Section Modulus calculation and optimization

Section modulus

Aim

• Calculate moment of inertia
• Calculate section modulus

What is section modulus

Section modulus is the geometric property for a given cross-section used in the design beam other geometric properties used in design include area for tension, radius of gyration for compression and moment of inertia for stiffness. Any equation for the section moduli , The elastic section modulus (S), plastic section modulus(Z)

The elastic section modulus is used , Applied up to the yield points for more metals.

The elastic section modulus is defined as S= I/Y

I= Moment of inertia

Y= y is the distance from the neutral axis to any given fiber

What is Moment of Inertia

• The moment of inertia is a measure of the 'efficiency' of a cross-sectional shape to resist bending caused by loading.

I going to calculate the strength of the hood inner panel by using same principal as I mentioned above.

Figure no. 1

Figure no.2

Here the Area moment of inertia calculated by Nx-CAD software obtained values are.

I_(Max) = 8.316710895 × 10⁵ mm⁴

I_{(min) =} 8.081805433 × 10³ mm⁴

Total length of the Y was 486.8406

We need Y value: - Y/2 = 486.8406/2

= 243.4203

1. Section modulus(S): - I/Y

I = 8.316710895×10⁵ mm⁴

Y = 243.4203

= 8.316710895×10⁵ /243.4203

= 3.416 × 10³ mm³(Maximum strength

2. Section modulus(S): - I/Y

I = 8.081805433×10³ mm⁴

Y= 243.4203

= 8.081805433×10³ / 243.4203

= 0.0332 × 10³ mm³(Minimum strength)

So, the strength of a hood differs from 0.0332 × 10³ mm³ to 3.416×10³ mm³

Design optimization

1. Here the inner panel curve offsetting by 0.5mm that is increasing cross sectional are

The results

Figure no.3

Figure no.4

Obtained the values of

I_max = 8.2999181×10⁵mm⁴

I_min = 8.334771430×10³mm⁴

Total length of the Y was 486.8406

We need Y value: - Y/2 =486.8406/2

= 243.4203

1)Section modulus(S):-I/Y

= 8.2999181×10⁵ / 243.4203

= 3.409×10³mm³(Maximum strength)

2)Section modulus(S): - I/Y

= 8.334771430×10³/243.4203 / 243.4203

= 0.0342×10³mm³(Minimum strength)

So, the strength of the hood varies from 0.0342×10³mm³ to 3.409×10³mm³

Here the inner panel curve offsetting by 1mm that is increasing cross sectional area.

Figure no.5

Figure no.6

Obtained the values of

I_max = 8.286021745×10⁵mm⁴

I_min =8.614078296×10³mm⁴

Total length of the Y was 486.8406

We need Y value: - Y/2 = 486.8406/2

=243.4203

1. Section modulus(s): - I/Y= 8.286021745×10⁵ / 243.4203

= 3.403×10³mm⁴(Maximum strength)

2.Section modulus(S):-I/Y = 8.614078296×10³ / 243.4203

= 0.035×10³mm³(Minimum strength)

So, the strength of the hood varies from 0.035×10³mm³ to 3.403×10³mm³

Conclusion

Hence when comparing these three cases,

1. The section modulus value of one has higher than the remaining two cases.
2. As we increase the cross-sectional area, the moment of inertia and section modulus increases (strength of material directly proportional to the moment of inertia) which means overall mass of the object and strength also increased .