Section Modulus calculation and optimization

SECTION OF MODULUS

Section modulus is a direct measure of the strength of a cross-sectional area of ​​an object about a reference (neutral) axis. Strength is nothing more than being able to withstand greater loads. The higher the strength, the greater the load it can withstand. This strength can be directly measured from the resistivity equation and defined by Section modulus represented by the symbol "S"

S = I / Y

where,

I = Moment of Inertia

Y= Distance from the reference line (Neutral axis) to the point at extreme end of the object.

Moment of inertia simply provides resistance to moments, bending, or torsion. In other words, how much resistance is provided to deform when an external load is applied to the body.

The higher the moment of inertia value, the greater the resistance to deformation under a given load.

Therefore, it can be said that the moment of inertia is directly proportional to the strength of the material, and the strength of the material can be calculated using the section modulus.

Varying the neutral axis to the positive or negative side reduces the overall strength of the body.

This is inversely proportional to the section modulus, the Y value here, as the strength is higher only at certain points if the neutral axis is in the middle of the section.

On the basis of this formula, calculations for the section modulus of Hood Assy are as explained below: -

Moment of inertia through Catia software for original section:

Length of section through Catia software for original section:

These given below values are obtained by the Calculating Moment of Inertia through Catia software

I_max:- 1.503x10⁸ mm⁴

I_min:- 8.602x10⁵ mm⁴

Total length of 'Y' value was 480.708 mm

So, at neutral axis we need 'Y' value:-Y/2=480.708/2=240.354 mm

1)Section modulus(S_min):-I/Y=8.602x10⁵ mm⁴ / 240.354 mm

=3.58x10³ mm³ (Minimum strength).

2) Section modulus(S_max):-I/Y=1.503x10⁸ mm⁴ / 240.354 mm

=6.253x10⁵ mm³ (Maximum strength).

The strength of hood varies from 3.58x10³ mm³ to 6.253x10⁵ mm³

Moment of inertia through Catia software for modified section:

New curve highlighted in orange colour for different calculations.

Modifications:-

1 mm offset to inner panel curve to increase cross sectional area.

These given below values are obtained by the Calculating Moment of Inertia through Catia software

I_max:- 1.61x10⁸ mm⁴

I_min:- 9.507x10⁵ mm⁴

Total length of 'Y' value was 480.708 mm

So,at neutral axis we need 'Y' value:-Y/2=480.708/2=240.354 mm

1)Section modulus(S_min):-I/Y=9.507x10⁵ mm⁴ / 240.354 mm

=3.95x10³ mm³ (Minimum strength).

2) Section modulus(S_max):-I/Y=1.61x10⁸ mm⁴ / 240.354 mm

=6.698x10⁵ mm³ (Maximum strength).

The strength of hood varies from 3.95x10³ mm³ to 6.69x10⁵ mm³

• Comparing both hoods here, it can be seen there is a change in both MAX and MIN strength values, increasing the cut area by 1mm increases the minimum thickness value from 58x10³ mm³ to 3.95 x10³ mm³. understood. Therefore, increasing the cross-sectional area increases the strength.
• However, seeing a slight reduction in maximum strength from 253x10⁵ mm³ to 6.69x10⁵ mm³, I believe this is due to the hood design. What we want to know is whether the minimum strength increases, the maximum strength increases, or both, as the cross-sectional area increases.
• So, Newton's First Law states that the greater the mass, the greater the resistance to moving an object, and therefore the greater the force required to move This resistor was called MOMENTUM OF INERTIA.
• For hoods, the same principle works here i.e., 1 mm increase in cross-sectional area increased the minimum load capacity or strength by about 8%. We know this from the explanation
• Thestrengthofamaterialalsodependsonitscomposition,itsthickness,andthecross-sectionalareaof​​the

• Conclusion: -

Since the strength of a material is directly proportional to its moment of inertia, increasing the cross-sectional area increases the total mass of the object, increasing its strength.