Section Modulus calculation and optimization

OBJECTIVE:

• To Find the section modulus for the current designed hood and feature hood.
• To Come up with the new section that has improved section modulus of the previous section.

MATERIAL OF THE HOOD:

• Stainless steel AISI 302 – cold-rolled – y = 520 MPa

SECTION MODULUS:

Section properties involve the mathematical properties of structural shapes. They are of great use in structural analysis and design. Note that these properties have nothing to do with the strength of the material, but are based solely on the shape of the section. It explains why some shapes are more efficient at supporting loads than others.

These properties are looked at in more detail following:

• centre of area (or centroid)
• second moment of area or moment of inertia (I)
• section modulus (S)
• radius of gyration (r)

All of these values are generally calculated for both axes of symmetry (x-x and y-y on the standard coordinate plane). These axes are shown in the following diagram.

There are two types of section modulus:

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

Let's see the basic calcultion for Section modulus:

Section modulus (S)= I/y

Where,

I = Moment of Interia;

y= extreme point from neutral axis.

For bending stress

σ = (M/I ) x y

where M is the Bending Moment

y is the distance between extreme point and neutral fiber

I is the Moment of Inertia

calculation of HOOD current design:

calculation no:1

Section Interia Analysis Report

The Maximum and minimum moment of inertia obtained are

I_max = 5.6360 x 10^*6 mm⁴

I_min = 1.8203 x 10^*4 mm⁴

y= 447.6 mm

The Section modulus is calculated using (1)

S_max = I_max / y = 5636009.025 / 447.6 = 12,591.619 mm³

S_min = I_min / y = 18203.755 / 447.6 = 40.669 mm³

calculation no:2

Section Interia Analysis Report

The Maximum and minimum moment of inertia obtained are

I_max = 5.618606 x 10^*6 mm⁴

I_min = 1.822890 x 10^*4 mm⁴

y= 447.6 mm

The Section modulus is calculated using (1)

S_max = I_max / y =5.618606 x 10^*6 / 447.6 = 12,552.739 mm³

S_min = I_min / y = 1.822890 x 10^*4 / 447.6 = 40.725 mm³

conclusion:

By comparing the values we can say that section modulus of the current hood (#Design 1) is good compared to Design 2.