION OF 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 the design include an area for tension and shear, the radius of gyration for compression, and the 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.

The Ratio of total Moment resisted by the section to the stress in the extreme fiber. It provides an idea about how much load the given structure can withstand for the pedestrian headlamp safety while undergoing serviceability considerations.

If the section modulus increases the moment of inertia also increases hence load-bearing capacity.

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 the design include an area for tension and shear, the radius of gyration for compression, and moment of inertia, and the 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.

The section modulus calculation for the hood assembly can be calculated by the given formula;

i.e. S=I/Y

Where,

S: Section Modulus.

I: Moment of inertia value from the Inertia analysis of the component.

Y: Distance from the axis to the outermost fiber.

There are two types of section modulus;

1) Elastic section modulus.

2) Plastic section modulus.

Elastic Section modulus can be explained below.

• Ze is the Elastic Section Modulus
• Resisting moment My = FY x Zy
• The elastic section modulus assumes the section remains elastic.
• If the failure is considered till the elastic
  zone then we consider elastic modulus.
• Elastic modulus is the steel modulus based on the stress-strain curve before yielding.
• Ze is used to determine the maximum bending moment up to the point where the extreme fiber has yielded elastically. All other fibers will be below their elastic yield stress.

Plastic Section modulus can be briefly explained below:

• Zp is the Plastic Section Modulus
• Resisting moment Mp = FY x Zp
• The plastic section modulus assumes the entire section yields.
• If the failure is considered till the plastic zone
  (breaking point) then we consider plastic modulus
• The plastic modulus is after yielding.
• Zp is used to determine the maximum bending moment at the point where all fibers have yielded elastically and the entire section is behaving plastically. This is the point when the so-called plastic hinge has developed.
• The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior 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 Section modulus analysis of the hood assembly can be explained below:

Case Study 1: Consider the Intersection of Designed Car Hood Outer Panel and Inner Panel.

The intersection curve for the closed surface hood designed outer and inner panel is shown in the below figure.

The closed surface of the intersection curves is shown in the below figure.

The section modulus analysis can be calculated in CATIA by the measure inertia command.

• Measure the length from the neutral axis to one of the ends (Y).

The section modulus analysis is calculated as per the designed method:

Consider the minimum value to calculate the section modulus of the hood assembly.

i.e. M1=1.052*10^4mm^4.

so, section modulus is given as,

S=I/Y

S=1.052*10^4/240.507

We get the result as,

S=43.74mm^3.

Case study 2: consider the intersection of the designed car hood inner and outer panel component with an offset of 0.5mm below of it.

Measure the length from the neutral axis to one of the extreme ends (Y).

The section modulus for the above surface can be calculated as per the below method:

Consider the minimum value to calculate the section modulus of the hood assembly.

i.e. M1=1.006*10^4mm^4. Y=480.937 we will consider half of that value i.e. Y= 480.937/2=240.4685mm.

S=I/Y.

S= 1.006*10^4/240.4685= 41.835mm^3.

Comparing the section modulus for both the cases;

The section modulus of case 1 is more than case 2. It seems that section modulus is directly proportional to the area of cross-section and we can also say strength and load-bearing capacity is more in case 1 compared to case 2.

If the section modulus increases there will be a more load-bearing capacity to withstand the designed hood compartment.

Conclusion:

Thus the section of modulus increases, more strength the material has and the section of modulus is directly proportional to the area of cross-section.