Section Modulus calculation and optimization

The section modulus of the cross-sectional shape is of significant importance in designing, as it is a direct measure of the strength of the member. A member that has a larger section modulus than another will be stronger and capable of supporting greater loads.

It is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (y) of extreme fiber from the neutral axis.

The symbol S is used for the section modulus. In general, as the section modulus becomes larger, the strength against bending also becomes larger.

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

Section of Hood outer panel and inner panel

Moment of Inertia

Imax=1.356*10^8mm4

Imin=4.376*10^5mm4

Distance between the neutral axis and the extreme end of the object

y=477.024/2=238.51 mm

Section modulus calculation before optimization

For Imax

S=Imax/y

=1.356*10^8/238.51

=5.6852*10^5mm3

For Imin

S=Imin/y

=4.376*10^5/238.51

=1.8347*10^3mm3

Optimization

Optimisation in this case is done by moving the inner panel by 0.5 mm in downward direction.

Section

Moment of Inertia

Imax=1.5*10^8mm4

Imin=4.642*10^5mm4

Distance between the neutral axis and the extreme end of the object

y=477.122/2=238.56 mm

Section modulus calculation after optimization

For Imax

S=Imax/y

=1.5*10^8/238.56

=6.2877*10^5mm3

For Imin

S=Imin/y

=4.642*10^5/238.56

=1.9458*10^3mm3

Results:Following are the values of section modulus obtained before and after optimimization

Sr.No	Description	Before optimization	After optimization
1.	Maximum moment of Inertia(Imax)	Imax=1.356*10^8mm4	Imax=1.5*10^8mm4
2.	Minimum moment of Inertia(Imin)	Imin=4.376*10^5mm4	Imin=4.642*10^5mm4
3.	Distance between the neutral axis and the extreme end of the object	Ymin=238.51 mm	Ymax=238.56 mm
4.	Maximum section modulus	Smax=5.6852*10^5mm3	Smax=6.2877*10^5mm3
5.	Minimum section modulus	Smin=1.8347*10^3mm3	Smin=1.9458*10^3mm3

Conlusion:From the above results we can clearly see that values of section modulus has increased considerably after optimization which is done by moving inner panel by 0.5mm downward .