Section Modulus calculation and optimization
SECTION MODULUS AND OPTIMIZATION
AIM:
To Calculate the section modulus of Hood to analyze the strength and also to optimize the design of Hood to Analyze the Improved Strength.
OBJECTIVE:
- To Create the Intersection curve along the 0-Y plane on the Inner and Outer panel.
- To Calculate the Section Modulus for the section of Hood.
- To Optimize the section to analyze the Improved strength of the Hood.
INTRODUCTION:
HOOD:
Hood is a main component of front portion of a car, hinged cover that rests over the engine bay of a front-engine vehicle. It is an opening body panel that covers the engine in front engine vehicle. It consist of an outer panel and inner panel. The inner panel provides the strength while the outer panel functions as the metal cover. It is an access panel to the engine compartment to enable maintenance of power train, drive belts, battery, fluid levels and lamp units.
SECTION MODULUS:
Section modulus is a geometric property for a given cross-section used in the design of flexural members. It is the direct measure of the strength of the section or Flexural Member sections. Higher the section modulus of a structure, the more the resistive it becomes to bending. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for stiffness.
Section modulus 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.
SIGNIFICANCE:
The section modulus of the cross-sectional shape is of significant importance in design. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.
TYPES OF SECTION MODULUS:
There are Two types of section Modulus,
(1). Elastic Section Modulus
(2). Plastic Scetion Modulus
(1). ELASTIC SECTION MODULUS:
The elastic section modulus is used, applying up to the yield point for most metals and other common materials. Elastic Section modulus is defined as the ratio of moment of inertia to the radius of the shaft or the distance from the neutral axis to the outer fibers.
EQUATIONS:
`S=I/Y`
Where,
S - Section Modulus
I - Moment of Inertia
Y - Distance from Neutral Axis to Outer Most Fiber
ELASTIC SECTION MODULUS FOR VARIOUS CROSS SECTIONS:
(2). PLASTIC SECTION MODULUS:
The plastic section modulus is used for materials where elastic yielding is acceptable and plastic behavior is assumed to be an acceptable limit. Designs generally strive to ultimately remain below the plastic limit to avoid permanent deformations, often comparing the plastic capacity against amplified forces or stresses.
The plastic section modulus depends on the location of the plastic neutral axis (PNA). The plastic section modulus is the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA.
EQUATIONS:
`Z_P=∑A_CY_C+∑A_TY_T`
Where,
SECTION MODULUS CALCULATION
CASE - 1:
In the Hood Assembly,the datum plane is created on the curve along the axis on the Inner and Outer panel the Intersection curve is taken along the plane with respect to the intersection between Inner and outer panel.
After creating the Intersection curve, the sketch as been drawn on the plane as same as the created Intersection axis.
By using the Project curve command, the tangent curves are been selected and projected on the plane.
By using the profiles and lines the gaps are been filles and Area cross section has been created. By using the Analysis Tool the Distance between the Outermost fibers are been Measured.
By using the section Inertia Analysis, the sketches are been selected with the section type has Hallow and thicknes of 0.75 mm.
RESULT CASE - 1:
CALCULATION:
From the data's,
`I_(Max) = 9.042101132 e^(+07)`(mm^4) and
`I_(Min) = 2.71795266 e^(+05)` (mm^4)
`Y = 877.0171` (Y has been calculated from the Neutral Axis to Outer Most Fiber)
Therefore,
`Y = 877.0171/2 = 438.508` (mm)
Section Modulus (S) (MAXIMUM)= `I_(Max)/Y=((9.42101132 )X10^(+07))/438.508 = (20.6201) X 10^(04) mm^3`
Section Modulus (S) (MINIMUM) = `I_(MIN)/Y=((2.71795266 )X10^(+05))/438.508 = (61.981) X 10^(1) mm^3`
The section Modulus for the Hood varies from 61.981* 10^1 to 20.6201 *10^4 mm^3.
CASE - 2:(OPTIMIZING TE DESIGN)
By using the Inetrsection curve, the curves are been projected into the plane, and uisng lines and profiles te gaps are been filled and the Outer panel Outermost curve been offsetted to 2 mm Outer (Downward).
By using the section Inertia Analysis, the sketches are been selected with the section type has Hallow and thicknes of 0.75 mm.
RESULT CASE 2: OPTIMIZING RSSULT:-
CALCULATION:
From the data's,
`I_(Max) = 9.044914028 e^(+07)`(mm^4) and`
`I_(Min) = 2.89435033 e^(+05)` (mm^4)`
`Y = 877.0171` (Y has been calculated from the Neutral Axis to Outer Most Fiber)
Therefore,
`Y = 877.0171/2 = 438.508` (mm)
Section Modulus (S) (MAXIMUM)= `I_(Max)/Y=((9.044914028 )X10^(+07))/438.508 = (20.62656) X 10^(04) mm^3`
Section Modulus (S) (MINIMUM) = `I_(MIN)/Y=((2.89435033 )X10^(+05))/438.508 = (66.0045) X 10^(1) mm^3`
The section Modulus for the Hood varies from 66.045* 10^1 to 20.62656 *10^4 mm^3.
CONCLUSION:
- The Intersection curve along the 0-Y plane on the Inner and Outer panel are been created and Analyzed.
- The Section Modulus for the Hood Initial Section are been Calculated and analyzed.
- The section to analyze the Improved strength of the Hood after optimizing the design are been Obsorved.
- Initial Section Modulus = `(61.981) X 10^(1) mm^3`
- Final Section Modulus (Optimized) = `(66.0045) X 10^(1) mm^3`
From the Above Conclusion it is abudent that, Increase in Cross Sectional Area will Increase the Bending Strength. From the Optimized Design (After Offsetting the Intersection Curve), the strength of the cross section increases.