Section Modulus calculation and optimization

DEFINITION OF SECTION MODULUS

Ratio of Area Moment of Inertia(I) to the Distance from the Neutral Axis to the Point where the Bending Normal Stress is determined(Y).

Section modulus (Z) = I/Y

In Detail:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.

Also Section modulus is the direct Measure of Strength of a beam. Higher the Section Modulus higher will be the Resistance to Bending.

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 is closed.

As we can see this is a closed surface.

MOI (max) = 9.133168707e+05 (mm^4)

MOI (min) = 4.028419155e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =487.6258mm

Y = 487.6258 / 2

= 243.8129 mm

Therefore, S = 40284.19155 mm^4/243.8129 mm

S = 165.225 mm^3

CASE 2: After optimization

OLD SECTION

NEW SECTION

1)5mm deep emboss done on the highlighted region of the inner hood panel.

2)0.5mm offset taken in the direction of the arrows.

new analysis after optimisation

MOI (max) = 9.337458821e+05 (mm^4)

MOI (min) = 7.199103083e+04 (mm^4)

As per the section modulus equation,

S = I/Y

I = MOI (min) value is considered

Y = Total distance /2, Total distance =487.6258mm

Y = 487.6258 / 2

= 243.8129 mm

Therefore, S = 71991.03083mm^4/243.8129 mm

S = 295.872 mm^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 material also increases.