## Calculating Yield and Tensile Strength

**Question:** How do I determine the yield and tensile strength of a specific diameter of bolt?

**Answer:** In most cases, the strength of a given material used to make a fastener has strength requirements or parameters described as pounds per square inch (psi) or thousands of pounds per square inch (ksi). This is helpful when analyzing what grade of material should be used for a given application, but this doesn’t tell us the actual strength of that diameter of material. In order to calculate the actual strength values of a given diameter, you would use the following formulas:

*Note: the formulas below do not depend on the finish of the fastener.*

### Ultimate Yield Strength

Take the minimum yield in psi of the ASTM grade (see our Strength Requirements by Grade Chart for this value), multiplied by the stress area of the specific diameter (see our Thread Pitch Chart). This formula will give you the ultimate yield strength of that size and grade of bolt.

*Example:* What is the ultimate yield strength of a 3/4″ diameter F1554 Grade 36 rod?

This is the minimum requirement for F1554 grade 36. In other words, a 3/4″ diameter F1554 grade 36 anchor rod will be able to withstand 12,024 pounds force (lbf) without yielding.

### Ultimate Tensile Strength

Take the minimum tensile strength in psi of the ASTM grade, multiplied by the stress area of the diameter. This formula will give you the ultimate tensile strength of that size and grade of bolt.

*Example:* What is the ultimate tensile strength of a 3/4″ diameter F1554 Grade 36 rod?

This is the minimum requirement for F1554 grade 36. In other words, a 3/4″ diameter F1554 grade 36 anchor rod will be able to withstand 19,372 pounds force (lbf) without breaking.

### Shear Strength

First, find the ultimate tensile strength using the formula above. Take that value and multiply it by 60% (0.60). It is important to understand that this value is only an estimate. Unlike tensile and yield strengths, there are no published shear strength values or requirements for ASTM specifications. The Industrial Fastener Institute (Inch Fastener Standards, 7th ed. 2003. B-8) states that shear strength is approximately 60% of the minimum tensile strength. For more information, please see our FAQ on bolt shear strength considerations.

i was curious if you could tell me how much weight a 5/8 inch by 12 inch lag bolt can hold up i have a tree stand 21 feet in the air so i would like to tell people this so they feel more comfortable thank you for your time

August 9, 2010 at 8:36 amcould you give me an estimated weight just for comfort is it atleast 5000 lbs per bolt

August 9, 2010 at 9:09 am@Ryan Mozingo – Unfortunately, the value that you are looking for is impossible to calculate with any accuracy. We have an FAQ that addresses the difficulty of calculating strength values for lag bolts.

If you are looking for a generic calculation, I can offer a strength calculation based on a mild steel rod. A 5/8″ lag bolt has a minor diameter of 0.471″, which calculates to a stress area of 0.17497 sq. in. Applying the formula for calculating tensile strength for a mild steel bolt, we get a value of 10,500 lbs. for the ultimate tensile strength of a 5/8″ mild steel bolt. The shear strength, which I think you are concerned about would be about 60% of that value.

August 9, 2010 at 9:39 amUnfortunately, there is no way of verifying what grade your bolt is, or what steel your bolt is made out of, so there is absolutely no way of verifying the validity of the above information. I would consult an engineer and have your bolts tested if you are concerned about safety.what is proof strength of material and how is it calculate,have any formula

December 4, 2011 at 11:25 pm@Ranjeet – there is not a one-size-fits-all formula for proof stress. Many ASTM specifications have published tables for proof load values, but not all do. Normally, the proof load values are about 90-92% of yield,but that can vary.

February 14, 2012 at 1:54 pmWhat is the shear strength required for an expansion bolt into concrete with a load of 3,500 # axial load. In what book is it shown in. can I download it on any website. What would be that website or manufacturer be?

February 21, 2012 at 7:55 am@Donald E Brundage – I would try to contact the International Code Council or look on their website; they write a lot of the specifications for expansion anchors and those types of construction products. http://www.iccsafe.org/Pages/default.aspx

February 21, 2012 at 11:48 amExample 1: Area of rectangular cross section

width (w) = 0.505 in.

thickness (t) = 0.5 in.

Area (a) = W x T

AREA (A) = 1.5 X 0.5

AREA (A) = 0.75

LOAD =12500 LBS

AREA = 0.2 IN. 2

Tensile = 12500 x 5

tensile = 62500

Must be an easier way of computing this Tensile Stength of Steel in question.

most of the time I deal with ASTM OR API CODES

SUCH AS X70 OR X65 FOR USE IN THE GAS AND OIL PIPELINE.

;

June 21, 2012 at 5:13 pmhow do you calculate 0.02% Proof stress. is it possible that your bolt passes in tensile strength and fails in proof stress.

September 24, 2012 at 3:34 am@Ravish – Yes it is possible, but not common, that a bolt can pass the tensile test but fail the proof load test. Typically speaking, the 0.2% offset is only used when testing for yield strength, not for testing proof stress. Proof stress is a simple pass or fail test where the full size bolt is tensioned to a predetermined proofload value, held for 10 seconds, then measured to see if it elongated. Yield strength differs in that the bolt or test coupon is pulled to failure, and the yield is calculated (using the 0.2% offset method) along with the tensile, elongation and reduction of area. In order to calculate using the 0.2% offset method, you must first secure data from which a stress-strain diagram may be drawn. More detailed information can be found by looking at ASTM F606 Section 3.6.3.1 or by contacting an accredited test lab.

September 24, 2012 at 6:59 amId be interested in the same thing that Ryan is asking above. Any thoughts?

Thanks,

Pierce from PBEMusic

November 13, 2012 at 12:21 pm@Pierce – Ryan’s question was answered by us directly above his question. I would agree with that response – it isn’t anything we can easily calculate.

