Mid-height deflection of a bar - Euler's Formula

SaRaH...

1. The problem statement, all variables and given/known data
I think I've got part of this question but it's multiple choice and nothing that I've got matches any of the options we were given. I'd really appreciate it if you could help me out.

A straight, vertical aluminium bar, 1.0-m in length and 12.5-mm x 4.8-mm in cross
section, is axially loaded until it buckles. Assuming Euler’s formula applies, determine
the mid-height deflection, in millimetres, of the vertical bar before the material attains
its plastic yield stress of 250-MPa.


2. Relevant equations

P = EIpi²/L²

I = bd³/12

deflection = PL/AE

3. The attempt at a solution

I = (12.5)(4.8)³/12 = 115.2mm⁴

P = (70*10⁹)(115.2*10^-12)*pi²/(1)² = 79.6N

Then when I tried to get deflection it came out as a huge answer. I'm not certain if that's the right formula I'm using but it's the only one we've used in class so I don't know what else it could be.

The answers we were given were 57mm, 150mm, 31mm, 145mm, 378mm

Sarah

nvn

SaRaH...: Hint 1: Your third relevant equation is inapplicable; you instead need the bending stress formula. Hint 2: Bending moment is force times distance. You correctly computed the force.

By the way, always leave a space between a numeric value and its following unit symbol. E.g., 79.59 N, not 79.59N. And, e.g., 250 MPa, not 250-MPa. See the international standard for writing units (ISO 31-0).

pongo38

For what it's worth, I found that the section is FULLY plastic when deflection is 45 mm. So you could check whether extreme fibres first reach yield stress at 31 mm. I think the question is a bit ambiguous, but it's a well intentioned question.

nvn

pongo38: I am thinking your statement currently appears incorrect, unless I am misinterpreting. Would you be able to show how you obtained your answer? I currently did not find the question ambiguous.

pongo38

Is th question asking for the deflection when the extreme fibres FIRST reach their yield stress, or when the whole section has gone plastic (about 50% more moment required)?

nvn

pongo38: Aluminum has no yield plateau. I interpreted the question as meaning it is asking for the deflection when only the extreme fibre reaches the tensile yield strength, Sty = 250 MPa.