P Delta Load Combinations As Per Is Code

[Alexandrin Chaples]

Ithelps to think of a P-Delta failure as an elastic buckling of your model. It may be a localized buckling of one member, or it may be a general buckling of the frame. The challenging part to understanding the failure is to determine what the buckled shape of the structure looks like.

Of the normal Load Combinations, LC#2 is the one which diverges for P-Delta. Therefore, we have created a number of load combinations to test this P-Delta failure. These load combination apply a fraction of the load (from 10% to 93%) from LC#2. In this way, we are reducing the load to a point where the structure is very close to buckling, but not quite there. While determining this point, it might be useful to temporarily set Processor Core Utlization to 'Single'. This will run one load combination at a time in order so that the divergence is triggered on the first possible load combination. To change Precessor Core Utilization, go to the Solution tab under Model Settings.

From these pictures, it becomes clear that the top chord of the truss is buckling out of plane. If there is any doubt about what the buckling is, then we would run LC#17 with and without P-Delta and compare the joint deflections to see which deflections are receiving the greatest amplification due to 2nd order effects.

Once the buckled shape is understood, the solution is a relatively simple structural engineering decision. It may involve modeling some form of lateral restraint to mimic a roof diaphragm. Or, it may involve rotating the top chord so that the strong axis will resist this type of buckling.

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Hi Berhan,

P-Delta analysis should be performed with adequate load combinations for the type of load analyzed. For example, using ASCE load combinations for wind and earthquake design I had used 1.2 D+L. For gravity loads I have used the most critical from 1.4 D and 1.2 D+1.6 L.

I hope this can help.

Best, regards

Berhan, There are a couple of ways to perform P-Delta analysis in Etabs or Sap2000. To learn the intricacies and make sure you are doing it right will probably require digging into the manuals and help section at the CSI web site.

The load combinations you use will depend on the code you use to some extent although as a general philosophy they should all be at a factored level. My comments are based on AISC Specifications Part C.

One way. You can create factored Load Cases that include your entire load combination such as 1.2D +1.6L + Lateral. My underline emphasis is intentional because I'm not talking about defining load combinations. Once the load case is defined, you can select non-linear under analysis type and then select P-Delta. Do this for each factored load case. Of course, you have to consider notional loads and all that too according to your code.

Second way. I often prefer this method. Create one factored Load Case for factored dead load and a factored lateral load such as 1.2D + Wind. I believe just about any lateral load to push the structure laterally will work as long as it has the full dead load you want to consider on it. Run this one as a non-linear P-Delta load case. The software calculates a softened stiffness matrix based on the P-Delta effects.

Then for the remainder of your load cases, the way you would normally define them, select the Stiffness at End of Nonlinear Case option under Stiffness to Use section. Pick the load case you defined above as the starting load case for all the rest of the load lases you want to consider and they run linearly including the P-Delta effect. Define all your load combination as you usually would in the Define:Load Combinations section.

Structural engineering design software can be an invaluable resource to perform efficient, engineered solutions of both simple and complex-framed structures. It can also be a source of much frustration if you lose sight of your precise data entry.

You've spent hours carefully inputting your structure, all the individual nodes, members, pinned or fixed connection types, getting the orientation of each member correct, checking the unbraced lengths, the k values. You've assigned the boundary supports, checked the code solutions, and double checked that the Y axis is vertical. You've assigned your loads, then applied your loads, and then created your load combinations.

"In the process of solving the model, RISA-3D detected instability. This means there is the potential for an unlimited displacement. Check your model. If you are unable to find the source of the instability it may be because of a setting in the program. Open Tools>Application Settings, uncheck the "Lock isolated ROTATIONAL instabilities without notification?" and then solve your model and you may see the problem." 1

For a structural frame system, modifying the boundary condition supports can resolve the instabilities. If pins are chosen for all support points, there are (6) joint aspects for the model to solve and it becomes unstable. In reality though, for a column with a pinned base, we can hold the Y rotation by setting the drop-down box to "reaction" as we do not expect to see this rotation in the field.

"When a model is loaded, it deflects. The deflections in the members of the model may induce secondary moments due to the fact that the ends of the member may no longer be co-linear in the deflected position. These secondary effects, for members (not plates), can be accurately approximated through the use of P-Delta analysis. This type of analysis is called "P-Delta" because the magnitude of the secondary moment is equal to "P", the axial force in the member, times "Delta", the distance one end of the member is offset from the other end." 1

If the P-Delta process is diverging dramatically, it will be stopped before numerical problems develop and an error will be displayed. If this error is displayed, the P-Delta displacements have reached a level where they are more than 1,000 times greater than the maximum original displacements. If this happens with your model, the model may be unstable under the given loads, or there may be local instabilities present." 1

Well, the first step is to check your code selection. AISC 14th will require you to specify either Yes or Compression. If you leave this blank and try to solve your model using AISC 14th, it will not perform calculations on your members.

If you have properly specified the PDelta, maybe you run the model and you get an error message saying "PDelta diverging". If this happens, run the model with PDelta turned off and check for huge deflections or instabilities, indicating improper modeling.

Type in "S" or "segment" in the member information. Designating a member as a segment will automatically calculate the unbraced length of a long girder with beams framing into it. Remember to specify the member is physical.

RISA-3D is a proprietary structural engineering and design software package developed and licensed by RISA Technologies, Inc., 26632 Towne Centre Drive, Suite 210, Foothill Ranch, CA 92610, www.risa.com. This product, along with all other engineering software packages, have proven to be powerful tools to aid in the development of structural engineered solutions. Use of all engineering software shall be performed by qualified, licensed professional engineers with the proper knowledge, training, and experience to responsibly execute the necessary requirements specific to their projects. Neither the author of this blog, nor HWH AEP Inc. make any warranties, either expressly or implied, as to the accuracy of results or proper usage of RISA-3D.

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Drift is a very complex topic in structural engineering. It involves too many factors to arrive at a suitable decision. It involves engineering judgment, the phenomenon fresh engineers might not feel. In this article, I have tried to explain what is building drift, allowable limits, ways and means to check in ETABS models and to control the excessive drift. Please keep in mind, this article is not about the building drift as far as structural science is concerned, rather this topic of drift is related to ETABS software.I am quoting here the definitions from UBC-97 code:-

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