Shear strength

File:Shear stress simple.svg

For shear stress $\backslash tau$ applies

:$\backslash tau\; =\; \backslash frac\; \{\backslash sigma\_1\; -\; \backslash sigma\_3\}\{2\}\; ,$

where

:$\backslash sigma\_1$ is major principal stress and

:$\backslash sigma\_3$ is minor principal stress.

In general: ductile materials (e.g. aluminum) fail in shear, whereas brittle materials (e.g. cast iron) fail in tension {{xref|(see: Tensile strength)}}.

To calculate:

Given total force at failure (F) and the force-resisting area (e.g. the cross-section of a bolt loaded in shear), ultimate shear strength ($\backslash tau$) is:

:$\backslash tau\; =\; \backslash frac\; \{F\}\{A\}\; =\; \backslash frac\; \{F\}\{\backslash pi\; r\_\backslash text\{bolt\}^2\}\; =\; \backslash frac\; \{4F\}\{\backslash pi\; d\_\backslash text\{bolt\}^2\}$

For average shear stress

$\backslash tau\_\backslash text\{avg\}\; =\; \backslash frac\{V\}\{A\}$

where

: $\backslash tau\_\backslash text\{avg\}$ is the average shear stress,

: $V$ is the shear force applied to each section of the part, and

: $A$ is the area of the section.{{Cite book|last=Hibbeler|first=Russell|title=Mechanics of materials|date=9 November 2017 |publisher=Pearson Education |isbn=978-1-292-17828-8|oclc=1014358513}}

Average shear stress can also be defined as the total force of $V$ as

: $V=\backslash int\; \backslash tau\; d\; A$

This is only the average stress, actual stress distribution is not uniform. In real world applications, this equation only gives an approximation and the maximum shear stress would be higher. Stress is not often equally distributed across a part so the shear strength would need to be higher to account for the estimate.{{Cite web|url=https://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=me&chap_sec=01.2&page=theory|title=Mechanics eBook: Shear and Bearing Stress|website=www.ecourses.ou.edu|access-date=2020-02-14}}

As a very rough guide relating tensile, yield, and shear strengths:{{cite web|url=http://www.roymech.org/Useful_Tables/Matter/shear_tensile.html|title=Shear Strength of Metals|website=www.roymech.org}}

USS: Ultimate Shear Strength, UTS: Ultimate Tensile Strength, SYS: Shear Yield Stress, TYS: Tensile Yield Stress

There are no published standard values for shear strength like with tensile and yield strength. Instead, it is common for it to be estimated as 60% of the ultimate tensile strength. Shear strength can be measured by a torsion test where it is equal to their torsional strength.{{Cite web|url=https://www.instron.us/en-us/home/our-company/library/glossary/s/shear-strength|title=Shear Strength - Instron|website=www.instron.us|access-date=2020-02-14|archive-date=2020-02-14|archive-url=https://web.archive.org/web/20200214030206/https://www.instron.us/en-us/home/our-company/library/glossary/s/shear-strength|url-status=dead}}{{Cite web|url=https://www.portlandbolt.com/technical/faqs/calculating-strength/|title=Calculating Yield & Tensile Strength|last1=Portl|last2=Portl|first2=bolt com|website=Portland Bolt|language=en-US|access-date=2020-02-14|last3=Bolt|last4=Company|first4=Manufacturing|last5=St|first5=Inc 3441 NW Guam|last6=Portl|last7=PT547-6758|first7=OR 97210 USA Hours: Monday-Friday 6 AM to 5 PM|date=10 October 2011 }}

When values measured from physical samples are desired, a number of testing standards are available, covering different material categories and testing conditions. In the US, ASTM standards for measuring shear strength include ASTM B769, B831, D732, D4255, D5379, and D7078. Internationally, ISO testing standards for shear strength include ISO 3597, 12579, and 14130.S. Grynko, "Material Properties Explained" (2012), {{ISBN|1-4700-7991-7}}, p. 38.

• Shear modulus
• Shear stress
• Shear strain
• Shear strength (soil)
• Shear strength (Discontinuity)
• Strength of materials
• Tensile strength

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Category:Shear strength