Section Modulus calculation and optimization

Section Modulus Calculation Of Hood

Aim

To calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Section modulus

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members, it is also referred to as the Polar Modulus or the Torsional Sectional Modulus. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus.

S=I/Y

Here,

S = Section modulus

I= Moment of Inertia (Unit mm 4)

Y= Distance from Neutral axis to the extreme end (unit mm)

The Unit of a “section modulus” is (mm3)

Changing the position can show the difference in bending which is because of the centroid distance from extreme fiber end.

In Layman's terms, in this position there is more material from axis to the specific direction, to resist the load which makes less bend amd improves the strength.

Elastic section modulus

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.

Section modulus equations
Cross-sectional shape	Figure	Equation	Comment
Rectangle			Solid arrow represents neutral axis
doubly symmetric I-section (major axis)		,	NA indicates neutral axis
doubly symmetric I-section (minor axis)			NA indicates neutral axis
Circle			Solid arrow represents neutral axis
Circular hollow section			Solid arrow represents neutral axis
Rectangular hollow section			NA indicates neutral axis
Diamond			NA indicates neutral axis
C-channel			NA indicates neutral axis

First Design Study

The Intersection of the design was taken and then section Inertia Analysis was done-

Calculation:

CASE 1: Before Optimization

The Hood which was already created is imported and the section inertia analysis is done.

We have to make sure that the curve obtained is a single/closed curve.

Fig 1.1

Fig 1.2

MOI (max) = 9.00839157e+07 (mm^4)

MOI (min) = 2.541234366e+05 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =879.7354mm

Y = 879.7354/ 2

= 439.8677mm

Therefore, S = 254123.4366mm^4/439.8677mm

S = 577.726mm^3

CASE 2: After optimization

The hood inner panel’s curve is offset by 0.5mm outwards and section inertia analysis is done same as case 1 for a closed curve.

Fig 1.3

Fig 1.4

MOI (max) = 9.076324836e+07 (mm^4)

MOI (min) = 2.632763899e+05 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =879.7354mm

Y = 879.7354/ 2

= 439.8677mm

Therefore, S = 263276.3899mm^4/439.8677mm

S = 598.535mm^3

Conclusion:

Hence when comparing case 1 & case 2,

1. The section modulus value of case 2 is higher than the case 1
2. As we increase the section area, the moment of inertia & section modulus increases which means strength and load materialalso increase