Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION

Aim:

To Determine the Section Modulus value of the existing Hood Design and to make changes that model to increase the Section Modulus value of the new Hood Model.

Material Used:

Stainless Steel AISI 302

Introduction:

Section modulus is a geometric property for a given cross-section used in the design of beams or 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.

S = I/y

Where S = Section Modulus

I = Area Moment of Inertia

Y = Distance from neutral axis to the outer fibre of a material

Area Moment of Inertia – It signifies the tendency of cross section to resist bending. Greater its value greater is its tendency to resist bending.

Types of Section Modulus:

• Elastic Section Modulus
  • The elastic section modulus is defined as S = I / y, where I is the second moment of inertia (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 My = S × σ_y, where σ_y is the yield strength of the material.
• 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: Zp = AcYc + AtYt

In this case we are using Elastic Section Modulus. The Elastic Modulus given by Stress-Strain curve is given below.

Hood Section:

Section Modulus Calculation for the Existing Model:

Moment of Inertia Imin = 1.381922e+04 mm^4

Distance from neutral axis y = 444.5 mm

Section Modulus S = Imin / y = 1.381922e+04 mm^4 / 444.5 mm

Section Modulus for the existing model S = 31.01 mm^3

Updated Hood Section:

Section Modulus Calculation for the Updated Model:

Moment of Inertia Imin = 1.44756947e+04 mm^4

Distance from neutral axis y = 444.5 mm

Section Modulus S = Imin / y = 1.44756947e+04 mm^4/ 444.5 mm

Section Modulus for the Updated model S = 32.56 mm^3

Conclusion:

Thus from the results it is clear that the section modulus value is increased from 31.01 mm to 32.56 mm. From the conclusion it is also clear that the strength of the material is directly proportional to the moment of inertia, hence increase in sectional area of the object have increase in the overall mass of the object. Thus we have increased strength.