Section Modulus calculation and optimization

section modulus calcultion and design optimization for better section modulus for hood assembly

section modulus

concept defenition

section modulus is value used to understand at a particular section of body the force taking abily before the yielding and we can also say that section modulus is the ability of a section to withhold the applied force without deforming permanently or is a elastic deformation

types

section modulus is of two types i.e elastic section modulus (Se) and plastic section modulus(Sp)

formula

Se = I/Y

Se - elastic section modulus(mm3)

I - area moment of inertia(mm4)

Y - max distance between netral axis and outermost fiber

Elastic section modulus:

this is the section modulus value upto the yielding point where the object can retrive to the original shape and size

Platic section modulus:

This is the section modulus value upto the ultimate point where the object will start to rupture and in this region the object will go into permanent deformation where it will not retrive back to its original shape and size

there is also a two subtypes they are symmentric and assymmentric and the first one is for the variant where the section is symmentric about the centroid axis

and the another one is where the section is assymmentric about the neutral axis and the symmentric variant has a single moment of inertia (I) whereas the assymmentric type has

max ans min moment of inertia (I)

SECTION MODULUS FORMULA DERIAVATION

M/I = SIGMA/Y (bending equation)

where

M - bending momemt

I - area moment of inertia

SIGMA - bending stress

Y - max distance between centroid and neutral axis

Se = I/Y

therfore

M/SIGMA = Se = I/Y

AREA MOMENT OF INERTIA

as we can see from the above derivation the section modulus varies directly as the moment of inertia of an object and the moment of inertia is from the concept that the object with min material available deflect more than object with max material at the particular section and the

moment of inertia = differential of area * distance in x axis from centroid axis

this moment is find out by dividing the section into smaller shapes and then the final inertia is found out by

intergration of the differential from the low limit of height to upper limit

SECTION MODULUS CALCULATION OF ACTUAL DESIGN

since the section modulus is calculated for the hood of the car and where the impact is as shown blelow the section is taken perpendicular to the force applied

the section is therfore taken in x direction and the open ends are connected through a sketch and then section inertia analysis is done on the closed profile

as the created section is assymmentric we got max and min area moment of inetia and we have taken the max condition the section and inertia analysis given below

the y value is give above

Y =429.5 = 430mm

detailed view of inetia value

we got the value of

Imax = 8.69*10^7mm4

section modulus

Se = 8.69*10^7/430

Se = 202*10^3mm3

SECTION MODULUS CALCULATION FOR MODIFIED DISIGN

as we have already seen the section modulus can be increased by increasing the inertia value or by decreasing the Y value

• decreasing the Y value is not feasible as the width is constrained by the styling team
• only varinng the inertia is possible
• here i have increased the inertia value by locally increasing the emboss value to about 3mm and also by varying the thickness of the section to about 5mm

new section

Y value is same

detailed view

we obtain

Imax = 9.45*10^7mm4

Se = 9.45*10^*/430

Se = 220*10^3mm3

comparision of two sections

S NO	VALUE	EXISTING	MODIFIED	CHANGE IN %
1	Y	430	430	0
2	Imax	8.69*10^7	9.45*10^7	8.75
3	T	0.75	0.8	6.66
4	Se	202*10^3	220*10^3	8.9

CONCLUSION

we can see from the above calculation and comparision the section modulus increase by almost 9% by varing the inertia by varying the area and by varing the thickness of the object and we have also understood the concept of section modulus and its significance in design