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)

1)Elastic section modulus (s):

* 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 (My) such that My = S ⋅ σy, where σy is the yield strength of the material.
2)Plastic section modulus (z):

* 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 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.
* The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a cross-section. The two terms are related by the yield strength of the material in question, Fy, by Mp = Fy ⋅ 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.
                                                                 k={\cfrac {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 = 8.20497119*10^5[mm^4]

Moment of Inertia (MOI), I min = 6.640400076*10^3[mm^4]

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

Y =  486.8282 mm/2 = 243.4141mm

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 = 6.640400076*10^3/243.4141

S = 27.2802606mm^3

case-2:Calculation of section modulus of optimized hood.

Calculating section modulus by 0.5mm changing the dimensions of the hood design

Moment of Inertia (MOI), I max = 8.300520798*10^5[mm^4]

Moment of Inertia (MOI), I min = 7.104332876*10^3[mm^4]

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

Y =  487.8236 mm/2 = 243.9118mm

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 = 7.104332876*10^3/243.9118

S = 29.1266828mm^3

RESULTS

case 1:

          S=27.2802606mm^3

case 2:

          S= 29.1266828mm^3

The difference between of case 1 and case 2 are the varying the distance between of hood inner panel and outer panel.

 So, the Moment of inertia has been increased and the strength of the hood also increased.

CONCLUSSION

          These calculation is necessary to know the design actual withstand capability of product. As we increase sectional area, the moment of inertia & section modulus increases it means capacity of material also increases