Section Modulus calculation and optimization

SECTION MODULUS CALCULATION - NX CAD

The section modulus is a measure of the resistance of a cross-section to bending. It is defined as the ratio of the moment of inertia of the cross-section about its neutral axis to the distance from the neutral axis to the outermost point of the section.

The section modulus is often used in structural engineering to design and optimize beams, columns, and other structural members.

#1 Section Modulus of Hood design

Here the obtained values of momenny of inertia generated by NX software is :

Section#: 1
Type: Hollow
CG: (-0.001486338, 746.215768923, -931.284894435) [mm]
MOI (Max):7.471225980e+06[mm^4]
MOI (Min):2.221559579e+04[mm^4]
Principal Directions:
Max: (-0.000000450, 0.985107587, 0.171939066)
Min: (1.000000000, -0.000001209, 0.000009541)
Section Length:5.546391054e+03[mm]
Section Area:110.903866903[mm^2]

The formula for the section modulus is:

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

Distance between the neutral axis and the extreme end of the object = y = 884.13/2 = 442.05

I_{MAX= 7471225.980 mm⁴}

I_{MIN= 22215.595 mm⁴}

y = 442.05 mm

_{S (max)= 7471225.980 / 442.05 = 16884.12 mm³}

_{S (min)= 22215.595 / 442.05 = 50.25 mm³}

#2 Section Modulus of Optimized Hood design

Section Modulus can also be represented as

S = Σ m_iA_i² / y where A is the area of the section and M is the mass of the body

From the above equation, it can be observed that the section modulus of the body is directly proportional to the sectional area of the body.

Here the section area is increased by reducing the embossing depth and offsetting the outer panel by 3 mm. This increases the value of section modulus.

Section#: 2
Type: Hollow
CG: (-0.001708607, 744.735810128, -931.543204024) [mm]
MOI (Max):5.115601111e+06[mm^4]
MOI (Min):1.667372331e+04[mm^4]
Principal Directions:
Max: (-0.000000413, 0.985107587, 0.171939066)
Min: (1.000000000, -0.000001245, 0.000009535)
Section Length:3.760449359e+03[mm]
Section Area:75.196194223[mm^2]

Y= 885.2107/2 = 442.60

I_{MAX= 5115601.111 mm⁴}

I_{MIN= 16673.72331 mm⁴}

_{S (max)= 5115601.111 / 442.60 =11558.068 mm³}

_{S (min)= 16673.72331 / 442.60 =37.6722 mm³}

_CONCLUSION

If we increase the gap between the inner and outer panel of hood eventually section length will increase thus MOI will increase.

When comparing both the Sections #1 and #2 there is changes in both MAX and MIN strength values, By increasing the cross sectional area we can see that the strength is also increased.

This concludes the calculation and optimisation of the section modulus of the hood design.