Section Modulus calculation and optimization

Aim:

To find the section modulus of the hood and optimization to improve the overall section modulus.

Objective:

Use the section from your Hood design and calculate the section modulus using the formula S= I/y.

Section Modulus:

The section modulus (S) is geometry property of the cross section used for designing beams and flexural members. It does not represent anything physically.

Formula of section Modulus: It may be defined as the ratio of total moment resisted by the section to the stress in the extreme fibre which is equal to yield stress.

Which is equal to yield stress.

Therefore;

S=I/y, Where

S= Section modulus (mm³)

I = Moment of inertia of the section to the stress in the extreme end of the object (mm⁴)

Y= Distance between the neutral axis and extreme end of the object (mm).

Area Moment of Inertia:

The area moment of inertia of a beam cross section area measures the beam ability to resist bending. The larger the moment of inertia less will be the bend.

Where,

M = Bending Moment

I = Area moment of Inertia

E = Young modulus

R = Radius of gyration

Neutral Axis: When beam is subjected to pure bending the top most fibres of the beam are subjected to maximum compression, while the bottom most fibre of the beams are subjected to maximum tension.

• This picture contains the following scene, Diagram of a beam on its narrow edge supported at both ends.
• A man is walking on a straight beam. Diagram of a beam resting on its flat side supported at both ends.
• A man is walking on the straight beam and its bending in the middle.

DESIGN 1: Section Modulus of Initial Hood Design:

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

I_max = 9023751.130 mm⁴

I_min = 28430.641 mm⁴

y = 438.5 mm

S_max = I_max / y = 9023751.130 / 438.5 = 20,578.67 mm³

S_min = I_min / y = 28430.641 / 438.5 = 64.83 mm³

DESIGN 2: 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 3 mm. This increases the value of section modulus.

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

I_max = 9007228.003 mm⁴

I_min = 28795.696 mm⁴

y = 438.5 mm

S_max = I_max / y = 9007228.003 / 438.5 =20,540.99 mm³

S_min = I_min / y = 28795.696/ 438.5 = 65.66 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.