A question on cover plate end connection design

[flyingcow1999a]

We all know that the connection beyond the theoretical cutoff point needs to be strong enough to support the induced(allocated) tension/compression forces of the cover plate due to bending moment at the theoretical cutoff point. The force can be conservatively calcualted as T = Fy*Sb/Sbr*Ac, where Sb the elastic section modulus of the beam w/o reinforcement, Sbr the elastic section modulus w/o reinforcement, and Ac the area of cover plate. Also, T = M*Sc/Ibr, whee Sc is the elastic section modulus of the cover plate and Ib the moment of inertia of the beam w/ reinforcement. The needed number of bolts (or welds) witin the terminal distance is determined accordingly.

Assume a constant width cover plate - not tapered end.

My question is: at locations along the terminal distance, the allocated tension/compression forces will be T = M*Sc/Ibr also. Since the terminal distance is not too long, I can assume that the bending moment will not decrease much. Therefore, T = M*Sc/Ibr would not change much. However, at locations moving closer to the end, the number of bolts beyond that point going outward become less and less, which means the bolts will not be enough to support the tension/compression forces in the terminal section of the cover plate.

Seems the only solutions are:

1. make the end of the cover plate gradually shrink to a small enough width so that the allocated tension/compression force (proportional to the ratio of section modulus) get small enough. For example, the end width is so small so that one bolt or end across welds can support the forces.

2. or extend the cover plate long enough beyond the cutoff point and close enough to the supports so that the bending moment will be small enough.

I ran some examples and found out this mechanics issue.

Can anyone help ? Thanks

 

[ishvaaag]

I read in Lothers' classical book, quoting it comes from AREA specification, that you have to have enough terminal distance as to place enough (weld or) fasteners to develop the structural capacity of the coverplate. This is, for constant thickness and section coverplates quite conservative for in fact the attainment of the full need of the coverplate won't happen at its end, but beyond, and it is really between the theoretical end and the point of the maximum requirement of the coverplate that the required shear transfer between flange and coverplate (or coverplates) brings the force at the added cover plate to its maximum, and where such shear transfer demand is notionally understood to be required. However it also says stress concentration has a say and so such practical rule was derived.

So by the present understanding of how the shear transfer between flange and coverplates happens, and the fact that it is called to cover not demand, but capacity, one would say that you have to place enough weld or fasteners as to develop the capacity of the plate, once at the terminal length, and then again to the point of where the full (or max) capacity is first demanded.

 

[flyingcow1999a]

ishvaaag, thanks for your reply.

Can you give me the full information of "Lothers' classical book" and the "AREA specification"? I want to get them and take a look. I didn't get them by searching google

You input is very helpful. However, that is not what I asked about. What I asked is about the need of gradual decreasing of the cover plate within the terminal distance - checking connection strength for any section within the terminal distance. Let me do some example and get back with a more clear statement later.

Thanks

 

[ishvaaag]

I have it in a spanish edition

Diseño de Estructuras Metálicas
John E. Lothers
Prentice Hall International 1973

it is a translation from

Design in Structural Steel, 3d ed.
John E. Lothers
Prentice-Hall, Inc., Englewood Cliffs NJ 07632 USA

the relevant section in the spanish translation is

709 Length of the Coverplates

the referred code is

Manual of Recommended Practice, 1970, Chapter 15
American Railway Engineering Association (AREA) Chicago, USA

That I remember such railway code at least by then forbade welds as fasteners. Anyway I think to remember that in other specifications or texts it is standard the procedure of providing full development of the coverplate capacity in the terminal length beyond theoretical cutoff point. Maybe a look to the AASHTO spec can be worth regarding this aspect.

 

[flyingcow1999a]

ishvaaag, thanks again for your input.

Let me put my question using a different case. It talks about the same issue. Attached is a drawing showing the elements of two wide flange beams connected using splice plates at top and bottom flanges.

The following may not be exactly correct for the details concerning design, but the principle should be correct.

