Question

A straight bar of mild steel, 1 m long 12 mm x 6 mm in section is mounted in strut testing machine and loads axially till it buckles. Assuming Euler's formula for pinned ends to apply, estimate the maximum central deflection before the material attains its yield point of $300N/m{m}^2.TakeE=2\times {10}^{5}N/m{m}^2$

• A. 49.08 mm
• B. 49.66 mm
• C. 49.78 mm
• D. 49.89 mm

Answer 1

The correct option is B 49.66 mm


$S_{yt}=300MPa$ $L_e=L=1m$(Hinge - Hinge)

$I_{min}=\frac{\left(12\right)(6{)}^3}{12}=216m{m}^4$

$P_e=\frac{{\pi }^{2}E{I}_{min}}{L_e^2}=\frac{{\pi }^2\times 2\times {10}^5\times 216}{{1000}^2}=426.366N$

Direct stress ${\sigma }_o=\frac{P}{A}=\frac{426.366}{12\times 6}=5.92Mpa$

We have $S_{yt}={\sigma }_o+f$
300 = 5.92 + f
f = 294.078 MPa
and $f=\frac{M}{Z}=\frac{Pe}{Z}$

$294.078=\frac{426.366\times e}{\left(\frac{12\times 6^2}{6}\right)}$

$\therefore e=49.66$ mm