Section Modulus calculation and optimization

Objective: 

To calculate the section modulus of the car hood previously designed by finding the Moment of Inertia using the NX CAD software, and also to optimise the cross section for a better result.

Section Modulus Definition:

Section Modulus is a geometric property used to calculate the bending stresses in a structural member.

Mathematically,

It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.

It is denoted by S.

S= I/ymax

Mathematically By bending stress equation,

M/I = σmax/ymax

M = σmax × (I/ymax)

M = σmax × S

Where,

S = Moment of Inertia(m⁴)

y = distance from NA to extreme layer(m)

The unit of section modulus is m³.

 Usually for calculating the Section Modulus, the most extreme fibre which is the farthest from the neutral axis is considered during the calculations.

The significance of Section Modulus is that it defines the resistance of a body to bending. Higher the value of Section Modulus, the more resistant is the body towards bending.

 In the above equation, M is the maximum bending moment (or moment of resistance offered by the section). Hence moment of resistance offered by the section is maximum when section modulus S is maximum. Hence section modulus represents the strength of the section.

Note: Section Modulus varies with respect to the shape of the cross-section.

Factors that influence the section modulus:

• Area - Area is directly proportional to section modulus
• Thickness of sheet metal- Thickness is also directly proportional to the section modulus
• Distance between the outermost layer to the neutral axis called Y. Y is inversely proportional to section modulus.

Case Study 1:

Hood design as per the master section without offset

 

From above images

Minimum Moment of Inertia I(min)             =2.514 x 10^5 mm^4

Maximum distance from NA axis ymax        =440 mm

                                                           S1= I/ymax

                                                               =2.514 x 10^5/440

                                                               =571.4 mm^3.

Case Study 2:

Hood inner panel offset 0.5mm from previous case

From above images

Minimum Moment of Inertia I(min)             =2.559 x 10^5 mm^4

Maximum distance from NA axis ymax        =440 mm

                                                           S2= I/ymax

                                                                =2.559 x 10^5/440

                                                                =581.5 mm^3.

Conclusion:

From the above case study analysis, we can say that the section modulus increases with an increase in offset value nothing but an increase in Cross-sectional area.

If section modulus increases then then component strength also increases. From the above 2 cases wee can see that S2 is greater then S1. Which implies that increase in area increases the section strength.

                                                  S2 > S1

In here comparing these two cases the percentage of increase in section modulus is 1.76% in case study two. Which gives good strength to hood.

                                                  S2 = 1.76%S1+S1

So, here section two is optimized section.