Section Modulus calculation and optimization

Aim

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more resistive it becomes to bending.

Section modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. 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. There are two types of section moduli, the elastic section modulus, and the plastic section modulus.

S=I/Y

Here,

S = Section modulus

I= Moment of Inertia (Unit mm 4)

Y= Distance from the Neutral axis to the extreme end (unit mm)

The Unit of a “section modulus” is (mm3)

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.

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 the moment of inertia) and y is the distance from the neutral axis to any given fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber, 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.

Hood Design Before Optimization

Here,

Moment of Inertia(Max) = 8.053021066*10^5 mm⁴

Moment of Inertia(Min) = 4.179726331*10^3 mm⁴

Section Modulus, S = I/y

S = Section Modulus

I = Moment of Inertia

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

here, y = 484/2

i.e, y = 242 mm

Therefore,

S = (4.179726331*10^3)/242

S = 17.2715964091 mm³

Hood Design After Optimization

Increase 1 mm offset to the inner panel

Here,

Moment of Inertia(Max) = 8.119754498*10^5 mm⁴

Moment of Inertia(Min) = 4.458770521*10^3 mm⁴

Section Modulus, S = I/y

S = Section Modulus

I = Moment of Inertia

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

here, y = 484/2

i.e, y = 242 mm

Therefore,

S = (4.458770521*10^3)/242

S = 18.4246715744 mm³

Conclusion

Thus we saw the section modulus get more strength by increasing the area.