Section Modulus calculation and optimization

SECTION MODULUS OF AN HOOD

• Section modulus is a direct measure of the strength of any sectional area of an object about a reference axis(neutral axis).
• Strength is nothing buy, capable of supporting greater loads, so the higher the strength it has highly capable of supporting greater loads.
• This strength can be measured directly from the section modulus formula, and defined by the below formula.
• Section Modulus is represented with a symbol of 's'.

S = I/Y

Where 'I' moment of inertia

'Y' is the distance from the reference line(neutral axis) to one of the extreme ends of the object.

• 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, the higher the value of the moment of inertia, have higher the resistance to deform under a certain load, hence we can say that moment of inertia is directly proportional to the strength of the material, and the strength of the material can be calculated with the help of section modulus.
• If we vary the neutral axis towards the positive or negative side overall strength of the body will decrease, because when the neutral axis line lies in the middle of the section only have higher strength at a particular point. So, here 'Y' value was intensely proportional to section modulus.

That's why the formula is represented as above.

By using the same principle, I'm going to calculate the strength of a hood panel.

Here, Strength is equal to the Moment of inertia divided by Distance.

DEFAULT DESIGN CALCULATION:

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

Here is the Maximum and Minimum Inertia values are,

So, at the neutral axis, we need the 'Y' value,

Here, the Section length is 884mm,

so,

1. Minimum Strength Calculation:

Therefore, the Minimum strength of Optimized Design is,

2. Maximum Strength Calculation:

Therefore, the Maximum strength is,

OPTIMIZED DESIGN CALCULATION:

We need to optimize the design by increasing the depth of the inner panel by 0.5mm.

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

Here is the Maximum and Minimum Inertia values of Optimized design,

There is no change in length while Optimizing, but we can notice the changes in Area and Inertia.

1. Minimum Strength Calculation:

Therefore, the Minimum strength of Optimized Design is,

2. Maximum Strength Calculation:

Therefore, the Maximum strength of Optimized Design is,

Here, The minimum strength of Optimized design > Minimum strength of Default design.

CONCLUSION:

So, the Minimum strength of the Optimized design has better than its default one.

• So, here when comparing both the hoods there are changes in both Maximum and Minimum strength values, what we came to know is that when we increased the sectional area by 1mm the value of minimum strength was increased from 0.0389 to 0.0396, Hence Increase in cross-sectional area results increase in Minimum strength.
• But, when we see the value of maximum strength it slightly decreases from 11.482 to 11.467, This is because of design. We need to know, when increase in cross-section, we may face sometimes increases in Minimum strength, an Increase in Maximum strength, and sometimes both. This is because of the design and its cross-section.
• So, Newton's first law also explains that, if higher the mass, then the force required to move the object is also high due to offering more resistance in order to move the object. This resistance we called Moment of Inertia.

Hence, the strength of the material is directly proportional to the moment of inertia, so with an increase in the sectional area there is an increase in the overall mass of an object, hence have increased in strength.