Section Modulus
Section Modulus is a geometric property used to calculate the bending stresses in a structural member.
Mathematically,
It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.
It is denoted by S.
S = I/ymax
Mathematically By bending stress equation,
M/I = σmax/ymax
M = σmax × (I/ymax)
M = σmax × S
Where,
I = Moment of Inertia(m⁴)
y = distance from NA to extreme layer(m)
The unit of section modulus is m³.
Types of Section Modulus
There are two types of section modulus:
- Elastic Section Modulus
- Plastic Section Modulus
Elastic Section Modulus
Elastic section modulus is calculated when we are to use the material behavior till the yield point.
For general design purposes, we use elastic section modulus.
Generally, elastic section modulus is denoted by Sₑ.
So,
Sₑ = I/ymax
Where,
I = Moment of inertia
ymax = Distance from NA to extreme layer
Plastic Section Modulus
The plastic section modulus is used for materials where the elastic yield is acceptable and the plastic behavior is considered to be an acceptable range
It depends on the location of the plastic neutral axis. The PNA is the axis that bisects the cross-section such that the compressive force from the region in compression is equal to the tension force from the region under tension. So, for sections with a constant yield stress, the area above and below the PNA will be equal, but for mixed sections, this is not necessarily the case.
Sₚ = (Ac × yc) + (Aₜ + yₜ)
Where,
Ac = Area of cross-section under compression.
Aₜ = Area of cross-section under tension.
yc = Distance from the plastic neutral axis to the center of gravity of the areas under compression.
yₜ = Distance from the plastic neutral axis to the center of gravity of areas under tension.
Since on the neutral axis, the area under compression is equal to the area under tension.
So,
Ac = Aₜ
And,
yc = yₜ
Case 1 study (original profile):
Profile:
Inertia Result :
Case 2 Study ( offset 1 mm outside):
Profile:
Inertial result:
Case 3 Study (offset 0.5 mm outside):
Inertia Result:
CONCLUSION :
As we can see from the case study, when the section area will increase the modulus value of section will increase.