Section Modulus calculation and optimization

SECTION MODULUS CALCULATION AND OPTIMIZATION

AIM

To increase the section modulus of a given hood by necessary changes

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, radius of gyration for compression, and moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus (S) and the plastic section modulus (Z).

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 is the second moment of area (or moment of inertia)

y is the distance from the neutral axis to any given fiber.

It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber.

CASE 1

Section modulus analysis for case 1

From the above analysis, following minimum and maximum moment of the inertia are obtained, using MOI (min)

Imin - 1.511 x 10^4 mm^4

S = I/y

y = 415 mm

S = 1.511 x 10^4 / 415 = 36.40 mm^3

S = 36.40 mm^3

CASE 2

Section modulus analysis for case

By increasing the depth of the inner panel by 2.00 mm

From the above analysis, following minimum and maximum moment of the inertia are obtained, using MOI (min)

Imin - 1.546 x 10^4 mm^4

S = I/y

y = 415 mm

S = 1.546 x 10^4 / 415 = 37.25 mm^3

S = 37.25 mm^3

When compared section values in case 1 and case 2, when increase in cross sectional area there will be increase in minimum strength or maximum strength.

RESULT

The strength of the material is directly proportional to the moment of inertia, hence increase in sectional area there is have increase in overall mass of an object ,hence have increase in strength.