Slenderness Ratio

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Slenderness ratio

Fundamentals

The slenderness ratio is used to evaluate the geometric suitability of test specimens for determining material values in compression tests and for calculating the critical buckling stress.

When subjected to compressive stress, the test specimen must not buckle, otherwise an EULERian stability failure will occur. To ensure this with sufficient slenderness, a slenderness ratio of λ = 10 is preferable, but at least λ = 6 must be maintained.

The slenderness ratio λ is the ratio of the test specimen height h to the smallest radius of inertia of its base area:

$\lambda \,=\,{\frac {h}{i}}$   mit   $i\,=\,{\sqrt {\frac {I_{y}}{A}}}$

prism:

$I_{y}\,=\,{\frac {bd^{3}}{12}}$ $A_{0}\,=\,b\cdot d$ $\Rightarrow$ $h\,=\,{\frac {d}{3{,}46}}\cdot \lambda$

cylinder:

$I_{p}\,=\,{\frac {\pi d^{4}}{64}}$ $A_{0}\,=\,{\frac {\pi }{4}}\cdot d^{2}$ $\Rightarrow$ $h\,=\,{\frac {d}{4}}\cdot \lambda$

with

i		smallest radius of inertia
Iy		smallest axial moment of inertia
Ip		polar moment of inertia
A0		specimen base area
h		specimen height
b		specimen width
d		thickness or diameter

See also

• Compression Test
• Specimen Compliance
• Stiffness
• Thermal Stress Analysis
• Creep Behaviour – Creep Compression Test

References

• Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 125–133 (ISBN 978-1-56990-548-7; ePub: ISBN 978-1-56990-808-2; E-Book: E-book: 978-1-56990-807-5; see AMK-Library under A 22)