Section Modulus Calculation and Optimization of the Hood Designed

1. Objective:

• To calculate the section modulus for the previously designed hood and optimized hood.
• To come up with the new section that has improved section modulus of the previous section.

2. Material of the Hood considered: Stainless Steel ASI 302 - Cold Rolled, y = 520MPa

3. Design Software Used: NX 12

4. 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 same for both above and below of centroid of the cross-section. An asymmetric section has two values for top and bottom of the centroid, the maximum section modulus (S_max) and minimum section modulus (S_min).

There are two types of section moduli:

• Elastic Section Modulus
• Plastic Section Modulus

Significance of Section Modulus:

• Section modulus is important factor for designing beams and flexural members.
• Higher the section modulus, higher will be the resistance to bending.
• Easier to calculate strength and stresses in beams.
• If two beams are made of same material and the section modulus of two beams are being compared and vice versa, the beam with larger section modulus will be tougher and more capable to withstand larger loads.

We know that stress (σ) in a beam or structure is given by

σ = My / I

where M is Bending moment and

Section Modulus is given by

S = I/y.......................(2)

Where I = Moment of Inertia

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

From equations (1) and (2),

σ = M / S........................(3)

Thus from equation (3), it can be said that higher the section modulus, higher will be the resistance to bending.

5. Section Modulus of Initial Hood Design (Hood Design 1):

Moment of inertia of the hood cross-section is found using a command called "Section Inertia Analysis" in NX 12. Following results are obtained as shown below.

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

I_max = 5.104 e⁺⁰⁶ mm⁴

I_min = 3.711 e⁺⁰⁴ mm⁴

^{_{"y" for section of Hood design 1 = 450 mm}}

S_max = I_max / y = 5.104 e⁺⁰⁶ / 450 = 11342.22 mm³ .......................(5.1)

S_min = I_min / y = 3.711 e⁺⁰⁴ / 450 = 82.47 mm³ .......................(5.2)

6. Section Modulus of optimized hood design (hood design 2):

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 by 2-3 mm and offsetting the outer panel by 1-2 mm. This in turn increases the value of section modulus.

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

I_max = 5.152 e⁺⁰⁶ mm⁴

I_min = 1.658 e⁺⁰⁴ mm⁴

"y" for section of hood design 2 = 450 mm

S_max = I_max / y = 5.152 e⁺⁰⁶ / 450 = 11448.89 mm³ .......................(6.1)

S_min = I_min / y = 1.658 e⁺⁰⁴ / 450 = 36.84 mm³ .......................(6.2)

7. Conclusion:

• By comparing the values (5.1) and (6.1) we can say that section modulus of the optimized hood (design 2) is increased by 1% .
• Section modulus for the previously designed hood (design 1) and optimized hood (design 2) are calculated.
• Section modulus for the previously designed hood (design 1) is optimized to increase the section modulus there by increasing the resistance against bending stress.