Section Modulus calculation and optimization

Section Modulus calculation and optimization

Scope:

Scope of this project is calculating the section modulus of our hood, which we have made design at last submission.

The below formula is section modulus,

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

Here I'm going to check my hood section modulus and then will do design change at emboss shape to improve the section modulus minimum value at best.

Definition 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 design include area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.

It is the ratio of moment of inertia (I) of the beam cross –section about the neutral axis to the distance (Y) od extreme fiber from neutral axis.

• Z=I/Y

The section modulus(Z) is cross sectional shape is significant in designing beams. It is a direct measure of strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

• The unit of section modulus is mm³.

Moment of intertia:

The second moment of area is also known as the moment of inertia of a shape. The second moment of area is a measure of the 'efficiency' of a cross-sectional shape to resist bending caused by loading.

Both beams have the same area and even the same shape.

Beam 1 is stronger than Beam 2 because it has a higher second moment of area (I).

Orientation can change the second moment of area (I).

For a rectangle, Where b is breadth (horizontal) and h is height (vertical) if the load is vertical.

• Symbol is I. Units are mm⁴

Second Moment of Area of a cross-section is found by taking each mm² and multiplying by the square of the distance from an axis.
Then add them all up.

Her below is few other shapes and its cross section and formula,

There are two type of section modulus,

1. Elastic Section modulus
2. Plastic Section Modulus

Have look about short explanation about above topics,

1. Elastic Section Modulus:

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 fibre, as seen in the table below. 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.

2. Plastic Section Modulus:

The plastic section modulus is used for materials where(irreversible) plastic behavior is dominant. The majority of the design do not intentionally encounter this behavior.

The plastic section modulus depands 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 to the tension force from the area of tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sectioon, this is not necessaily 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:

M+/I =

Hood assembly - Sectioin Modulus:

Here below image is my hood assembly.

Here first i would check section modulus from the front side impact strength check, it does mean load wil be apply from front side so i have made datum plane accourdingly,

To create cross section of the hood assembly, I did use curve on datum then made profile help of tool curve intersection.

Then I have made sketch with help of projection, and studio spline for gap filling by polse.

Then with help of section inertia analysis tool via found the below value of my hood.

Here my hood moment of inertia value at minimum side is 2.876 mm^4.

Current hood:

Section modulus (Z)=I/Y

I = 2.876e⁺⁵ mm⁴

Y = 879.9/2 = 439.95mm

Z = 2.876e⁺⁵ /439.95 = 426.84/439.95

Z1 = 0.971mm³

Now we going to improve the moment of inertia as much as better and then will check again to find out differences how our hood improved.

New improved hood:

I have updated my inner panel deep increased by 0.5mm and the moment of Inertia slightly improved.as below image shown earlier MOI (Min) is 2.876e⁺⁵ mm⁴ and now it has been improved to 2.913e⁺⁵ mm⁴

So here we can improve and make strengthen out hood assembly with increaseing the emboss deep or inner panel deep values.

Section modulus (Z)=I/Y

I = 2.913e⁺⁵ mm⁴

Y = 879.9/2 = 439.95mm

Z = 2.913e⁺⁵ /439.95 = 432.33/439.95

Z2 = 0.983mm³

So we can improve our hood via strengthen our hood inner panel by increaseing the deep of the emboss deep / Hood inner panel deep.

Here I have checked the section modulus for load applying the front side of the vehicle in this same way we can check the section modulus to applying th load from side of the vehicle.