Challenge

Section Modulus calculation and optimization

BBhaumik Chavda4 Nov 2022

Section Modulus Optimization

Objective: To calculate section modulus for hood assembly and to optimize it by modifying parameters of same.

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members.
There are two types of section modulus, the elastic section modulus and the plastic section modulus.

Here, elastic section modulus is defined as

S = I / y,

where, I is the second moment of area (or area moment of inertia) and y is the distance from the neutral axis to any given point.

It is often reported using y = c, where c is the distance from the neutral axis to the most extreme point.
It represents the strength of the section.
Greater the value of Z, greater will be the strength of the section.
The section modulus depends upon the moment of inertia which again depends not only on the total area of the cross-section but also on the disposition of the area with respect to neutral axis.

Plastic Section Modulus

The plastic section modulus is used for materials where the elastic yield is acceptable and the plastic behavior is considered to be an acceptable range.

It depends on the location of the plastic neutral axis. The PNA is the axis that bisects the cross-section such that the compressive force from the region in compression is equal to the tension force from the region under tension. So, for sections with a constant yield stress, the area above and below the PNA will be equal, but for mixed sections, this is not necessarily the case.

Mathematically,

The plastic section modulus is the sum of the areas of cross-sections on each side of the plastic neutral axis that may or may not be equal and multiplied by the distance from the local centroid of the two regions to the plastic neutral axis.

Zₚ = (Ac × yc) + (Aₜ + yₜ)

Where,

Ac = Area of cross-section under compression.

Aₜ = Area of cross-section under tension.

yc = Distance from the plastic neutral axis to the center of gravity of the areas under compression.

yₜ = Distance from the plastic neutral axis to the center of gravity of areas under tension.

Since on the neutral axis, the area under compression is equal to the area under tension.

So,

Ac = Aₜ

And,

yc = yₜ

Section modulus calculation for hood is given below:

Case 1: As shown in the image minimum and maximum values of Moment of Inertia are obtained through simulation.

As shown in image minimum and maximum values of moment of inertia are given.
Considering minimum value of it.
Calculations are listed below:

Here, Moment of inertia (I) is: 1.454×10ˆ4 mmˆ4

Now the distance denoted by y is 484/2= 242mm

So, Section Modulus is : 1.454*10^4 / 242= 60.08 mm^3

Now Case 2: Optimized Design

For that the inner panel was given 5 mm offset from it’s initial position.

As image shown below:

Here, Moment of inertia (I) is: 1.781×10ˆ4 mmˆ4

Now the distance denoted by y is 484/2= 242mm

So, Section Modulus is : 1.781*10^4 / 242= 73.60 mm^3

Conclusion:

By increasing gap between Inner and outer panel value of MOI and section modulus increased.
From above analysis we can say that strength of hood is increased.

Section Modulus calculation and optimization

Plastic Section Modulus

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Plastic Section Modulus

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.