Shear studs for composite steel stringers

[NS4U]

I am having a debate with a colleague of mine regarding the number of shear studs required for fatigue and an example in "Design of highway bridges" by Barker and Puckett, 2nd Edition.

In it they do an example for the number of shear studs required to satisfy the fatigue stress range... long story short they find that they need a pitch of 6" with 3 transverse studs per pitch.

They proceed to say "the distance from zero moment to positive moment is 40ft=480in"

Thus the total number of studs needed in the is 3*(480/6)=240 studs.

Should this number be multiplied by two??

They proceed to check the strength limit as well, and determine that 226 studs are needed for the entire length and that fatigue (240 studs) controlled, so clearly they must be considering the entire length when they did fatigue.

I say it should be x2 for fatigue, my colleague says no because it is a "stress range." Can any one offer some insight?

Thanks!

 

[Qshake]

No, I don't see why this value should be factored by 2. What is your reasoning for the 2?



Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[NS4U]

Well because, it says from zero moment to positive moment is 40ft... Thus, if the bending moment diagram is symmetric, the overall length of the beam in positive bending is 80'= 40'x2

Thus the number of in positive bending should be x2

 

[NS4U]

typo- number of *studs* in positive bending should be x2

and I misspoke earlier the text says "length from zero moment to MAX positive moment is 40ft"

 

[71corvette]

It looks like the calculation you referenced in your post is for strength design, and not fatigue. The calculation for fatigue design should generate a maximum spacing value, or alternately, a stress range in the shear stud.

That said, I'm not sure which code is referenced in the book you're looking at, but for design using the LRFD code you need to check two cases - strength and fatigue.

For the strength case you calculate the number of required studs between points of DL contraflexure, mamimum positive moment, and maximum negative moment. This calculation ensures the number of studs provided is adequate to resist the horizontal shear between the top flange and concrete haunch. You will calculate two values per span (they will be the same for simple spans, and probably different for continous spans). These values added together will yeild the total studs per span.

For fatigue, you calculate the maximum stud spacing that can be used while keeping the stress range in the shear stud below acceptable levels (this will variy based on the number of expected live load cycles and the load intensity). The maximum spacing for fatigue will vary across the bridge span.

If the spacing used to provide the required number of studs for strength design is larger than the maximum allowable spacing for fatigue design, the stud spacing will need to be reduced to satisfy the fatigue requirement.

In my experience, fatigue has almost always governed stud spacing.

 

[NS4U]

Yes, tinytim, I agree. I am working with AASHTO 2004, 6.10.10.

What I am saying is that in the example, the maximum stud spacing, for a stress range that is assumed constant, is 6" with 3 studs per transverse section.

With that said, I am trying to determine the number of studs needed. In the example it says the distance from "0 moment to maximum positive moment is 40ft" and the number of studs req'd for fatigue is 3*(480in/6in)=240studs...

My argument is that the amount of the beam in positive bending is therefore 80ft, and the number studs needed should be x2. Similar to the reasoning for the number of studs needed using the strength check.

My colleague says the 240 studs is correct and doesn't need to be multiplied by 2, and I don't seem to understand why.

 

[Qshake]

Sorry, I missed the part about the 0 to Mmax(+). yes, I agree that the number should be multiplied by 2 for a simple beam. For the continuous beam there is more to it because the maximum positive moment isn't symmetrical so you space the studs from 0 to the point of contraflexure and then add a set for anchorage into the negative moment area. Unless the DOT requires full length composite action.



Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.

 

[71corvette]

Based on your description of the problem, I tend to agree with your conclusion. If fatigue requires a constant stud spacing of 6" along the entire length of hte beam (an unrealistic assumption), and the formula calculates the number of studs based on 1/2 the span length, then yes, I would double the number of studs required.

Assuming you have a simply supported beam, 240 studs would need to be placed @ 6" o.c. on each side of midspan. As has been stated previously though, for continuous spans it won't be simply 2x the value since the point of M+max will probably not be at midspan.

 

[Panars]

AASHTO has a good design example for LRFD that includes the shear stud design. You can download it for free at

http://lrfd.aashtoware.org/?siteid=34&pageid=339

On page 5-2, it covers the shear studs. For fatigue, it calculates the pitch. Then for the strength limit states it compares the number required for the length between the point of maximum positive moment and the point of zero moment to the number of studs provided by the earlier calculated pitch over the same length. If you were to multiply the number of provided studs by two to cover the entire length of the span, then you would have to multiply the number required by two also.

Is it possible that your colleague is saying you don't need to double the number when making the comparison at the strength limit state, because you would just end up doubling both sides of the equation?

 

[NS4U]

Excellent example. Although they do not multiplied the number of fatigue studs by 2, they do not multiply the number of studs req'd for strength by 2 eithier.

In the example from Barker and Puckett I am referring to, they actually multiple the number of studs need for strength design by 2. But they do not multiply the number of studs for fatigue by 2.

 

[Panars]

Which example are you looking at? In the second edition (2007) that I am looking at, the simple span example is only 35 feet long, and the other composite deck example is a three span continuous that is done in SI units.

 

[NS4U]

i am referring to example 8.12

 

[Panars]

On the bottom of page 827, they calculate the number of shear connectors required in the distance from maximum moment to zero moment as 113. Then they double that number to get the number of shear connectors for "both sides". They do not directly compare either 113 or 226 to the required number of shear connectors for fatigue, 240. They only say that fatigue controls.

Nowhere do they state that it is a simple span or what the total length of the bridge is. They only state that the distance from the maximum positive moment to the point of zero moment is 40 feet. The result is that the number of connectors required over a length of 40 feet is 240.

I agree that the equation at the bottom of page 827 where they double the number of shear connectors required for "both sides" for the strength limit state is a little confusing. They could have left this entire line out.

If it were a simple span with a total length of 80 feet, then you would need 480 shear connectors along the total length of the beam.

 

[NS4U]

Ok great... thanks

I agree it is very confusing... the fact that they double the number of studs for the strength limit state but for fatigue confused me. And I thought there was some nuance of the shear stud design for fatigue I was missing.

Thanks for all of your help. and just an FYI there are at least 3 errors I found in the example (not considering this).. Ex. 8.12 was definitely not one of his better examples