Section Modulus calculation and optimization

SECTION MODULUS

(of previously designed hood)

Objective

• to calculate the section modulus for the previously designed good and optimized hood
• to come up with a new section that has improved the section modulus of the previous section

Material of the hood

• stainless steel AISI-302 Cold Cold Y= 520 MPa

Section modulus

• section modulus is the geometric property of a given cross-section used in the design of flexural member section modulus depends only on the cross-section shape of the beam or structure
• for a symmetric section, the value of section modulus is the same for the both above and below of centroid of the cross-section and a symmetric section has two values for the top and bottom of the centroid the maximum section modulus and minimum section modulus

There are two types of section modulus

• elastic section modulus (S)
• plastic section modulus(Z)

Significance of section modulus-

• section modulus is an important factor for designing beams and flexural member
• higher the section modulus higher will be the resistance to bending
• easier to calculate strength and Stress in the beam
• If two beams are made of the same material and the section modulus of two beams are being compared with vice versa the beam with a larger section model will be tougher and more capable to withstand the longer load

we know that Stress (`sigma`) in a beam or structure is given by

`sigma`=M.yI`sigma`=M.yI.................................(1)

Where

I = moment of inertia

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

M = the moment about the neutral axis

section modulus is given by

S=Iys=Iy.............................(2)

from 1 & 2 equation
S=MS`sigma`=MS............(3)

that's from equation 3 it can be said that higher the section modulus higher will be the resistance to bending

Design 1): section modulus of initial hood design

-from the above analysis following minimum and maximum moment of inertia are obtained

I(max)=1.19e-006mm4

I(min)=1.57e-004mm4

y=478.505/2

y=239.2525

s=I/y

s=1.19*105/239.2525

s=4973.824

Design 2) section modulus of optimised Hood design

I(max)=1.299e-005mm4

I(min)=0.002e-001mm4

y=478.505/2

y=239.2525

s=I/y

s=1.299*105/239.2525

s=5429.41

Conclusion

• By comparing the values we can say that the section modulus of the optimal told is increased by 1%
• As we got the first result s=4973.824 and second result s=5429.41 i.e s=455.586 is the increased difference the both
• If we increase the gap between the outer and inner pannel of the hood the strength is also increased.