Section Modulus calculation and optimization

#6 SKILL LYNC

COURSE: Automotive Sheet Metal Design using Siemens NX CAD / CATIA V5

NAME: SRI RAGUL PREMKUMAR CHALLENGE: Section Modulus calculation and optimization

Bending Stresses in Beam:

It is that in which bending moment (Torsion) is constant along the length, i.e. shear force is zero.

• Material is Homogenous, Elastic which Hooke’s law is valid.
• Distance Y is directly proportional to the Neutral axis.

Neutral Axis:

• In beam, the layer does not undergo any change in length even after bending, which is called the neutral axis.
• The line of intersection of the neutral layer with the plane of the cross-section of the beam is called the neutral axis.
• In pure bending, the Neutral axis of the beam always passes through the centroid of the cross-section area and is homogenous.

Pure Bending Equation:

Where, σ – bending stress M- Bending Moment I- Moment of Inertia of area

y - Distance between the neutral axis and the extreme end of the object

E- Young modulus of elasticity R- curvature

From, Hood design and calculates the Section Modulus using the formula:

S = I/y

Where S = Section Modulus I = Moment of Inertia of area

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

Section Modulus is directly proportional to the Moment of Inertia in the area

“Section modulus represents the strength so the section modulus depends on the area of the section “

CASE 1: INNER PANEL CREATED WITH EMBOSS

Hood design, in the inner panel, created a emboss to increase section area and strength in the Case1

I created an intersection curve in the hood for finding section inertia analysis.

And then intersection curve is projected using the project curve command.

Value of case 1:

Section#: 1
Type: Hollow
CG: (-75.207869097, 749.081678205, 0.000000000) [mm]
MOI (Max):7.043333994e+06[mm^4]
MOI (Min):2.488253451e+04[mm^4]
Principal Directions:
Max: (-0.007783744, 0.999969706, 0.000000000)
Min: (0.999969706, 0.007783744, 0.000000000)
Section Length:5.660357640e+03[mm]
Section Area:113.098535882[mm^2]

I_{max =} MOI (Max):7.043333994e+06[mm^4]
I_min = MOI (Min):2.488253451e+04[mm^4]

Total length of 'Y' value: 897.9mm

So, at neutral axis we need 'Y' value: Y/2=897.9/2

=448.95mm

Section modulus(s) = I_max /Y

= 7.043333994e+06[mm^4]/448.95mm
= 15.688×10³ mm³ (Max strength)

Section modulus(s) = I_min/Y

= 2.488253451e+04[mm^4]/ 448.95mm

= 5.542×10³mm³ (Min strength)

As a result, the strength of a hood can vary between 15.688×10³ mm³ (Max strength) and 5.542×10³mm³ (Min strength)

CASE 2: AN INNER PANEL CREATED WITHOUT EMBOSSING

Hood design, in the inner panel, created a without emboss for increase section area and strength

I created an intersection curve in the hood for finding section inertia analysis.

And then intersection curve is projected using the project curve command.

Value of case 2:

Section#: 1
Type: Hollow
CG: (5.736244015, 743.979176275, 0.000000000) [mm]
MOI (Max):7.593090795e+06[mm^4]
MOI (Min):2.681896506e+04[mm^4]
Principal Directions:
Max: (0.001439721, 0.999998964, 0.000000000)
Min: (0.999998964, -0.001439721, 0.000000000)
Section Length:5.515115298e+03[mm]
Section Area:110.259037795[mm^2]

I_{max =} MOI (Max):7.593090795e+06[mm^4]
I_min = MOI (Min):2.681896506e+04[mm^4]

Total length of 'Y' value: 879.2mm

So, at neutral axis we need 'Y' value: Y/2=879.2/2

=439.6mm

Section modulus(s) = I_max /Y

= 7.593090795e+06[mm^4]/ 439.6mm
= 17.272×10³ mm³ (Max strength)

Section modulus(s) = I_min/Y

= 2.681896506e+04[mm^4]/ 439.6mm

= 0.061×10³ mm³ (Min strength)

As a result, the strength of a hood can vary between 17.272×10³ mm³ (Max strength) and 0.061×10³ mm³ (Min strength)

CONCLUSION:

• Section Modulus is directly proportional to the Moment of Inertia in the area
• Section modulus represents the strength so the section modulus depends on the area of the section

From the above point, we are comparing both cases 1 and 2

VALUE OF CASE 1: Section#: 1 Type: Hollow CG: (-75.207869097, 749.081678205, 0.000000000) [mm] MOI (Max):7.043333994e+06[mm^4] MOI (Min):2.488253451e+04[mm^4] Principal Directions: Max: (-0.007783744, 0.999969706, 0.000000000) Min: (0.999969706, 0.007783744, 0.000000000) Section Length:5.660357640e+03[mm] Section Area:113.098535882[mm^2] At neutral axis we need 'Y' value: Y/2=897.9/2 = 448.95mm	VALUE OF CASE 2: Section#: 1 Type: Hollow CG: (5.736244015, 743.979176275, 0.000000000) [mm] MOI (Max):7.593090795e+06[mm^4] MOI (Min):2.681896506e+04[mm^4] Principal Directions: Max: (0.001439721, 0.999998964, 0.000000000) Min: (0.999998964, -0.001439721, 0.000000000) Section Length:5.515115298e+03[mm] Section Area:110.259037795[mm^2] At neutral axis we need 'Y' value:Y/2=879.2/2 =439.6mm
1. Section modulus(s) = Imax /Y =15.688×103 mm3 (Max strength) 2. Section modulus(s) =Imin/Y = 5.542×103mm3 mm3 (Min strength)	1. Section modulus(s) = Imax /Y =17.272×103 mm3 (Max strength) 2. Section modulus(s) =Imin/Y = 0.061×103 mm3 (Min strength)

As a result, case 2 is more strength of a hood can vary between 17.272×10³ mm³ (Max strength) and 0.061×10³ mm³ (Min strength)