- #1
LDC1972
- 65
- 0
Second moment of area "I" and deflecton relationship
What I value will halve the beam deflection
I = bd^3 / 12
and
y max = - 5wL^4 / 384EI
Transpose y max = - 5wL^4 / 384EI to:
I = - 5wL^4 / 384Ey max
This makes the value of I (2nd moment of area) double to achieve a halved deflection. Is this just a commonly known relationship?
Obviously I'm not inferring that the beam CSA be doubled, only 'I', and I'm also aware that when thinking of CSA, it takes approximately 26% of a rectangular beam depth increase to halve deflection.
Homework Statement
What I value will halve the beam deflection
Homework Equations
I = bd^3 / 12
and
y max = - 5wL^4 / 384EI
The Attempt at a Solution
Transpose y max = - 5wL^4 / 384EI to:
I = - 5wL^4 / 384Ey max
This makes the value of I (2nd moment of area) double to achieve a halved deflection. Is this just a commonly known relationship?
Obviously I'm not inferring that the beam CSA be doubled, only 'I', and I'm also aware that when thinking of CSA, it takes approximately 26% of a rectangular beam depth increase to halve deflection.