Objective

To calculate the Section Modulus cation for the Hood section and optimize the section of hood to improve the Section modulus.

Introduction

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 value for top and bottom of centroid, the maximum section modulus (S_max) and Minimum section Modulus (S_min)

Important of Section Modulus

• Section Modulus is vital factor for designing beam 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 tougher and more capable to withstand larger loads.

The elastic section modulus is defined as

`S=I/Y`…………………………………… (1)

Where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to extreme end. It is often reported using Y = c, where c is the distance from the neutral axis to the most extreme end.

The symbol S is used customarily for the section modulus. In general, as the section modulus becomes larger, the strength against bending also becomes larger. Regarding bending, the maximum bending stress σ acting on the outer surface of the part can be calculated using the following equation.

`σ=M/S`…………………………………… (2)

Where σ is the Maximum bending stress (kgf/cm²) and M is the maximum bending moment (kgf*m)

Thus from equation (1) and (2), it can be said that higher the section modulus, higher the section modulus, higher will be the resistance to bending.

            Given section would be in stainless steel AISI 302- Cold Roller- y = 520MPa, here the section would be consider as Hoods cross section.

Case 1:- Section Modulus of the Initial Hood Design

            Moment of the 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.

Figure 1 Cross section of hood 1

Figure 2 Section Inertia for the hood 1

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

I_max = 5.145 e⁺⁰⁶ mm⁴

I_min = 1.537 e⁺⁰⁴ mm⁴

^“Y^” for section of Hood 1 = 447.3mm

 S_max = I_max/Y = 5.145 e⁺⁰⁶ / 447.3 = 11502.34 mm³

S_min = I_min/Y = 1.537 e⁺⁰⁴ / 447.3 = 34.37 mm³

Case 2:- Section Modulus of the Hood Design after modification

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 with 2-3 mm, offsetting the outer panel by 1-2 mm and increases few more embosses for better inertia. This in turn increases the value of section modulus

Figure 3  Cross section of hood 2 after modification

Figure 4 Section Inertia for the hood 2 after modification

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

I_max = 5.190 e⁺⁰⁶ mm⁴

I_min = 1.696 e⁺⁰⁴ mm⁴

^“Y^” for section of Hood 2 = 447.3mm

 S_max = I_max/Y = 5.190 e⁺⁰⁶ / 447.3 = 11603.01 mm³

S_min = I_min/Y = 1.696 e⁺⁰⁴ / 447.3 = 37.93 mm³

Conclusion:

• When compared section values in case 1 and case 2, we can see the improved model has increased by 1%.
• Initial hood design is optimized to design the second hood model are calculated.
• By increasing resistance against bending stress will optimizing the design.