Section Modulus calculation and optimization

SECTION MODULUS OPTIMIZATION AND CALCULATION

AIM:-

• Our aim is to calculate the section modulus of the previously designed hood for analyzing its strength and also optimizing the design to see the difference in the bending strength of the hood. Higher the section modulus of a structure, the more the resistive it becomes to bending.

Defination of Section Modulus:-

• Ratio of total moment resisted by the section to the stress in the extreme fibre.
• It gives us an idea about how much of load the given structure can take.
• If the section modulus increases the moment of resistance increases and hence its load bearing capacity.

Formula Of Section Modulus:-

S=I/Y

Here,

• S = Section modulus ( Unit mm 3 )
• I= Moment of Inertia ( Unit mm 4 )
• Y= Distance from Neutral axis to the extreme end ( Unit mm )

Types of Section Modulus :-

• Elastic Section Modulus
• Plastic Section Modulus

• Elastic Section Modulus :-

The elastic section modulus is defined as the ratio of the second moment of area (or moment of inertia) and the distance from the neutral axis to any given (or extreme) fiber. It can also be defined in terms of the first moment of area.

• Plastic Section Modulus:-

  The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.

  The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case.

  The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

  .

HOOD SECTION MODULUS CALCULATION

Step-1

• First intersection taken from existing Hood design.
• Then to caluculate the moment of inertia we have create surface from the intersection curve on NX CAD 12 .
• After that calculate using Measure inertia for to get Maximum and Minmum Moment of Inertia for the Hood design.

Moment of Inertia(Maximum) = 4.81*10^6 mm^4

Moment of Inertia(Minimum) = 1.40*10^4 mm^4

y = 463.84/2 = 231.92 mm

S = I/y

Smax = 4.81*10^6/231.92 = 20.739*10^3 mm^3

Hood Design After Optimization:-

Step 2 :-

Here i have increased the inner panel and outer panel hood by 0.5 mm offset.

Moment of Inertia(Maximum) = 4.84*10^6 mm^4

Moment of Inertia(Minimum) = 1.46*10^4 mm^4

y = 451.69/2 = 225.84 mm

S = I/y

Smax = 4.84*10^6/225.84 = 21.431*10^3 mm^3

Conclusion :-

Here we have seen difference in change in section modulus and difference in moment of inertia by changing the design of inner panel and outer panel of hood ( Offset ).