Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION OF HOOD

AIM:

To calculate the section modulus of the previously designed hood by analyzing its strength and also optimizing the design to see the difference in the bending strength 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. Other geometric properties used in design include area for tension and shear, radii of gyration for compression, and second moment of inertia and polar second moment of area for stiffness. There are two types of section moduli, the elastic section modulus and the plastic section modulus.

S = I/y

Where,

S = Section Modulus (mm^3),

I = Moment of Inertia (mm^4),

y = distance between the neutral axis and the extreme end of the object (mm).

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.

PLASTIC SECTION MODULUS:

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, and equal compressive and tensile 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:

CALCULATION:

The Moment of Inertia is measured by using CATIA V5 for which the intersection is taken.

Moment of Inertia (Max.) = 5.663 e^-007m^4.

Moment of Inertia (Min.) = 1.336 e^-004m^4.

Y (Length) = 488.8252 mm.

Length from neutral axis = 488.8252/2 = 244.412 mm.

We know that, Section modulus S = I/y

S = 5.663 x 10^5 mm^4/244.412 mm

S = 2.316989 x 10^3 mm^3.

For a new section, where the inner panel depth is offsetted to about 0.5mm. The resultant calculation are as follows,

Moment of Inertia (Max.) = 5.992 e^-007m^4.

Moment of Inertia (Min.) = 1.389 e^-004m^4.

Y (Length) = 488.8252 mm.

Length from neutral axis = 488.8252/2 = 244.412 mm.

We know that, Section modulus S = I/y

S = 5.992 x 10^5 mm^4/244.412 mm

S = 2.451598 x 10^3 mm^3.

CONCLUSION:

From the above calculation, the section modulus for section 1 is S = 2.316989 x 10^3 mm^3 and for section 2 is S = 2.451598 x 10^3 mm^3. Which shows that with a new section has an improved Section Modulus compared to the previous one. Increase in thickness between outer and inner panel of hood increases the section modulus of the hood. Higher the section modulus of a hood, increases its resistance to bending.