Section Modulus calculation and optimization

Report On Section Modulus Calculation Of Hood

Aim :

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to come up with a new section that has an improved Section Modulus compared to the previous one 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.

THEORY:

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.

Section modulus represented with a symbol of 'S'.

S=I/Y

Here,

• S = Section modulus
• I= Moment of Inertia
• Y= Distance from Neutral axis to the extreme end
• The Unit of a “section modulus” is (mm^3)

Bending Equation Derivation

The following is the equation for simple bending:

M / I = σ /y = E / R

where,

• I = Moment of Inertia,
• E = Modulus of Elasticity,
• y = Distance from the neutral axis to the outer most fibre of the part
• σ = Stress at any fibre at a distance of y from the neutral axis,
• M = Bending moment and
• R = Radius of curvature.

Relationship between Section modulus & Bending Equation

considering,

M / I = σ /y

M = I /Y * σ

M = S * σ

Hence we can say that the bending moment and the section modulus are directly proportional to each other

Higher the section modulus, Higher the bending moment and vice versa.

Section modulus calculation :

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.

By using the same principle I am going to calculate the section modulus of an hood panel.

Here the moment of inertia was calculated by using the NX CAD-software, obtained values are

• IMax: 8.98928X10^7 (mm^4)
• Imin: 2.96941x10^5 (mm^4)

Total length of 'Y' value was 876.4647 mm

So, from neutral axis we need 'Y' value: y/2= 876.4647/2= 438.23235 mm

1)Section modulus(S): I/Y=8.98928X10^7 (mm^4)/ 438.23235 mm

= 2.05125X10^5 mm^3(Maximum strength).

2) Section modulus(S): I/Y= 2.96941x10^5 (mm^4)/ 438.23235 mm

= 0.677x10^3 mm^3(minimum strength).

So the strength of an hood varies from 0.677x10^3 mm^3 to 2.05125X10^5 mm^3.

Now, one more trail is that, here the inner panel curve offsetting outside by 0.5 mm

i.e increasing in cross sectional area,the results shown below.

obtained values are

• IMax: 8.97259X10^7 (mm^4)
• Imin: 3.00706x10^5 (mm^4)

Total length of 'Y' value was 876.4647mmm

So, from neutral axis we need 'Y' value: y/2= 876.4647 /2= 438.23235 mm

1)Section modulus(S): I/Y= 8.97259X10^7 (mm^4)/ 438.23235 mm

= 2.04745x 10^5 mm^3 (Maximum strength).

2) Section modulus(S): I/Y= 3.00706x10^5 (mm^4)/ 438.23235 mm

= 0.68617x10^3 mm^3 (minimum strength).

So the strength of an hood varies from 0.68617x10^3 mm^3 to 2.04745x 10^5 mm^3.

Comparitively, The section modulus whose cross section was offseted by 0.5mm (increased) is higher, therefore increase in cross sectional area increases the section modulus and increase in bending resistance.

CONCLUSION

Now, The calculation of the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to come up with a new section that has an improved Section Modulus compared to the previous one is done. And proved that increase in cross sectional area increases the section modulus and increase in bending resistance.