Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION

By considering the Section from Hood design we should calculate the Section Modulus using the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object.

Section modulus:-
Section modulus is the property of the cross-section that is used while the design of
beams by referred to as the Polar Modulus and 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.

Bending Stress Equation (Flexural Equation), used in calculating the moment of inertia in the Section Modulus.

M/I = 6b/y = E/R

Where, M=Maximum bending moment(N-mm)

I=M.I. @ neutral axis(mm^4)(MOMENT OF INERTIA)

6b=Bending Stress (N/mm^2)

y =Distance from Neutral axis (mm)

E=Modulus of elasticity(N-mm^2)

R= Radius of curvature (mm)

The section modulus is classified into two types:-
1. Elastic section modulus:- The elastic section modulus is applicable up to the yield
point of material.
It is used in most engineering applications.
2. Plastic section modulus:- The plastic section modulus is generally used for material
in which plastic behavior is observed.
Let’s know about each of them in detail.

Elastic section modulus:
Elastic section modulus is the ratio of moment of inertia about a neutral axis I @ N.A
and the maximum distance between the neutral axis and outermost fibre of beam Y @N.A.

Plastic section modulus:-

The plastic section modulus is necessary to calculate plastic moment capacity of the
section. The plastic section modulus is the addition of moment of area of area under compression
about PNA (plastic neutral axis) and the moment of area of area under tensile stress.

SECTION MODULUS EQUATION FORMULAES:-

Cross-sectional shape	Figure	Equation	Description
Rectangle		Iab=bd^3/12	Solid arrow represents neutral axis
Symmetrical Equation I section		A=A1+A2+A3 Ixx= 1/12(BH^3-(B-b)h^3)	NA indicates neutral axis
Circle		Area=3.14d^2/4 IAB=5*3.14d^4/64	Solid arrow represents neutral axis

IMAGE FRONT VIEW OF THE SECTION MODULUS VIEW

IMAGE THE CALCULATED SECTION MODULUS IN NX.

By these challenge we should understand to how to calculate and optimize the Section Modulus of the Hood.

Max moment of Inertia is calculated = 7.102 mm^4

Section area is Calculated = 363.589 mm^2