Section Modulus calculation and optimization

OBJECTIVE :-

• Calculate section modulus of the previously created design of car hood by taking a cross-section of it and analyzing the result.
• To come up with a new design that would increase or improve the section modulus of the existing car hood and optimize our design to obtain better results.

SECTION MODULUS :-

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It defines the strength of beams which depends upon the cross-section area of that beam.

Though section modulus is generally calculated for the extreme tensile or compressive fibers in a bending beam, compression is often the most critical case due to onset of flexural torsional (F/T) buckling. Generally (except for brittle materials like concrete) tensile extreme fibers have a higher allowable stress or capacity than compressive fibers.

In the case of T-sections if there are tensile fibers at the bottom of the T they may still be more critical than the compressive fibers at the top due to a generally much larger distance from the neutral axis so despite having a higher allowable stress the elastic section modulus is also lower. In this case F/T buckling must still be assessed as the beam length and restraints may result in reduced compressive member bending allowable stress or capacity.

Formula for calculating Section Modulus:

S or Z = I/y

S or Z - Section modulus of material

I- Moment of inertia

y- Length of extreme fiber from the neutral axis

For symmetrical sections the value of Z is the same above or below the centroid.

For asymmetrical sections, two values are found: Z max and Z min.

The Unit of a “section modulus” is in.3 (mm3)

Section modulus depends only on the cross-section shape of the structure. For symmetric sections, the value of “section modulus” is for both above and below of centroid of the fiber. An asymmetric section has two values for top and bottom of the fiber due to different distance from the centroid to the top and bottom of the material, the maximum “section modulus” is S max and the minimum section modulus is S min.

relation between area moment of inertia and resistance to bending :-

considering the first two terms and rearranging them :-

WHERE , M = BENDING MOMENT

I = AREA MOMENT OF INERTIA

Y = DISTANCE FROM OUTERMOST FIBER TO NEUTRAL AXIS

σ = BENDING STRESS

Importance:

• It is significant for beam and flexural member design.

• More the section modulus, the more the member is resistant to the bending of the beam.

• It is easier to calculate stresses in the beam and an exact measure of the strength of steel.

• If two beams are made of the same material and comparing the “section modulus” of two beams, the beam with bigger section modulus will be tougher and more capable to withstand larger loads.

Section Modulus calculation of the Hood Design:

CASE 1: Initial Hood Design.

Calculating Section modulus of existing design by using NX-CAD by taking cross-section of hood along x-x axis and calculating moment of inertia.

Area Moment of Inertia :-

MOI(min):- 2.787537129e+05[mm^4]

Y DISTANCE :- 876.45/2 = 438.22 mm

SECTION MODULUS :-

S=I/Y
S = 2.787537129e+05 mm^4/438.22mm
S = 636.1044 mm^3

CASE 2: Optimized Hood Design

Aim: Our Aim here is to increase the I(min)

MOI(min):- 2.824368178e+05 mm^4 (increased)

Changes made: I increased the distance of 0.5mm between the outer hood panel & the inner hood panel.

Increased MOI :-

Y DISTANCE :- 876.45/2 = 438.22 mm

SECTION MODULUS :-

S=I/Y

S = 2.824368178e+05 mm^4/438.22mm
S = 644.5091 mm^3

Final result: Thus the stiffness of the car hood has been increased by increasing its area moment of inertia (min).

CASE 1 :- S = 636.1044 mm^3

CASE 2 :- S = 644.5091 mm^3

Conclusion :-

• Hence, from the above study, it is clear that optimization helps to improve the results in a design as we have increased the Section Modulus of our hood.
• Gain crucial insight about Section Modulus its relationship with bending stress, Moment of inertia and got an idea of how the section modulus changes with respect to change in section area of a body and its effect on the value of section modulus.
• Importance of section modulus when it comes to the selection of right material or right design which will have more strength.
• Factors affecting Section modulus and how to enhance the strength of a material by using section modulus as a check parameter.