Section Modulus calculation and optimization
SECTION MODULUS CALCULATION AND OPTIMIZATION
OBJECTIVE
To find the section modulus value for the hood design and optimize the design of hood to get better section modulus value.
SECTION MODULUS
This is a geometrical parameter which directly connects the area moment of inertia or second moment of area. Moment of inertia is a measure of resistance to angular acceleration. Higher magnitude of moment of inertia states the object resists angular acceleration and even greater torque required increase its angular acceleration. The unit of MOI is mm^4. The section modulus is a direct measure of strength. Higher section modulus objects are stronger in load bearing capacity. It is directly given as a input for the bending equation. i.e.
Bending moment = bending stress / section modulus
The quoted general formula to calculate this parameter is
S = I/d mm^3
Were
s – Section modulus (mm^3), I – Area moment of inertia or second moment of area (mm^4), d – distance from the neutral axis to the extreme fiber of the component (m).
CALCULATING SECTION MODULUS OF HOOD
Hood section
Section analysis
Info Analysis - Section Inertia Analysis
The mass properties are for hollow sections
Sect# CG-XC CG-YC CG-ZC CG-X CG-Y CG-Z SL SA
1 0.000000000 1.548519647 5.534924746 -0.621693770 750.968694919 -931.220088512 2.032759055e+03 40.655367629
Sect# Max-MI Max-X Max-Y Max-Z Min-MI Min-X Min-Y Min-Z Max-RL Min-RL
1 8.192026577e+05 0.000000000 0.982057744 0.188580455 3.650412121e+03 0.000000000 -0.188580455 0.982057744 478.495088213 19.400
006006
Sect#: Number of Section
CG-XC, CG-YC, CG-ZC: Center of Gravity (WCS) [mm]
CG-X, CG-Y, CG-Z: Center of Gravity (Absolute) [mm]
Max-MI: Maximum Principal Moments of Inertia [mm^4]
Max-X, Max-Y, Max-Z: Maximum principal Direction
Min-MI: Minimum Principal Moments of Inertia [mm^4]
Min-X, Min-Y, Min-Z: Minimum principal Direction
Max-RL: Equivalent rectangle section length in Max principal direction [mm]
Min-RL: Equivalent rectangle section length in Min principal direction [mm]
SL: Section Length [mm]
SA: Section Area [mm^2]
This section has
MOI (max) = 8.192026577e+05 mm^4
MOI (min) = 3.650412121e+03 mm^4
Section area = 40.655367629 mm^2
Sectional inertia of hood is taken along the Y axis which is the vertical axis of section. The minimum value of the area moment of inertia gives the value of I(yy) along y axis. The distance of the section’s extreme fiber and the neutral axis is measured.
Length of hood section
Section length (L) = 484.2966mm. The value of d is L/2 which is 484.2966/2 = 242.1498 mm.
Therefore
Section Modulus = I(yy) / d
= 3.650412121e+03 / 242.1498
= 15.075016 mm^3
Therefore the calculated Sectional Modulus of the hood is 15.075016 mm^3.
OPTIMIZATION OF SECTION MODULUS
To optimize this value some changes in the geometry of deisgn can be done to improve the sectional inertia.
1. The thickness of the outer panel is increased from 0.75mm to 1mm. This makes considerable change in the section area which reflects in the moment of inertia of the section.
Change of thickness
Section
Section analysis
Info Analysis - Section Inertia Analysis
The mass properties are for hollow sections
Sect# CG-XC CG-YC CG-ZC CG-X CG-Y CG-Z SL SA
1 -0.621693770 751.161254430 -931.169883079 -0.621693770 751.161254430 -931.169883079 2.219374643e+03 44.369895971
Sect# Max-MI Max-X Max-Y Max-Z Min-MI Min-X Min-Y Min-Z Max-RL Min-RL
1 1.005974539e+06 0.000000000 0.981947210 0.189155166 4.051135874e+03 0.000000000 -0.189155166 0.981947210 513.361338703 19.737
685641
Sect#: Number of Section
CG-XC, CG-YC, CG-ZC: Center of Gravity (WCS) [mm]
CG-X, CG-Y, CG-Z: Center of Gravity (Absolute) [mm]
Max-MI: Maximum Principal Moments of Inertia [mm^4]
Max-X, Max-Y, Max-Z: Maximum principal Direction
Min-MI: Minimum Principal Moments of Inertia [mm^4]
Min-X, Min-Y, Min-Z: Minimum principal Direction
Max-RL: Equivalent rectangle section length in Max principal direction [mm]
Min-RL: Equivalent rectangle section length in Min principal direction [mm]
SL: Section Length [mm]
SA: Section Area [mm^2]
This section has
MOI (max) = 1.005974539e+06 mm^4
MOI (min) = 4.051135874e+03 mm^4
Section area = 44.369895971 mm^2
Section Modulus = I(yy) / d
= 4.051135874e+03 / 242.1498
= 16.72987 mm^3
2. In this case the emboss distance is reduced by 2mm from 5mm to 3mm and the draft angle reduced to 45degress from 60degrees. This might considerably increase the sectional area.
Change of offset distance
Section
Section analysis
Info Analysis - Section Inertia Analysis
The mass properties are for hollow sections
Sect# CG-XC CG-YC CG-ZC CG-X CG-Y CG-Z SL SA
1 -0.621693770 750.761923486 -935.775146923 -0.621693770 750.761923486 -935.775146923 2.433120255e+03 48.612589397
Sect# Max-MI Max-X Max-Y Max-Z Min-MI Min-X Min-Y Min-Z Max-RL Min-RL
1 1.036041988e+06 0.000000000 0.982615718 0.185651151 4.823080514e+03 0.000000000 -0.185651151 0.982615718 517.021304668 21.449
169073
Sect#: Number of Section
CG-XC, CG-YC, CG-ZC: Center of Gravity (WCS) [mm]
CG-X, CG-Y, CG-Z: Center of Gravity (Absolute) [mm]
Max-MI: Maximum Principal Moments of Inertia [mm^4]
Max-X, Max-Y, Max-Z: Maximum principal Direction
Min-MI: Minimum Principal Moments of Inertia [mm^4]
Min-X, Min-Y, Min-Z: Minimum principal Direction
Max-RL: Equivalent rectangle section length in Max principal direction [mm]
Min-RL: Equivalent rectangle section length in Min principal direction [mm]
SL: Section Length [mm]
SA: Section Area [mm^2]
This section has
MOI (max) = 1.036041988e+06 mm^4
MOI (min) = 4.823080514e+03 mm^4
Section area = 48.612589397 mm^2
Section Modulus = I(yy) / d
= 4.823080514e+03 / 242.1498
= 19.91775 mm^3
COMPARISON OF VALUES
| S.no | HOOD SECTIONS | SECTIONAL MODULUS |
| 1. | ORIGINAL SECTION | 15.075016 mm^3 |
| 2. |
OUTER PANEL THICKNESS CHANGED SECTION |
16.72987 mm^3 |
| 3. | EMBOSS OFFSET SECTION |
19.91775 mm^3 |
CONCLUSION
Hence the sectional Modulus value is optimized by slightly varying some geometrical features of hood. Finally the sectional modulus of hood is improved 4.842734 mm^3 from 15.075016 mm^3 to 19.91775 mm^3.