Section Modulus calculation and optimization

AIM:To calculate section modulus for the previously designed Hood assembly and to optimize the Design to have improved section modulus.

Why go for section modulus ?

As we know the bending equation M / I = σ /y = E / R.

Where M=Bending moment

I=Moment of Inertia

σ =Bending Stress

E=Modulus of elasticity

R=Radius of curvature

Taking M / I = σ /y and replacing them with M / I / y = σ

therefore M/Z = σ (since I/Y = Z or S)

So if we increase the z value the stress value decreases,similarly is the stress value decrases the strength of the object will increases,so just by increasing the section modulus we can control teh strength of the particular object ,so we are going to calculate the section modulus of the hood.

SECTION MODULUS:It is a geometric property used to Calculate the Bending stresses in a structural member.Section modulus is the direct measure of the strength of the shaft section or the beam section. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Mathematically,

Section modulus is defined as the ratio of the moment of inertia(I) of a section to the distance between the neutral axis and the extreme end of the object(Y).

The formula for the section modulus is given as: S= I/Y

Where S=Section modulus(mm^3)

I=Moment of Inertia(mm^4)

Y=The distance between the neutral axis and the extreme end of the object(mm)

For calculating the section modulus,we need the section of the hood and the value of 'y'.FOr taking the section we can go for the intersection curve and take the intersection w.r.t the datum plane.

Here the sectional modulus of hood design before optimization

calculation of section modulus:

I(max)=9.032432083 x 10^7(mm^4)

I(min)=2.800061775 x 10^5(mm^4)

Y=Total length/2=876.6195/2

=438.309 (mm)

section modulus for minimum = 2.800061775 x 10^5 / 438.309

S(min) = 0.638832 x 10^3(mm^3)

Hood Optimized Design: If the cross sectional area incerases,th momet of inertia also gets increased due to this the section modulus also willl incerase.

Optimization can be done in two ways,1)offseting the inner panel,2)creating extr a embosses

We are going to optmise our hood by offseting the inner panel to 0.5mm downward.

calculation of optimised section modulus:

I(max)=9.017884217 x 10^7(mm^4)

I(min)=2.836182983 x 10^5(mm^4)

Y=Total length/2=876.6195/2

=438.309 (mm)

section modulus for minimum = 2.836182983 x 10^5 / 438.309

S(min) = 0.647073 x 10^3(mm^3)

So we can say that by optimising the model we can increase the section modulus of our hood from 0.638832 x 10^3 to 0.647073 x 10^3.

Conclusion:

The Strength of the material is directly proportional to the moment of interia, thus increasing the cross-sectional area of the component the strength of component of the component also gets increased.