Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION :

AIM : The main objective to this project to understand the Hood design of the parent car,

Improved to the strength of the car hood with parent car hood, and calculation and

optimization car hood.

SECTION MODULUS : Section modulus is a geometric property for a given cross-section used in the design

of beams or flexural members. Other geometric properties used in design include area for tension and shear,

radius of gyration for compression, and Second moment of area and polar second moment of area for stiffness.

Section modulus are two types : Elastic modulus and Plastic modulus .

Use the Section from your Hood design and calculate the Section Modulus using the formula

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object

Elastic modulus : The elastic section modulus is defined as S = I / y, where I is thesecond 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 (M_y) such that M_y = S ⋅ σ_y, where σ_y is the yield of strength of the material.

Plastic modulus :

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 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, and equal compressive and tensile 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:

{\displaystyle Z_{P}=A_{C}y_{C}+A_{T}y_{T}}

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.

Section Modulus calculation and optimization :

1.HOOD DESIGN :

CALCULATION OF SECTION MODULUS OF MAIN HOOD :

Moment of Inertia, Imax =4.638803170*10^6mm^4

Moment of Inertia, Imin =1.333322664*10^4mm^4

Distance between the neutral axis and the extreme end of the object, y =881.0923/2 =440.54.

Section Modulus, S = Moment of Inertia (I) / Distance of the neutral axis and the extreme end of the object (y)

For Maximum (MOI) ,

S (max) = I max / y =10.52981153 *10^3

For Minimum (MOI),

S(min) = Imin / y =0.030265*10^3

HOOD OPTIMIZED DESIGN :

Change in Offset of curve in Inner panel

Moment of Inertia, Imax =4.2099480868*10^6mm^4

Moment of Inertia, Imin =1.365468303*10^4mm^4

Distance between the neutral axis and the extreme end of the object, y =881.0923/2 =440.54.

Section Modulus, S = Moment of Inertia (I) / Distance of the neutral axis and the extreme end of the object (y)

For Maximum (MOI) ,

S (max) = I max / y =9.556335604*10^3

For Minimum (MOI),

S(min) = Imin / y =0.0309953308*10^3