Can anyone direct me to a reference which actually states the general
relationship between shear strength and tensile strength?
I have been told many times (by people that do this type of testing)
that shear strength of metals is generally 2/3 to 3/4 the tensile
strength. However, no one can seem to give a reference for this
Thank you in advance.
I answered this question back in Feb 2003 on sci.engr.mech, so I'll
The original question was how to estimate shear strength of steel from
There is one common definition of shear strength. In ASTM E6 it is
defined as "the maximum shear stress which a material is capable of
sustaining. Shear strength is calculated from the maximum load during
a shear or torsion test and is based on the original dimensions of the
cross section of the specimen." (The ASM Materials Engineering
Dictionary has the exact same definition except for using the word
"that" rather than "which").
To answer the original question I just combined two rules of thumb:
A. Convert hardness to tensile strength.
B. To get the shear strength take 50% of the tensile strength.
Rule of thumb B has different percentages of tensile strength
depending on where you look. I took the lowest one (50%) to be
conservative, and assuming that the question (#1) related to having
enough strength in a bolt connection loaded in shear. You might also
take the highest one if what you really need to know (question #2) is
if your punch press has enough force to shear some cross section of
For question #1 you can see the rules of thumb on page 34 in the notes
for the first part of the GMRC Bolted Joint course at:
[This link now is gone]
where the 50% of tensile strength (UTS) is listed as having come from
ASME B1.1 and a value of 60% is listed for carbon steels with hardness
of less than 40 HRC as having come from Mil Handbook 5.
Also, in A. Blake's Practical Stress Analysis in Engineering Design,
2nd edition, page 593 the shear strength of a bolt is given as equal
to about 60% of the specified minimum tensile strength.
Approximately 60% of specified minimum tensile strength is also given
for carbon steel fasteners in the IFI Fastener Standards book, 6th
ed., 1988, page B-8.
For question #2 you can find 70% of the tensile strength listed on
page 658 of G. E. Dieter's book, Mechanical Metallurgy, 3rd edition,
McGraw Hill, New York, 1986 (see equation 20-1).
Both Mr. Duerr and Mr. Vojcak took issue with my mentioning the Von
Mises relationship as a theoretical basis for doing the conversion in
rule of thumb B. They said that the relationship applies only to the
ratio between shear yield strength and tensile yield strength (being
57.7% or 1/sqrt(3)).
Actually, experimentally for steels the same ratio applies to much
higher strains, so the true stress-true strain curve measured in
torsion for a low carbon steel can converted and superimposed with
that measured in tension. See Figure 10-7 on page 280 of G. E.
Dieter's book, Mechanical Metallurgy, 1st edition, McGraw Hill, New
York, 1961. Also see page 344 of the 3rd edition of Dieter.
I said it wasn't rocket science, but there is a reason for the
constant in rule B being 0.5 to 0.7.
We don't believe what we write, and neither should you. Information
furnished to you is for topical (external) use only. This information
may not be worth any more than either a groundhog turd, or what you
paid for it (nothing). The author may not even have been either sane
or sober when he wrote it down. Don't worry, be happy.
Can you think of a good reason why there would be a "universal"
relationship between tensile strength and shear strength?
I know that people would wish that there were such a relationship, so as
to make life easy in terms of analysis and to give them a feeling of a
greater knowledge of the fracture phenomena (By simplifying it).
Get on Google and enter:
+"shear strength" +metals
You will get a variety of answers depending upon the alloy. Copper is among the
more difficult to
apply a rule of thumb with the wide range of shear strength values for the
various alloys of copper.
Not knowing how you intend to use the shear strength prompt me to state the
following.. You must
look up, or test, the shear strength of each alloy that you require and not rely
on rule of thumb
unless you know for a fact the rule is correct for that alloy.. Only then can
you make a *safe*
decision. If you are shearing the metal, you consider the highest value. If
you are designing a
device that may cost someone their life or physical harm, use the lowest value
and include a *safe*
margin for error.
On page 359 of D. R. H. Jones's book "Engineering Materials 3:
Materials Failure Analysis", Pergamon Press, Oxford 1993 under the
topic of mechanical property correlations he states that the failure
stress in shear is approximately 5/8 of the tensile strength. Any good
failure analyst would already know this.
The question as stated was naive. Most engineers would have added the
details of what materials were being tested and how (single or double
shear, etc). However, this is a newsgroup and we entertain naive
questions. The phrase "generally" when used by engineers or scientists
often just means that "a couple of my drinking buddies and I think this
might be right".
The "Guide to Design Criteria for Bolted and Riveted Joints (2nd ed)"
notes on page 47 of the hard copy that for ASTM A325 and A490 steel
structural bolts in single or double shear the average factor is 0.62
or almost exactly 5/8. Any good fastener testing laboratory already
would have a hard copy of this book. It can be downloaded free at:
Thanks Pete, I had no idea how to argue it, but knew that there
had to be some sort of relationship between hardness and tensile
strength and shear strength.
Alvin in AZ
ps- Hey, DD, even this dumb fly-over know-ed (or at least fiNgured)
Many scientists studied the question.
Brinell was one, Mohr another, there is a topic in stuructural engineering
called 'complex stresses' the principle stresses set up complementary
stresses and they are given in some sources as occuring 45 degrees to each
other and other sources state differently. 45 degrees implies 1/2 as a
Tazaghi stated that a set of stresses set up in shear asa result of axial
stress always resulted in a stress of a given degree of the applied stress.
Testing I did in the labs at uni proved this wrong, it depends upon the
degree of consolidation of the material under test, i.e. upon the density of
the material. Whether this dependence is relative to some absolute density
for each material or not is a matter for investigation but I coined the
phrase (as a memory jogger) 'over consolidated iron' to help me remember how
steel was working under principle and complementary stresses.
Simply, materials react differently, you cannot rely upon any proportion as
a blanket 'rule of thumb' for all materials.
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