Section Modulus calculation and optimization

                                                                             REPORT ON SECTION MODULUS CALCULATIONS AND OPTIMIZATION

SECTION MODULUS-

IT IS A GEOMETRIC PROPERTY WHICH IS USED TO FIND BENDING STRESS IN A STRUCTURAL MEMBER.

MATHEMATICALLY IT CAN BE DEFINED AS, IT IS THE RATIO OF AREA MOMENT OF INERTIA ABOUT THE NEUTRAL AXIS AND TO THE DISTANCE OF OUTERMOST FIBER FROM THE NEUTRAL AXIS.

IT IS GIVEN BY THE FORMULA  S = I/y

WHERE, 

S = SECTION MODULUS

I = MOMENT OF INERTIA

y = DISTANCE OF OUTERMOST FIBER FROM THE NEUTRAL AXIS. 

EXPLAINATION-

• THE SECTION MODULUS IS THE MEASURE OF BEAM OR STRUCTURES ABILITY TO WITH STAND THE BENDING STRESS WHEN THE LOAD IS APPLIED TO IT.
• THE SECTION MODULUS DEPENDS ON MOMENT OF INERTIA AND DISTANCE BETWEEN THE OUTERMOST FIBER TO THE NEUTRAL AXIS. HERE SECTION MODULUS IS DIRECTLY PROPORTIONAL TO THE MOMENT OF INERTIA, INCREASING MOMENT OF INERTIA OF STRUCTURE INCREASES THE SECTION MODULUS AND DECRESING THE DISTANCE BETWEEN THE OUTERMOST FIBER TO NEUTRAL AXIS INCREASES THE SECTION MODULUS.
• AREA MOMENT OF INERTIA FOR BEAM WITH SAME BREADTH AND DEPTH, WHERE ONE BEAM IS PLACED BY ROTATING AT 90 DEGREE IS AS SHOWN IN BELOW IMAGES.

         

         CASE. 1 -IN THIS CASE THE AREA MOMENT OF INERTIA IS GIVEN BY I=bd^3/12.

         CASE. 2 -IN THIS CASE THE AREA MOMENT OF INERTIA IS GIVEN BY I=db^3/12.

BY COMPARING BOTH THE CASES WHERE b>d IN CASE.2 AREA MOMENT OF INERTIA IS PROPORTIONAL TO b^3 SO AREA MOMENT OF INERTIA IS GREATER IN CASE.2

SO BY PLACING THE BEAM AND APPLING THE LOAD AS SHOWN IN CASE.2 PROVIDES MUCH RESISTANCE TO BENDING MOMENT THUS INCREASES THE SECTION MODULUS OF THE STRUCTURE OR BEAM.

SECTION MODULUS CALCULATION AND OPTIMIZATION-

HERE THE SECTION MODULUS IS CALCULATED FOR HOOD ASSEMBLY

CASE.1 

HERE, AREA MOMENT OF INERTIA I(1)=2.664*10^5 mm^4 WHICH IS OBTAINED FROM ANALYSIS OF HOOD ASSEMBLY

          DISTANCE BETWEEN OUTERMOST FIBER AND NEUTRAL AXIS y(1)=876.56/2 

                                                                                                               y(1)=438.28mm

          THEREFORE, SECTION MODULUS (S)=I/y

                                                                  S(1)=2.664*10^5/438.28

                                                                  S(1)=607.83mm^3

CASE. 2

 

HERE, AREA MOMENT OF INERTIA I(2)=2.701*10^5 mm^4 WHICH IS OBTAINED FROM ANALYSIS OF HOOD ASSEMBLY

          DISTANCE BETWEEN OUTERMOST FIBER AND NEUTRAL AXIS y(2)=876.56/2 

                                                                                                               y(2)=438.28mm

          THEREFORE, SECTION MODULUS (S)=I/y

                                                                  S(2)=2.701*10^5/438.28

                                                                  S(2)=616.27mm^3

ON COMPARING BOTH CASES AS CALCULATED ABOVE, IN CASE 1 THE SECTION MODULUS IS CALCULATED FOR EXISTING HOOD ASSEMBLY WE OBTAINED S(1) =607.83mm^3 AND IN CASE.2  BY OFFSETTING THE LOWER SURFACE OF INNER HOOD PANEL TO 0.5mm THAT IS INCREASING THE BREADTH OR THICKNESS OF THE HOOD ASSEMBLY WE GET S(2)=616.27mm^3

HERE S(2)>S(1) THE SECTION MODULUS WHICH IS INCREASED INTURN INCREASE THE BENDING MOMENT AT PARTICULAR INTERSECTION ON THE HOOD ASSEMBLY.

THEREFORE THE THICKNESS OR BREADTH CREATED IN CASE.2 IS MUCH PREFERED FOR CONSIDERING IN HOOD DESIGN IF THE SECTION MODULUS OBTAINED IN CASE.1 IS NOT SATISFACTORY OR DOES NOT MEET THE REQUIREMENT.