Section Modulus calculation and optimization

Come up with a new section that has an improved Section Modulus compared to the previous one and mention what changes you made which resulted in the increased strength.

Refer the grading policy

The report is to be made available in the Answer box provided below

SECTION MODULUS

Section modulus is a geometric property for a given cross-section used in the design of beam and flexural members. by finding the section modulus we can find the resistance to remain unchanged/ resistance against bending when the force is applied on the member.

Z = I (about neutral axis) / Y

Z - Section modulus

I - Area moment of inertia about neutal axis

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

1. Section modulus is directly proportional to Area moment of inertia

2. Section modulus is inversly proportional to Distance between the neutral axis and the extreme end of the object.

WAYS TO INCREASE SECTION MODULUS

1. Increasing the area moment of inertia (by fixing y value)

Area moment of inertia

I = Ak^2

A = Area of cross section

K = Radius of gyration

From this formula, if i need to increase the moment of inertia , i need to increase either cross section area or radius of gyration.

2. Decreasing the Distance between the neutral axis and the extreme end of the object. (by fixing I value)

As a sheetmetal design engineer i can not change the Y value, because it is already designed by class A designers which is length of the hood. I am allowed to change the cross section area by changing the thickness or increase the length of emboss of the hood.

Here i am going to calculate the section modulus for the hood i created:

Initial cross section area

Y value

SECTION MODULUS FOR HOOD WHICH I CREATED

m1=1.164*10^-6 m^4

=1.164*10^-6*10^12 mm^4

I= 1.164*10^6mm^4

Y=484.216/2

=242.105

Z=I/Y

=1.164*10^6mm^4 / 242.105

=4791.3mm^3

Z(Exsisting hood) =4791.3mm^3

If i need to increase the section modulus i can only increase a cross section area :

Increase cross section area → Area moment of inertia increases → Section modulus increases ( Y value can not be modified )

To increase the cross section area

1. I can increase the length of the emoboss.

2. I can increase the distance between hood top surface to inner panel bottom surface.

In this case i have offseted the inner panel bottom surface by 1mm to increase the cross section area as well as the section modulus:

Modified section

Section modulus for modified cross section area

m1=1.172*10^-6 m^4

=1.172*10^-6*10^12 mm^4

I= 1.172*10^6mm^4

Y=484.216/2

=242.105

Z=I/Y

=1.172*10^6mm^4 / 242.105

=4840.2mm^3

Z(Modified hood) =4840.2mm^3

CONCLUSION

Here i took cross section area for frontal crash and i have increased the section modulus ( Resistance against bending/resistance to remain unchanged) by changing the cross section area of the given member.