Section Modulus calculation and optimization

OBJECTIVE:-

• To Calculate the section modulus for the previously designed hood.
• To Come up with a new section that has improved the section modulus of the previous section.

SECTION MODULUS:-

• Section modulus is the geometric property of a given cross-section used in the design of flexural members. Section modulus depends only on the cross-section shape of the beam or structure.
• For symmetric sections, the value of section modulus is the same for both above and below of centroid of the cross-section. An asymmetric section has two values for the top and bottom of the centroid, the maximum section modulus (S max) and minimum section modulus (S min).

FORMULA:-

Section modulus S = I/y

where I = Moment of Inertia

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

SECTION MODULUS OF INITIAL HOOD DESIGN:-

From the above analysis, the maximum and the minimum moment of inertia is obtained,

I(max) = 4937835.52 mm⁴

I(min) = 13124.73 mm⁴

y = 440 mm

S(max) = 4937835.52/440 = 11222.35 mm³

S(min) = 13124.73/440 = 29.82 mm³

SECTION MODULUS FOR OPTIMISED DESIGN #1:-

We know that, S = I/y

and the moment of inertia I = ∑ m A²

where A = Area of the section

and m = mass

So by applying the value of I in S, it becomes

S = ∑mA² /y

which indicates the Area of the section is directly proportional to the Section modulus.

thus, by increasing the area of the section, the section modulus can be increased. For increasing the area, the outer panel of the hood should be offsetted outwards.

DESIGN #1 is offsetted to 3mm from the original position,

From the above offsetted model analysis,

I(max) = 5137485.03 mm⁴

I(min) = 15295.46 mm⁴

y = 440 mm

S(max) = 5137485.03/440 = 11676.10 mm³

S(max) = 15295.46/440 = 34.76 mm³

The section modulus increases when the area increases.

To recheck the model, the outer panel is offsetted again with another 1mm and analyzed.

SECTION MODULUS FOR OPTIMISED DESIGN #2:-

The outer panel is offsetted for 4mm in this design,

From the above offsetted model analysis,

I(max) = 5218461.75 mm⁴

I(min) = 16241.64 mm⁴

y = 440mm

S(max) = 5218461.75/440 = 11860.14 mm³

S(min) = 16241.64/440 = 36.91 mm³

CONCLUSION:-

Thus the section modulus of the initial design of the car hood is calculated and compared with the optimized design and better results were found.