Section Modulus calculation and optimization

Aim:-

Use the Section from Hood design and calculate the Section Modulus using the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

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).

There are two types of section modulus:

• Elastic section modulus(S).
• Plastic section modulus(Z).

Elastic section modulus

For general design, the elastic section modulus is used, applicable up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S = I / y, where I is the area moment of inertia, not to be confused with moment of inertia and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yeild strenthof the material.

Section Modulus of Initial Hood Design:-

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

I_max = 4823086.87 mm⁴

I_min = 13868.06714 mm⁴

y = 877.9044/2 mm

=438.9522 mm

S_max = I_max / y =4823086.87 / 438.9522 = 10987.7258 mm³

S_min = I_min / y = 13868.06714 / 438.9522 = 31.5937 mm³

^{Section Modulus of Optimized Hood design:-}

What changes I made and Why?

Section Modulus can also be represented as

S = Σ m_iA_i² / y where A is the area of the section and M is the mass of the body

From the above equation, it can be observed that the section modulus of the body is directly proportional to the sectional area of the body.

Here the section area is increased by reducing the embossing depth and offsetting the outer panel by 2 mm. This increases the value of section modulus.

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

I_max = 4949922.127 mm⁴

I_min = 16227.8484 mm⁴

y = 878.6032/2 mm

=439.3016 mm

S_max = I_max / y = 4949922.127 / 439.3016 =11267.70794 mm³

S_min = I_min / y = 16227.8484 / 439.3016 = 36.9041 mm³

^Conclusion:

By comparing the values we can say that section modulus of the optimized hood (#Design 2) is increased .MOI increases with the increase of section area.MOI increases with the increase of section length.If we increase the gap between the inner and outer panel of hood eventually section length will increase thus MOI will increase.