Section Modulus calculation and optimization

Section Modulus Calculation and Optimization

Objective-

The main objective of this project is to learn the basic tools, commands, and the calculation and optimization of the section modulus using NX CAD. The objectives of this project are as follows.

• To understand and learn the calculation and optimization of section modulus of hood design using NX CAD.

Section Modulus-

Section modulus is a geometrical property for a given cross section used in the design of beams or flexural members. Other geometrical properties used in the design include an area for tension and shear the radius of gyration for compression and the moment of inertia and polar moment of inertia for stiffness.

Types of section modulus

Elastic section modulus (s)

Plastic section modulus (z)

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 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 (My) such that My = S × σ_y, where σy 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 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 can also be called the 'First moment of area'

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: - K=Z/S.

Section modulus Calculation

Case.1-Frontal crash analysis of Hood main design (No optimization)

Calculation of Section Modulus of Main hood.

Moment of Inertia (MOI), I max = 5.084989200×10^6 (mm^4)

Moment of Inertia (MOI), I min = 1.665750744×10^4 (mm^4)

Distance between the neutral axis and the extreme end of the object,

Y = 901.46 mm/2 =450.73 mm

Section modulus, S = Moment of inertia I / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

For MOI Max-

S = 5.084989200×10^6 mm^4/450.73 mm

S = 11.2816742×10^3 mm^3

For MOI Min-

S = 1.665750744×10^4 mm^4/450.73 mm

S = 0.36955×10^2 mm^3

Case -2 Frontal crash analysis of Hood optimized design

In this case we have to modify the section curve of 1mm offsetting the both outer and inner panel curve outward.

Calculation of section modulus of optimized hood.

Moment of Inertia (MOI), I max = 5.138218556×10^6 mm^4

Moment of Inertia (MOI), I min = 1.822605036×10^4 mm^4

Distance between the neutral axis and the extreme end of the object,

Y = 901.46 mm/2 =450.73 mm

Section modulus, S = Moment of inertia I / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

For MOI Max-

S = 5.138218556×10^6 mm^4/450.73 mm

S = 11.399×10^3 mm^3

For MOI Min-

S = 1.822605036×10^4 mm^4/450.73 mm

S = 0.4043×10^2 mm^3

Case -3 Side crash analysis of main hood design

Calculation of Section Modulus of Main hood.

Moment of Inertia (MOI), I max = 8.257971862×10^5(mm^4)

Moment of Inertia (MOI), I min = 7.548275466×10^3 (mm^4)

Distance between the neutral axis and the extreme end of the object,

Y = 486.77 mm /2 = 243.385 mm

Section modulus, S = Moment of inertia I / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

For MOI Max-

S = 8.257971862×10^5 mm^4/243.385 mm

S = 3.3929×10^3 mm^3

For MOI Min-

S = 7.548275466×10^3 mm^4/243.385 mm

S = 0.31013×10^2 mm^3

Case -4 Side crash analysis of optimized hood design

In this case we have to modify the section curve of 1mm offsetting the both outer and inner panel curve outward

Calculation of Section Modulus of optimized hood.

Moment of Inertia (MOI), I max = 8.410991402×10^5(mm^4)

Moment of Inertia (MOI), I min = 8.528217820×10^3 (mm^4)

Distance between the neutral axis and the extreme end of the object,

Y = 486.77 mm /2 = 243.385 mm

Section modulus, S = Moment of inertia I / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

For MOI Max-

S = 8.410991402×10^5 mm^4/243.385 mm

S = 3.4558×10^3 mm^3

For MOI Min-

S = 8.528217820×10^3 mm^4/243.385 mm

S = 0.350400×10^2 mm^3

Conclusion-

From the above calculation of section modulus of before and after optimization of hood design. We cocluded that section modulus is directly proportional to the moment of inertia so if we increase the value of moment of inertia then section modulus increases.we observe that in this design the section modulus is less in side crash analysis as compared to frontal crash analysis. in both the cases if we increases the cross sectional area the moment of inertia also increases and section modulus also increases.