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

AI Thread Summary
The discussion revolves around calculating the mid-height deflection of a vertical aluminum bar using Euler's formula and related equations. The user initially struggles with obtaining a deflection value that matches the provided multiple-choice options. Key insights include the need to apply the bending stress formula instead of the deflection formula used, as well as clarification on whether the question pertains to the deflection at the yield stress of extreme fibers or the entire section. Participants emphasize the importance of precise calculations and interpretations of the problem's requirements. The conversation highlights the complexities involved in applying theoretical formulas to practical scenarios in structural engineering.
SaRaH...
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Homework Statement


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.

Homework Equations



P = EIpi2/L2

I = bd3/12

deflection = PL/AE

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
 
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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[/color] (ISO 31-0[/color]).
 
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.
 
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.
 
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)?
 
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.
 
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