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Created page with "{{Language_sel|LANG=ger|ARTIKEL=Schlankheitsgrad}} {{PSM_Infobox}} Slenderness ratio __FORCETOC__ ==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..."

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{{Language_sel|LANG=ger|ARTIKEL=Schlankheitsgrad}}
{{PSM_Infobox}}
Slenderness ratio
__FORCETOC__

==Fundamentals==

The slenderness ratio is used to evaluate the geometric suitability of test [[Specimen|specimens]] for determining [[Material Value|material values]] in [[Compression Test|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:

{|
|-
|width="20px"|
|width="500px" | <math>\lambda\,=\,\frac{h}{i}</math>   mit   <math>i\,=\,\sqrt{\frac{I_y}{A}}</math>
|}

'''prism:'''
{|
|-
|width="20px"|
|width="500px" | <math>I_y\,=\,\frac{bd^3}{12}</math> <math>A_0\,=\,b\cdot d</math> <math>\Rightarrow</math> <math>h\,=\,\frac{d}{3{,}46}\cdot\lambda</math>
|}

'''cylinder:'''
{|
|-
|width="20px"|
|width="500px" |<math>I_p\,=\,\frac{\pi d^4}{64}</math> <math>A_0\,=\,\frac{\pi}{4}\cdot d^2</math> <math>\Rightarrow</math> <math>h\,=\,\frac{d}{4}\cdot \lambda</math>
|}

with
{|
|-
|''i''
|width="15px" |
|smallest radius of inertia
|-
|''I''y
|
|smallest axial moment of inertia
|-
|''I''p
|
|polar moment of inertia
|-
|''A''0
|
|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, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|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-Büchersammlung|AMK-Library]] under A 22)

[[category:Compression Test]]

Slenderness Ratio - Revision history