Section Modulus calculation and optimization

Section modulus: It is a geometric property for a given cross-section used in the design of beams or flexural members. It may also 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.

The ratio of total moment resisted by the section to the stress in the extreme fibre. It gives us an idea about how much of load the given structure can take. If the section modulus increases the moment of resistance increases and hence its load-bearing capacity.

• section modulus tells about the strength of a section under bending.
• from bending equation we have (f/y=M/I=E/R).
• where f= Yield stress or Bending stress, y= Distance from the neutral axis, M= Bending moment and I= Moment of inertia.

• Using the formula S = I/y

  S = Section Modulus

  I = Moment of Inertia

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

• Given that: Consider Stainless steel AISI 302 – cold-rolled – y = 520 MPa

• From the bending equation, section modulus and constant value of bending stress as 520 MPa
• We get a relation that is M= f*(S), where S=I/y which indicates if maximum permissible bending stress kept constant then bending moment is directly proportional to the section modulus.
• hence states that higher the section modulus value higher will be resistance to bending and vice versa.

• We have to consider minimum MOI value given in inertia analysis of the hood section as from this value only the structure starts breaking and at maximum MOI value the structure gets broken down completely.

First Section of the hood

Section Inertia Analysis of hood Section

Minimum MOI- 3.031478994e+05 mm^4

Y distance from the neutral axis to the extreme end.

Y= 440.1

Therefore Section modulus value of the hood section is S=(I/y)= 688.9724986363636 mm^3

Improved section

Section Inertia Analysis of improved hood Section

Minimum MOI- 3.102260783+05 mm^4

Y distance from the neutral axis to the extreme end.

Y= 440.6

Therefore Section modulus value of the hood section is S=(I/y)= 704.0991336813436223 mm^3

Thus from the above analysis, we can see that the section modulus has improved and hence strength also improved by doing some necessary changes to the previous hood section.

The study of section modulus on this section was very important to improve its strength locally as it is a geometric property so it does not depend upon the property of the material.

Likewise, section modulus for any structure plays a very important role in knowing its strength and indicates the ways to improve its strength further