November 13, 2012 at 12:31 pmFrequently people are concerned about threads pulling through the nut (shearing the threads). If nut and bolt are made from the same material,and thread engagement is at least 55% the bolt will pull into (tensil) before the thread shears.(General Electric standard 12A1200),

December 3, 2012 at 4:21 pmTensil strength of any material is available in many metalurgical sites on the internet. You only need to calculate the cross section area of the bolt X tensil strength of material bolt is made of. That will tell you how many bolts are needed to support the load + safety factor

I am trying to calculate the yield strength of that 5/8″ bolt and I’m not seeing how you are doing your math. If I take the area (pie x r sqd) I get 3.14 x .312 x.312 =1.962 x 36,000psi tensile = 70,650 yield. what am I doing wrong?

January 29, 2013 at 4:49 amThanks Ted

Ted again

January 29, 2013 at 6:42 amI did make a mistake but the question is the same.

.312 x.312 x 3.14 = .305 x 36,000psi =11,003

Thanks Ted

@Ted – The error you are making is a common one. When calculating the strength of a fastener, the tensile stress area you use is the area of the minor(root) diameter of the threads, in this case 5/8-11 is 0.226 sq in. So 36,000 x 0.226= 8,136lbs. If instead, you are trying to calculate the strength of a full sized bar with no threads, then you did the math correctly.

January 29, 2013 at 7:08 amI have a welded test coupon that is made of x70 pipe. the cross section of the coupon is .250x.250. I am using a tensile tester to measure tensile strength. what is the formula to see what tensile the material actually is?

December 6, 2013 at 10:18 am@JD – I am sorry, but we do not have any experience with testing pipe or special samples like that. You will need to contact a test lab for more information. Apologies.

December 6, 2013 at 10:32 amhow do I calculate the ultimate tensile strenght of Ti6Al4V from hardness values.

January 5, 2014 at 10:20 am@Erinosho – There are conversion charts available to convert hardness to tensile for steel and steel alloy products, but I do not know if they are accurate for Titanium alloys. I can happily send you a copy if you are interested.

January 6, 2014 at 7:25 amhow to calculate the strength of the steel for tension member without using tensile load method?

January 10, 2014 at 1:00 amany other method to calculate strength of steel with or without using IS(indian standard) code book?

@Adhi – I am sorry, I do not completely understand your question. We can help in calculating tensile strength values for fasteners using the above methodology. If you have some specifics about what you are trying to calculate, please email me and perhaps I can assist.

January 10, 2014 at 7:24 amSy = 58 Ksi ER316L rode yield strength

January 18, 2014 at 7:44 amPr=2.94Ks Hydrostatic test pressure

0 = 1.13in Bolt diameter

l=1.375 in Bolt’s head size

T (in) Weld fillet throat dimension

P (lbs) Load applied on the bolt by the internal pressure

SVP, comment calculer la gorge du boulons apres soudage.

Merci

@Rachid- Apologies, but that is a little out of our realm of expertise.

January 20, 2014 at 7:56 amhow can i compute the 8-1/2″ diameter steel to find the ultimate yield and tensile strength?

February 20, 2014 at 1:33 am@John – You could simply use Pi x r^2, so 56.74sq in of stress area. Then multiply that by your tensile and yield (in psi) and that will give you your ultimate strength.

February 20, 2014 at 8:01 amIm looking for a simple steal tensile strength calculator for metal tubing/axles. Specifically 35mm diameter 3mm thick 1000 mm long. Looking for the minimum tensile strength that would be needed to be applied in the center in order to distort/bend the tube/axle.

March 17, 2014 at 11:51 am@Chris Lumbricusland – Sorry, but we do not have any information on calculating that. Apologies.

March 18, 2014 at 7:05 amI’m hanging a porch swing into a 7foot long 2×12 that is supporting my balcony. The total weight it needs to support is 700lbs and my mounting hardware has two bolt holes for each chain. Spread over four galvanized lag bolts, what’s the minimum diameter and length of a lag bolt I need?

July 4, 2014 at 6:16 am@Matt – from a bolt strength standpoint, anything 1/4″ diameter or larger would support the weight. However, the weakest point will be where the bolt screws into the wood and the strength will be limited by the pull out value of the wood. That is information we do not have. Apologies.

July 10, 2014 at 8:22 amI’m standing a 5000lb tare on top of another 5000 lb tare. Each has a 115 ton capacity. They are supporting a 100 ton rod shaped stator field. The field can move in the axial direction some which is why I’d like to bolt the two tare’s together. My question is what size bolts would I need to be able to support the stress of the field moving in the axial direction?

July 15, 2014 at 6:12 am@Ryan- Apologies, but this is slightly above our level of expertise, as we do not have any engineers on staff.

July 15, 2014 at 7:38 amI have a question.

What would be the tensile strength of a fastener Shoulder bolt: .500 dia shaft 3/8-16 thread?

THANKS

LENTES

August 6, 2014 at 6:09 am08/06/14

@Al – I think shoulder bolts are made per the same standard as regular socket head cap screws (ASTM A574). If that is true, your 3/8-16 shoulder bolt would have an ultimate minimum tensile strength of 13,900lbs. You may want to confirm that your bolts were made to the A574 standard, we don’t usually handle shoulder bolts, so I am not certain.

August 7, 2014 at 9:59 amIf i have a Cabinet that weights 200 to 2000 pounds and we are using 3/8″ grade 2 bolts, will we have any problem?

thank you

August 26, 2014 at 6:40 am@Shaira – You should be OK, but it depends a bit on exactly how the bolts are being used and how the cabinets are attached to the framing. Your best bet would be to consult an engineer to confirm.

August 29, 2014 at 7:49 am