Sectional Modulus calculation optimization Car Hood

Sectional Modulus Calculation & its optimizations

Problem Statement:Use the Section from your Hood design and calculate the section modulus using the formula S = I/y

S or Z = Section Modulus

I = Moment of Inertia

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

Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.

Consider Stainless steel AISI 302 – cold-rolled – y = 520 MPa

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question.There are, the

Two types of section moduli

1. Elastic section modulus (Wel or Z or S)

• The elastic section modulus assumes the section remains elastic.
• Elastic modulus is the steel modulus based on the stress strain curve before yielding

1. The plastic section modulus (Wpl or Z or S)

• The plastic section modulus assumes the entire section yields.
• Plastic modulus is the steel modulus based on the stress strain curve after yielding.

As we know in problem they given a stainless steel material with Young\'s modulus of 520Mpa therefore we need to optimize elastic section modulus type:

This is the PMI Screenshot of the MOI of the hood at section YC

As we know the formulae of bending (Bending Equation)

M/I=𝛔/Y=E/R

Where,

M=Bending Moment

I=Moment of inertia of the area of the cross section.

σ=Bending stress

y=distance of extreme fibre from the neutral axis

E=Young’s modulus

R=radius of curvature.

But,

Z=M/𝛔=I/Y

Where,

I=2.23*10⌃4 mm⌃4 (Taking smallest value for better optimization)

Y=922/2=461 mm

Therefore,

Z1=48.37 mm⌃3

• From the formulae, as increase in the length of neutral axis (Y) then section modulus gets decreased because this both are inversely proportional to each other
• To increase section modulus need to increase the MOI means area of the section.

After changing the sectional area

Z=I/Y

Z2=49.457 mm⌃3

As we see the section modulus value it gets increase by increasing the sectional inertia

Conclusion

Increasing in the sectional modulus means it increases moment of the resistance or it can bear more moment it means it increases strength and decreases chances of the failure.

Result:

From the calculated result of section modulus of the hood in this second section modulus (Z2 ) is greater than the Z1.

Therefore, the second section has more strength than the first section.

Here is the drive link to know more about this:

https://drive.google.com/open?id=1t5TRxElaaZoQzvPOQWseS8wfoVr-bQBV