Section Modulus calculation and optimization

Aim :

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus :

Section modulus is a direct measure of strength of any sectional area of an object about an reference axis(neutral axis). Strength is nothing but, capable of supporting greater loads, so higher the strength it has a high capable of supporting greater loads. This strength can measured directly from Section modulus formula, and defined by below formula.

Formula of Section Modulus : It may be defined as the ration of total moment resisted by the section to the stress in the extreme fibre which is equal to yield stress.

Therefore ; S = I/Y, Where

S = Section modulus (mm^3)

I = Moment of Inertia of the section about the bending axis. (mm^4)

Y = Distance between the neutral axis and extreme end of the object (mm)

• Moment of inertia is nothing but offering resistance against of moment, bending or twisting, i.e if we applied any external load on the body, how much resistance its offering to tend to deform.
• So, higher the value of moment of inertia , have higher resistance to deform under certain load, hence we can say that moment of inertia directly proportional to the strength of the material , and strength of the material can be calculated with the help of section modulus.
• If we vary the neutral axis towards positive or negative side the overall strength of the body will decrease , because when nuetral axis line lies on the middle of the section only have higher strength at particular point, so, here 'Y' value was inversely proportional to section modulus.

Calculation

Case - 1 :

Considering the Hood assembly designed previously let us calculate the section modulus for the same.

Above figure shows the section that is extracted from the hood assembly where calculations needs to be carried out.

After calculation we get the following data,

Maximum moment of inertia = 4.844553734e+06[mm^4]

Minimum moment of inertia = 1.275331926e+04[mm^4]

The total distance of the hood Y = 881.0282 mm

Distance between the neutral axis to the extreme end = (881.0282/2) = 440.5141 mm

Hence section modulus considering minimum MOI of HOOD section is as follows

S= 12753.31926/440.5141

= 28.9509 mm^3

Case - 2 :

After optimization (0.5 offset of inner panel boundary.Thus, increasing the section area) of the Hood assembly designed previously let us calculate the section modulus for the same.

Above figure shows the optimized section that is extracted from the hood assembly where calculations needs to be carried out.

After calculation we get the following data,

Maximum moment of inertia = 4.835703690e+06[mm^4]

Minimum moment of inertia = 1.299871217e+04[mm^4]

The total distance of the hood Y = 881.0282 mm

Distance between the neutral axis to the extreme end = (881.0282/2) = 440.5141 mm

Hence section modulus considering minimum MOI of HOOD section is as follows

S= 12998.71217/440.5141

= 29.5080 mm^3

Conclusion:

From the above results we can observe that by increase in the sectional area, the moment of inertia & section modulus increases which again means its resistance towards bending increases.