topic Question about section shear under under biaxial moment and shear in Structural Bridge Design Forum

Question about section shear under under biaxial moment and shear

caojin259 — Sun, 16 Jun 2024 09:18:06 GMT

Hi Colleagues,

I have recently used the program to analyze and calculate sectional shear capacity for an unsymmetrical RC traffic barrier subject to biaxial bending moment in associated with biaxial shear as well. Australia code AS5100.5 is chosen so that the shear capacity is also a function of bending moment.

One "myth" puzzles me is how the program works out the "Resultant Moment" and "Resultant Shear" values, and how these values are adopted in the shear capacity equation. See below for an example:

The load case under investigation including biaxial Mx, My and Vx, Vy is shown below:

I've selected Neutral Axis angle to be "Free" and Capacity as "*Not used*". Below is the interface showing the position of the neutral axis of the traffic barrier, analyzed by the program for the above load case.

Results Report then shows the neutral axis angle of -78.527 degree. Resultant M* and V* is 176.101kNm and -31.5kN, respectively.

My First Question:

It can be seen in the proceeding calculation, that the program adopts the resultant shear V* in estimating V*eq and shear strain. However, in shear strain calculation, a very large value of bending moment M* (1.5E3) rather than the Resultant Moment M*=176.101kNm, is adopted in the equations. See below snippet.

Could anyone advise any reasons for that and how to fix it if this is a bug for M*?

My Second Question:

With the input biaxial bending moment and shear force, i have independently calculated the resultant moment and shear force, of which the value is quite different for the M* given in the Results Report (i.e. 228.854kNm c.f. 176.101kNm); resultant shear is similar though (i.e.31.838kN c.f. 31.5kN). See below snippets where my version of the resultant moment and shear force is presented in vectorial format.

Why the value for resultant M* is different?

Also when solving shear capacity for unsymmetrical RC section under biaxial moment and shear, the neutral axis is found as shown below by the program. Do below vectorial resultant M* and V* directly determine shear capacity of the section for this load case as per MCFT theory (that AS5100.5 method is based on)? What are the value and vectorial directions for M* and V* that the program is assuming? Could this leads to the discrepancy for M* between mine and the program?

Many thanks for your attention and appreciate for all advises.

Kind regards,

John

Re: Question about section shear under under biaxial moment and shear

dave_geeves — Fri, 21 Jun 2024 22:19:01 GMT

Hi,

I don't have your data file so I have had to create an example of my own to look at your questions. This is just a rectangular section but I have used the same values of applied load effects as you have.

The resolved moment is calculated as

M(resolved) = Mx cos(theta) + My sin(theta) where theta is the angle of the neutral axis. If I apply this to your values I get a similar value as the program calculates as 176.0993

With regards to the value of M* which is the factored moment, clause 5/8.2.4.4 suggests that this has a minimum value as defined by a particular function. I can't apply this to your section as I don't have the data file but in my example this seems to correct as shown:

I hope that this has answered your two questions. However, I should like to suggest that as this parapet section is part of a larger cross section of a bridge deck, yhat the neutral axis angle is restrained to be close to the horizontal as the section is restrained from rotation by the membrane action of the slab. In this respect I would restrain the neutral axis angle in the analysis form to something close to horizontal and then the calculation would be related to just vertical shear which would define the vertical shear reinforcement requirements. The horizontal transverse shear reinforcement requirements can then be determined by restraining the neutral axis to the vertical direction.

I hope that this has given you some useful suggestions and if this has answered your query then please mark my reply as a solution so that others may benefit. Thanks

Kind regards

Dave Geeves

Re: Question about section shear under under biaxial moment and shear

caojin259 — Wed, 03 Jul 2024 03:06:54 GMT

Hi Dave,

Sorry for the delayed response and much appreciated for your response.

Regarding M* values, now i agree with you this is governed by AS5100.5 Cl.8.2.4.4. No doubt about it.

Coming to the resultant M* value, i am still not fully confident about it. Does the direction of the bending moment matter? See below the two components Mx cos(theta) and My sin(theta) based on the sign convention in ASBD for my load input. As in the opposite directions, i think it builds up that M(resolved) = Mx cos(theta) + My sin(theta)= -140.7kNm+35.4kNm=-105.3kNm. The ASBD results show it to be 175.922kNm. A very different outcome. See below.

Also, i've chosen below options for the above analysis. "FREE" is chosen in "Internal Axis Angle" drop list.

By doing so, will ASBD work out a TRUE RESULTANT M* as shown below or just the component resulted to neutral axis direction (i.e. M(resolved) = Mx cos(theta) + My sin(theta))?

I think the whole bunch of these issues link together. Many thanks if you could give some guidance.

I've tried to drop my SAM file for the traffic barrier model in the attachment, however it seems SAM file is not accepted format. Hence, i could only upload the Results report in pdf in the attachment.

King regards,

Jing

Re: Question about section shear under under biaxial moment and shear

dave_geeves — Wed, 03 Jul 2024 21:52:36 GMT

Hi Jing,

I think that you have taken theta to be 78.957 instead of -78.957, as determined by the strain compatabilty analysis. Here is a screenshot of the spreadsheet I use to check the calculations:

It also seems to me that from your diagram you are trying to determine the resultant moment on an uncracked linear elastic section, which would determine the neutral axis angle for the uncracked section. However, as the section is cracked, a strain compatibility analysis is carried out to determine the neutral axis direction and the applied moments are resolved in a direction along the line of the neutral axis. My understanding is that this will always be a positive moment.

However, I understand your concerns and I have rushed through the checks on this so I'm not entirely happy with my findings. Unfortunately I am away for the next few days so I will not be able to check this out thoroughly until I get back. I will keep you posted.

Kind regards

Dave Geeves

Re: Question about section shear under under biaxial moment and shear

caojin259 — Fri, 05 Jul 2024 07:54:05 GMT

Thanks Dave for the quick response and sharing below calculation. Will be delighted to hear from you for more feedback to continue this talk.

An associated issue i am willing to raise is that when neutral axis does not align with any sectional principal axes, for example, more often with asymmetric sections such as the traffic barriers under discussion now, the bending moment M* in the shear capacity equation may more refer to the resultant moment Mx and My (see below snippet), instead of the M* resolved to the neutral axis (=MX*COS(THETA)+MY*SIN(THETA)).

Not sure if you agree with me or not for the above. Having said that, currently there seems no existing literatures and experiments, coping with MCFT shear theory (adopted in AS5100.5) adopted for asymmetric section under biaxial bending moment scenario.

Regards,

Jing