Section Modulus calculation and optimization
Objective:
Analyze section inertia of a hood designed using UG NX cad software and calculate the section modulus of a hood.
Study of variation of section modulus varying hood geometry and improvise the section modulus.
Section modulus:
Section modulus is a geometric property for a given cross section used in the design of beams or flexural members. It is the ratio of moment of inertia (I) of the beam cross section about the neutral axis to the distance (y_max0 of extreme fiber from the neutral axis.
General unit of section modulus is mmᶟ. Section modulus is calculated based on geometry and we have different formulas for calculating for different geometry.
The general shape formulas are,
Section modulus for circular geometry calculated by,
Z_circular section=Πdᶟ/32
Section modulus for rectangular geometry calculated by,
Z_circular section=bd⊃2;/6
Similarly we can calculate the section modulus for different cross section geometry.
Even if a shape does not have a pre-defined section modulus equation, it’s still possible to calculate its section modulus.
Where,
dA = the area of an element of the cross-sectional area of the irregular shape
l = the perpendicular distance from the element to the neutral axis passing through the centroid
Therefore, the section modulus of an irregular shape can be defined by,
Methods to improvise section modulus:
Section modulus can be increased along with the cross sectional area, although some methods are more efficient than others. Take for example, a rectangular cross section whose section modulus is defined by the following equation:
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Doubling the width of the rectangle, b, will increase the section modulus by a factor of 2. However, doubling the height of the cross-section will increase the section modulus by a factor of 4. This would be a much more efficient way to use material to increase the section modulus.
Section Modulus of a Hood:
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Taking a cross section at the center of hood and close the section to make it close loop.
Taking inertia section analysis for the intersection curve.
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Section modulus calculations:
Moment of inertia_max=4.82X10⁶ mm⁴
Moment of inertia_min=1.70X10⁴ mm⁴
While designing we always focus our study to improvise minimum moment of inertia hence we will calculate section modulus for min moment of inertia.
S = I/y
Where,
S = Section Modulus
I = Moment of Inertia
y = distance between the neutral axis and the extreme end of the object.
Y=876.5/2
=438.25 mm
S_min=I_min/y
= 1.70X10⁴/438.25
S_min =38.79 mmᶟ
S_max= 4.82X10⁶/438.25
S_max= 10.99X10ᶟ
Section modulus for a modified cross section of Hood
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Section modulus calculations:
Moment of inertia_max=4.78X10⁶ mm⁴
Moment of inertia_min=1.80X10⁴ mm⁴
Y=876.5/2
=438.25 mm
S_min=I_min/y
= 1.80X10⁴/438.25
S_min =41.07 mmᶟ
S_max= 4.78X10⁶/438.25
S_max= 10.90X10ᶟ
Results:
<!-- [if !supportLists]-->01. <!--[endif]-->Computed section modulus obtaining moment of inertia data from analysis rom UG NX.
<!-- [if !supportLists]-->02. <!--[endif]-->Modified hood geometry so that height can be increased by 4 mm and then modulus section data calculated the results were obtained.