To design the connection, we use the maximum moment at location "a" which is M(a). Neglecting the design factors and assuming the splice plate being fully used, the equation to determine the plate size W and T is Fy*W*T*(H+T)=M(x). Using this equation, we can determine the size, width and thickness, of the splice plate. Correspondingly, the number of bolts should be determined as N_bolt=Fy*W*T/SH_perbolt, where SH_perbolt is the shear strength per bolt.

My question similr to the one I asked above for cover plate will be:

Do we need to check the adeuqcy of bolts for the tension/compression force at locations such as "b","c"? : Will the total shear strength of bolts from "b" or "c" to the end greater than the tension/compression force at location "b" or "c" which is determined as T(c)=M(c)*Q_pl/(I_beam+I_pl)?

------------------
Expanded:
If the splice plate deforms the same as the beam, then following the material mechanics, the compression and tension force in plate at location "c" will be T(c)=M(c)*Q_pl/(I_beam+I_pl), where Q_pl is the 1st moment of area of plate at one side, I_beam the 2nd moment of area(inertia) of the beam, I_pl the 2nd moment of area(inertia) of the top and bottom plates. Based on my calculation, T is very possible larger than the the total shear strength of all bolts from the location to the end. For example, T(c)>3*SH_perbolt. Based on this checking, the width going to the end, bolt layout need to be design properly, instead of one time calculation at location "a".
------------------

What if welding connection is used? Do we have to have end across welds so that at the very end, where T(o)=M(O)*Q_pl/(I_beam+I_pl),the end shear strength of across weld will >= T(o)?

Thanks for your attention.

 

[hokie66]

Just design the plate and the bolts on each side for the force required. Don't worry about checking each line of bolts, as the maximum controls. For the cover plate, provide a termination weld to develop the plate. Probably best not to weld across the end.

 

[ishvaaag]

In a first reading of your last post I seem to see the issue in the same light than hokie66. Of course one may follow the notional elastic behaviour and maybe here or there an elastic check is not met. That uses to be the case for limit strength where the total amount of strength of bolts is counted, not to forget that complementary clauses are normally given, that ensure sound behaviour both at service level and targeted limit strength. Later will try to follow your question in more detail.

 

[ishvaaag]

Regarding your first question, examining the function of a coverplate, it becomes apparent that its cutoff point is determined looking where it becomes unnecessary. From that point and in the direction in which the moment requirement grows it is that we need to augment moment strength and then add a coverplate. Assuming solidary action, and forfeiting any stress concentration etc, we see then than from the cutoff point towards maximum requirement, the axial stresses on the combined section make a jump downwards exactly at the cutoff point and then grow with the moment considering the modulus of section with the coverplate.

The description above is to remark that everything structurally interesting about the coverplate happens within its theoretical necessary length, and not beyond. And it is within such necessary length that the proper transfer of the tributary compression to the coverplate must be ensured in shear; the shear transfer requirement at every point within the coverplate theoretical length can be determined by elastic computation considering the standing moment and sectional properties, but some code may or not decide if simply developing in shear the coverplate axial capacity between the point of 0 requirement (cutoff, stress 0 in the coverplate) and maximum requirement (Fy if optimized and limit states) is a measure good enough.

Then comes the question about if we could ensure proper behaviour just within the theoretical required length, why are we adding some development (terminal) length?.

I can't say by what considerations this came to be customary practice, but I can attest that even when composite beams in the seventies were being designef for shear transfer through the studs by elastical evaluation of the shear transfer requirement, it was customary to add a stronger end anchor point, most surely to forfeit from the start the unzipping of the set of studs even if they were being proportioned along the length of the beam in proportion to the expected shear requirement.

Hence, my view about the terminal development length for coverplates is exactly the same than what was being made for composite beams, its akin problem: by providing as strong a transfer at the end as the capacity itself of the coverplate, we are forfeiting entirely any bad effects of flaws in the shear transfer fastening between flange and coverplate.

