Section Modulus calculation and optimization

OBJECTIVE : To understand and calculate the section modulus of the section of hood design and optimise its to get improved strength of hood section.

SECTION MODULUS

Section Modulus is the geometric property of the given cross-section of any structures. It is the direct measure of the strength of the sections. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Mathematically,

Section modulus is the Area moment of inertia divided by the maximum distance from the centroid to the outer fibre of a cross section.

`S=I/(y_max)`

where S is Section modulus `(m^3)`

I is Area moment of inertia `(m^4)`

`y_max`= distance between Distance between neutral axes and outermost fibre (m).

Area moment of inertia - The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or second moment of inertia. The area moment of inertia has dimensions of length to the fourth power.

From Bending moment equation,

`M/I=sigma/y_max`

M is Bending moment

`sigma` is maximum bending stress of material

so,

`M=sigma*S`

here, Bending moment is direct proportionate to the section modulus of the body and bending stress of the material

INPUT

Calculate the section modulus of section of the BIW Hood panel.

First evaluate the moment of inertia by using Section Inertia Analysis feature in NX cad of the hood design and then calculate the section modulus of the section.

Section of the hood

Section view of hood

Section inertia analysis Report of hood section

MOI (min) = `2.583613038**10^5 mm^4`

y=879.0117/2 = 439.50585 mm

`S_min = 587.8450 mm^3`

New section

Increase the numbers of emboss of the inner panel of the hood which increase the section area of hood.

Section view of hood with increase no. of emboss in inner panel of hood

Section inertia analysis Report of new section of hood

MOI (min) = `2.662715598**10^5 mm^4`

y=879.0117/2 = 439.50585 mm

`S_min = 605.8430 mm^3`

Results

Section modulus of new section is more than previous one, and the difference between the value of both section modulus is 17.9980 mm^3.

CONCLUSION

After increasing the section area of hood by increasing the emboss in inner panel, the section modulus of the hood also increased. And the strength of section directly proportionate to the section modulus of the structure.