Section Modulus calculation and optimization

SECTION MODULUS

AIM:

      To calculate the section modulus of the hood design by using CATIA V5 and improve the strenght of the hood design.

INTRODUCTION:

      Section modulus is a geometric property for a given cross section used in the design of beams or flexural members. Other geomertic 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 modulus of common shapes are given below. There are two types of section modulus, the elastic section modulus and the plastic 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 the second moment of area and y 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 (M1) such that M1=S x σy,, where σy is the yield strength of the material.

     It gives us and idea about how much of load the given structure can take or if the section modulus increases the moment of resistance increases and hence its load bearing capacity or ratio of total moment resisted by the section to the stress in the extreme fiber.

FORMULA:

     Where,

      S = Section modulus

      I = Moment of inertia

      Y = Distance between the neutral axis and extreme end of the object 

SECTION MODULUS:

     Using the 'Measure inertia' tool in CATIA V5, We have to find the minimum & maximum moment of inertias (M1 & M2 respectively). 

Here M1 denotes the 'I' value in section modulus formula we are going to use.

                     

MINIMUM VALUE = 2.043e-006m^4

                         = 2.043e-006 x 10^12 mm^4

                        = 2.043e006 mm^4

MAXIMUM VALUE = 8.156e-004m^4

                          = 8.156e-004 x 10^12 mm^4

                          = 8.156e008 mm^4

                    

Y = 879.687/2

  = 439.8435 MM

Hence section modulus,

                               S = I/Y

                                  = 2.043e006/439.8435

                                  = 4644.8339 mm^3

SECTION MODULUS OF PART 2 BY OFFSET OUTERWARD 0.5MM:

           Now, in order to improve the strength, I tried changing the distance between inner and outer panel of hood assembly. So,I offset to outer contour of inner panel by 0.5mm (outwards).

                   

MINIMUM VALUE = 2.133e-006 m^4

                         = 2.133e-006 x 10^12 mm^4

                        = 2.133e006 mm^4

MAXIMUM VALUE = 8.445e-004 m^4

                         = 8.445e-004 x 10^12 mm^4

                         = 8.445e008 mm^4

                    

Y = Distance between the neutral axis and the extreme end of the object

Y = 879.687/2

   = 439.8435 mm

Hence section modulus,

                                 S = I/Y

                                    = 2.133e006 / 439.8435

                                    = 4849.4521 mm^3

CONCLUSION:

        The section modulus of hood is  4644.8339 mm^3 and increasing the 0.5mm value it is 4849.4521 mm^3, Hence by increasing the value the section modulus strength also increases.