That many other aspects, experimental, actual stresses in the web, stress concentrations and so on may have helped to establish such practice is even stated in the Lothers' text and I do not know its history to support in one or another way, but my view of the main function served by the coverplate development length is as above described: to forfeit the disengagement of the coverplate and ensure the functionality within the length it is required.

 

[flyingcow1999a]

ishvaaag, thanks for your detailed input. Very helpful for my understanding of the overall of cover plate design.

Currently, seems I am more stucked with the mechanics aspect concerning the connection within the terminal distance, from the theoretical cutoff end to the actual end.

Thanks,

 

[flyingcow1999a]

First, I want to correct one equation in my initial post:
In "T = M*Sc/Ibr", Sc should be replaced with Q, the 1st moment of area.


hokie66, thanks for your input. I know the design should be done as you said. About you answer, I want to ask more questions:

----hokie66
Just design the plate and the bolts on each side for the force required. Don't worry about checking each line of bolts, as the maximum controls.
----hokie66

I believe by "maximum", you are talking about the tension to be taken by the splice plate at location "a". Yes, we are going to use that tension to determine how many bolts is needed. The assumption for this is that all the bolts experience the same deformation and therefore the contribution of shear strength of each bolt is the same.

However, considering the situation at locations such as "c", "b", if linear deformation of the cross section from top of the top plate to bottom of the bottom plate is valid, the tension/compression force in the plate should be determined using T(c)=M(c)*Q_pl/(I_beam+I_pl), or T(b)=M(b)*Q_pl/(I_beam+I_pl). T(c) and T(b) is possibly larger than the summation of nine(c) and three(b) bolts as indicated in the attachment in my previous post.

So far, my guess to explain this contradict, at least in my understanding, is that the bolt and splice plate will deform/displaced different from the beam itself and therefore, T(c)=M(c)*Q_pl/(I_beam+I_pl) is not valid for the tension determination in the plate at location "c". However, how about if the connection is welded?

Welded plate should deform the same as the existing beam, right? No slippage shoule happen before it fails.

----hokie66
For the cover plate, provide a termination weld to develop the plate. Probably best not to weld across the end.
----hokie66

A good case to conside is to study the situation at a location that is very close to the end but not the end yet. If the tension force is to be determined using T(c)=M(c)*Q_pl/(I_beam+I_pl), obviously, there need some weld across the end of the splice end because welds at the two sides are almost negligible, though I know some studies show that it is not good for fatigue strength, which is not within the scope of current consideration yet.

Just stuck with the reconcilation between the material mechanics and design practice.

Thanks for your attention and appreciate your input.

 

[hokie66]

Think in terms of the ultimate or limit state capacity of the joint, not the elastic stress at every section. For the bolts, check the plate section minus the holes at the first bolt row. If that is good, the rest of the plate is good. For the welds, I don't know why you say the side welds are "almost negligible". And yes, welding across the end is detrimental to fatigue strength.

Is this an academic exercise or a real world problem?

 

[flyingcow1999a]

Thanks..

The "almost negligible" of the welds at sides is due to the negligible length of the welds at two sides when the location studied is "very close to the end but not the end yet". If no slippage assumption is still valid, the tension force in the plate is still to be determined using T(?)=M(?)*Q_pl/(I_beam+I_pl). Therefore, unless the end shrinks to an end with zero width at tip or some value less than a limit when with end across weld, then theoretically, it does not work because the negligible welds would not be able to support T(?). However, experimental and real project did not show this kind issues. Quite often no end across weld at all.

I still believe the reason for this kind of inconsistency is the actual existing slippage between the plate and the existing beam. However, I did not see any explanation in the text books. Therefore, I have been wondering.

I have background more in mechanical engineering but structural engineering. However, I am doing structural design job in a structural company. While doing the design of cover plate design and design of beam full strength connection, I came up this questions. It is for my personal interest. The design job is done, but the question is still hanging in my mind..

Thanks for your discussion.