Section Modulus calculation and optimization

CHALLENGE : SECTION MODULUS OF THE HOOD

Aim:

To find the section modulus of the hood and optimisation to improve the overall section modulus.

Section Modulus:

1) The section modulus (S) is geometric property of the cross section used for designing beams and flexible members.

Formula of Section Modulus:

It may be defined as the ration of total moment resisted by the section to the stress in the extreme fibre which is equal to yield stress.

S = I/Y

Where,

S = Section modulus (mm^3)

I = Moment of Inertia of the section about the bending axis. (mm^4)

Y = Distance between the neutral axis and extreme end of the object (mm)

Trail 1 : Calculation

Before Optimization

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

2) We have to make sure that the curve obtained is a single & closed curve.

Fig : Section modulus of trail 1

Fig : Section modulus of trail 1

MOI (max) = 4.805634938e+06 (mm^4)

MOI (min) = 1.418350172e+04 (mm^4)

Total length of 'Y' value is 875.5854mm

So,at neutral axis we need 'Y' value :

Y/2 = 875.5854/2

Y = 437.79 mm

1) Section modulus max (S) :

I/Y = 4.805634938X10^6mm⁴/437.79mm

S (max) = 10.977X10³mm³(Maximum strength).

2) Section modulus min (S) :

I/Y = 1.4183501x10⁴mm⁴/437.79mm

S(min) = 0.032397x10³mm³(minimum strength).

So the strength of an hood varies from 0.032397x10³mm³to 10.977X10³mm³

Trail 2 : Calculation

After optimization

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

Fig : Section modulus of trail 2

Fig : Section modulus of trail 2

MOI (max) = 4.809023586e+06 (mm^4)

MOI (min) = 1.421858320e+04 (mm^4)

Total length of 'Y' value is 875.5854mm

So,at neutral axis we need 'Y' value :

Y/2 = 875.5854/2

Y = 437.79 mm

1) Section modulus max (S) :

I/Y = 4.809023586X10^6mm⁴/437.79mm

S (max) = 10.984X10³mm³(Maximum strength).

2) Section modulus min (S) :

I/Y = 1.421858320x10⁴mm⁴/437.79mm

S(min) = 0.0324780x10³mm³(minimum strength).

So the strength of an hood varies from 0.0324780x10³mm³to 10.984X10³mm³

Conclusion :

Hence when comparing Trail 1 & Trail 2,

1. The section modulus value of Trail 2 is higher than the Trail 1

2. As we increase the section area, the moment of inertia & section modulus increases which means strength and load material also increases.