Section Modulus calculation and optimization

Objective

• To prepare a brief report about Section Modulus.
• To calculate the Section modulus of Hood design and compare it with a modified hood design.

Equations Used

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

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

SECTION MODULUS

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. Equations for the section moduli of common shapes are given below.

There are two types of section moduli, the elastic section modulus and the plastic section modulus.

• Elastic section modulus: 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.

• 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 is used to calculate the plastic moment, M_p, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, F_y, by M_p = F_y ⋅ Z. Plastic section modulus and elastic section modulus are related by a shape factor which can be denoted by k, used for an indication of capacity beyond elastic limit of material. This could be shown mathematically with the formula :-

  

STUDY

• Software Used: Simens NX 12 Cad

• Input

• Commands Used:

1. Sketch
2. Intersection Curve
3. Section Intertia

• Section Modulus of Existing design:

(I)Moment of inertia (min) = 1.4470 x 10^4 mm^4

(y)Length from the end to the neutral axis = 440.6mm

Section modulus , S=I/y

by calculation ,

S = 32.842 mm^3 .

• Section Modulus of Modified Design: Created an additional emboss area in the inner panel.

(I)Moment of inertia (min) = 3.7593 x 10^4 mm^4

(y)Length from the end to the neutral axis = 440.6 mm

Section modulus , S=I/y

by calculation ,

S = 85.32 mm^3 .

Conclusion

We can coclude that introducing or modifying the existing design parameters will also modify the Section Modulus.