Section Modulus calculation and optimization

SECTION MODULUS & OPTIMIZATION

AIM- The main objective of this project is to understand and learn the basic tools and advanced tools used in NX and calculation as well as section modulus and optimization of Car Hood

INTRODUCTION-

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 and polar second moment of area for stiffness.

The section modulus of the cross-sectional shape is of significant importance in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

It includes the idea that most of the work in bending is being done by the extreme fibres of the beam, i.e., the top and bottom fibres of the section. The distance of the fibres from top to bottom is therefore built into the calculation.

The elastic modulus is denoted by S. To calculate S, the distance (y) to the extreme fibres from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.

SECTION MODULUS- It is the ratio of Moment of Inertia (I) of the beam cross-section about the neutral axis to the distance (ymax) of extreme fibre from the neutral axis.

Section Modulus, S = I/y

where I = Moment of Inertia (mm⁴).

Y = distance between the neutral axis and the extreme end of the object (mm).

SECTION MODULUS OF VARIOUS SHAPES-

• TRIANGULAR SECTION-

Moment of Inertia at neutral axis, I_N.A = bh³ / 36

y_max = 2h/3

Section Modulus, S_N.A = I_N.A/y_max = [(bh³/36) / (2h/3)] = bh²/24

• SQUARE SECTION (HORIZONTAL & VERTICAL SIDES)

Area, A = a²

Moment of Inertia, I_N.A = a4/12

y_max = a/2

Section Modulus, S_N.A = [(a⁴/12)/ (a/2)]= a³/6

• SQUARE SECTION (HORIZONTAL & VERTICAL DIAGONAL)

Area, A = a²

Moment of Inertia, I_N.A = a4/12

y_max = a/√2

Section Modulus, S_N.A = [(a⁴/12) / (a/√2)] = a³/6√2

• RECTANGULAR SECTION

Moment of Inertia at neutral axis, I_N.A = bd³/12

y_max = d/2

Section Modulus, S_N.A = I_N.A/y_max = [(bd³/12) / (d/2)] = bd²/6

• CIRCULAR SECTION

Moment of Inertia at neutral axis, I_N.A = πd⁴/64

y_max = d/2

Section Modulus, S_N.A = I_N.A/y_max = [(πd⁴/64)/(d/2)]= πd³/32

CALCULATION FOR SECTION MODULUS & OPTIMIZATION

CASE 1- SECTION MODULUS OF HOOD DESIGN

Moment of Inertia (MOI), I_MAX = 1.589722955x10^7 [mm⁴]

Moment of Inertia (MOI), I_MIN = 1.341436139x10^5 [mm⁴]

Distance between the neutral axis & the extreme end of the object, y = 484.5245mm/2 = 242.26225mm

Section modulus, S = Moment of Inertia, (I) / Distance b/w the neutral axis & the extreme end of the object (y)

For Maximum (MOI)

S = (1.589722955 x 10⁷) / (242.26225mm)

S_max = 65.6199 x 10³

For Minimum (MOI)

S = (1.341436139 x 10⁵) / (242.26225mm)

S_min = 0.5537 x 10³

CASE 2 – OPTIMIZATION OF HOOD DESIGN

Moment of Inertia (MOI), I_MAX = 1.580637837x10⁷ [mm⁴]

Moment of Inertia (MOI), I_MIN = 1.098597566x10⁵ [mm⁴]

Distance between the neutral axis & the extreme end of the object, y = 484.5245mm/2 = 242.26225mm

Section modulus, S = Moment of Inertia, (I) / Distance b/w the neutral axis & the extreme end of the object (y)

For Maximum (MOI)

S = (1.580637837x10⁷) / (242.26225mm)

S_max = 65.2449 x 10³

For Minimum (MOI)

S = (1.098597566x10⁵) / (242.26225mm)

S_min = 0.45347 x 10³

CONSLUSION- Section modulus of hood of a car was calculated & optimized section modulus with some optimization & found some better results.