HumanPoweredDesigner
Well-Known Member
Skinny beams buckle at a load that is determined by their modulus of elasticity, effective length, and moment of area, not their cross sectional area or compression strength, according to Euler:
Critical Load = (pi squared)(mod of elast)(area moment)/(effective length squared)
and
area moment for this beam is reported as thin width cubed x thick width / 12.
I got those equations from many sites, so hopefully it is correct.
Many sites say the modulus of elasticity for a wood stick I have is
1000 Kg per square mm, or 10 GPa, depending on the site and units. They match.
The column is a simple rectagular, that is 6.4mm x 12.7mm x 60mm tall.
It can pivot on the floor or under a weight, so the effective length is 60mm.
For the moment of area, I got 6.4x6.4x6.4x6.4x12.7/12 = 277 mm4.
So the millimeters should cancel and give me Kg of load capacity. I know from experiment that the load capacity is 3kg. And the column is not warped. Yet Eulers equation gives me 759Kg as the load this could take. That is way above the theoretical compression strength. Even if the weight I put on it is considered free moving, that still is almost 200 Kg Euler says it should carry.
What am I doing wrong? Isn't this supposed to be a simple calculation? I know this beam should be in the Euler's range because it buckles at way less than compression strength.
Critical Load = (pi squared)(mod of elast)(area moment)/(effective length squared)
and
area moment for this beam is reported as thin width cubed x thick width / 12.
I got those equations from many sites, so hopefully it is correct.
Many sites say the modulus of elasticity for a wood stick I have is
1000 Kg per square mm, or 10 GPa, depending on the site and units. They match.
The column is a simple rectagular, that is 6.4mm x 12.7mm x 60mm tall.
It can pivot on the floor or under a weight, so the effective length is 60mm.
For the moment of area, I got 6.4x6.4x6.4x6.4x12.7/12 = 277 mm4.
So the millimeters should cancel and give me Kg of load capacity. I know from experiment that the load capacity is 3kg. And the column is not warped. Yet Eulers equation gives me 759Kg as the load this could take. That is way above the theoretical compression strength. Even if the weight I put on it is considered free moving, that still is almost 200 Kg Euler says it should carry.
What am I doing wrong? Isn't this supposed to be a simple calculation? I know this beam should be in the Euler's range because it buckles at way less than compression strength.
