Section Modulus calculation and optimization

Objective: To calculate the section modulus of the Hood and optimisation to improve the overall section modulus.

Section Modulus:

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

Mathematically, S= I/Y

ASSUMPTIONS IN THEORY OF BENDING

The material of the beam is stressed within elastic limit and obeys Hooke’s law.

The transverse sections which are plane before bending remains plane after bending.

The material of the beam is perfectly homogenous.

Each layer of the beam is free to expand and contract independently of the layer, above or below it

The value of young’s modulus for the material of beam is same in tension and compression

Bending Equations for Beams:

M/I=σ/y=E/R

M= Bending moment

I= Movement of inertia of the area of cross section

σ = Bending stress

y= distances of extreme fibre from the neutral axis

E=Young’s modulus

R= Radius curvature

From the bending Equation M/I=σ/y

Or, M=σ*I/Y =σ*S [ where S is the section modulus]

The line of intersection of the neutral layer with any normal cross section of a beam is known as neutral axis of that section or the neutral axis through a beam where the stress is zero ,that is there is neither compression nor tension.

As per formula Bending movement proposal to the section modulus and bending stress.

We are taking σ value constant, then if we increase section modulus then bending movement also increase.

So we can conclude if bending movement increasing then bending resistances also increasing.

Bending resistances increasing that means strength also increasing.

S ↑ M ↑Strength ↑Failure mode decreasing ↓

Case 1: Section modulus in the Hood design.

In Hood design created one plane at the natural axis then help of intersection curve created sketch on the outer and inner panel.

Used section analysis comment then got below mentioned data in NX software .

Imax = 5.579e+06 mm^4

Imin = 1.725e+04 mm^4

Y= distances of extreme fibre from the neutral axis= 442mm

Smax = Imax/y= 5.579e+06 /442= 15.1788 mm^3

Smin =Imin/y=1.725e+04/442= 4.6980mm^3

Case 2 : Section modulus in the Hood design

In this time increased outer panel and inner pane width increased so hood area also increased. Now again used Section Analysis comment.

Offset outer panel 1mm upware direction.

Smax = Imax/y= 5.7125e^+06 /442.21=15.54175 mm^3

Smin =Imin/y=1.7928e+04/442.21 = 4.8823 mm^3

If I compare both the section then I have got some improvement in the second section modulus around 0.1843mm^3 increased.

Conclusion:

1. Section modulus value increased as compared to 1^st and 2^nd
2. Section modulus increased so strength also increased and failure mode decrease.