Section Modulus calculation and optimization

Section Modulus calculation and optimization of CAR HOOD(BIW closure)

INTRODUCTION 

                   Section modulus is a geometric property of the cross section used for designing beams and flexural members. It does not represent anything physically.

To define section modulus, it may be defined as the ratio of total moment resisted by the section to the stress in the extreme fibre which is equal to yield stress.

AIM 

        The main obkective and aim of this section modulus calculation is to find find optimized section modulus value for the design of hood to find out the strength and makes optimized the design and data to finish high strength hood of a car 

Section Modulus

        In elastic bending, the stress distribution in the beam is as follows

  As per theory of pure bending :

 Where M= bending moment

 I = moment of inertia of the section about the bending axis.

 Sigma=fibre stress at a distance ‘y’ from the centroidal/neutral axis.

 R = radius of curvature of the bent beam.

 E = Young’s Modulus of the material of the beam.

 If y is replaced by c, the distance to remotest element, from the neutral axis or centroidal axis, then

             Where, Z= section modulus and is given by

 This Z is the elastic section modulus used for elastic design for beam. It is usually denoted by Ze.

     When the stress distribution in the beam becomes plastic, the analysis changes.

        In the case of plastic bending:

            The stress distribution within a cross section in plastic bending is:

       Moment resisted by a section that has attained full plasticity is given by:

                                                 M = Fy* (A/2) * ( Yc +Yt )

            Where,

            M = Moment

            Fy = Yield stress

            A = Area of the cross section

            Yc = distance of centre of area under compression from equal-area axis.

            Yt = distance of centre of area under tension from equal-area axis.

            Now,

                                      M = Fy* (A/2) * ( Yc +Yt )

                                      Zp = M/Fy.

          Hence,

                           Zp = (A/2) * ( Yc +Yt )

             This is the plastic section modulus and may be used for the plastic design of beams.

For the same section, the plastic and elastic modulus are different. The difference in their values indicates the reserve in strength or moment resisting capacity that a section made from sufficiently ductile material possesses. The ratio between plastic and elastic section modulus is known as shape factor. The more is the value of shape factor the more is the reserve strength in the section on attaining plasticity.

                                                                Shape factor = Plastic modulus/ Elastic modulus

         It can be intuitively seen that as more and more material is concentrated near centre or equal-area axis (as in circular or rhombus section) the value of shape factor increases and as more and more material is concentrated away from centre or equal area axis (as in I section) the value of shape factor decreases.

 SECTION MODULUS CALCULATION 

             The section modulus calculation is to be done for hood design in NX CAD .The ultimate Aim is to be to get a optimized value for section modulus 

Higher value of section modulus calculation leads to high strength of HOOD 

CALCULATION 

                       S=I/Y

             S=Section Modulus

             I=Moment of inertia

             Y=Distance Between neutral axis to extreme end of the object 

  For this section modulus optimization we consider two cases which default data and optimized data 

CASE 1

       With use of NX CAD taking a area moment inertia value for intially designed value 

     

  From the above given data 

           Moment of inertia (MAX) = 469106.5026mm*4

           Moment of inertia (MIN) = 135941.8181mm*4

            S=I/Y 

Where Y value is Y=D/2 

                         D=870.9 /2

                           =435.45mm

     

           S=135941.8181/435.45

       Section modulus for intial  case    =312.1869746mm*3       ........................................................(1)

CASE 2 OPTIMIZED VALUE 

       since when compared with intial value of date the second case is optimized data which the area is to be increased for section modulus 

           

          

         

From the above given data 

           Moment of inertia (MAX) = 688016.6626mm*4

           Moment of inertia (MIN) = 182980.4618mm*4

            S=I/Y 

Where Y value is Y=D/2 

                         D=870.9 /2

                           =435.45mm

 S=182980.4618/435.45

       Section modulus for optimized case    =420.2100397mm*3       ........................................................(2)

CONCLUSION

       While comparing the both result value of case 1 and case 2 the case 2 optimized value as high section modulus value has more strength provided to hood .

 At end the the section modulus value has to be increased for the hood design .