Section Modulus calculation and optimization

Aim

To calculate the section modulus of the previously designed hood for analysing 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.

Section modulus is a geometric property for a given cross - section used in the design of beams of flexural members. other geometric properties used in design include area for tension and shear radius of gyration for compression and moment of inertia and polar moment of inertia for stiffness. any relationship between these properties is highly dependent on the shape in question equations for the section moduli of common shapes are given below there are two types of section moduli the elastic modulus the section moduli of different profiles can also be fond as numerical values for common profiles in tables listing properties of such.

Elastic section modulus

For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield strength of the material.

Use the Section from your Hood design and calculate the section modulus using the formula S = I/y

S = Section Modulus

I = Moment of Inertia

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

Come up with a new section that has improved the section modulus of the previous section and mention what change you made that has increased the strength.

Section modulus equations :

Plastic section modulus:

The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behaviour 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:

The Plastic Section Modulus is not the 'First moment of area. Both relate to the calculation of the centroid, but Plastic Section Modulus is the Sum of all areas on both sides of PNA (Plastic Neutral Axis) and multiplied with the distances from the centroid of the corresponding areas to the centroid of the cross section, while the First moment of area is calculated based on either side of the "considering point" of the cross section and it is different along the cross section and depends on the point of consideration.

First Design Study

The intersection of the design was taken and then section inertia Analysis was done

^{Moment of inertia (max)=6.173x10^8 mm4}

^{Moment of inertia (min)=1.727x10^6 mm4}

Y=440.04/2=220.02

S=I/Y

S=1.727 x 10^6 /220.02 =4.7 mm^3

Hood Design Optimization

By increasing the depth of the inner panel by 0.5mm

^{Moment of inertia (max)=6.471x10^8 mm4}

^{Moment of inertia (min)=1.835x10^6 mm4}

Y=440.04/2=220.02

S=I/Y

S= 1.835x10^6 /220.02 = 5.0mm^3

Conclusion

Here the difference will be seen in the moment of inertia and the change in the section modulus can be seen by the change in the design Depth