P-Delta effect plus Time-History analysis or Response Spectrum analysis.

Dear Seniors:

 When I want to make a Time-History analysis or a Response Spectrum analysis is necessary to make a P-Delta analysis to include the second-order effect due the deformation of the structure produced by horizontal forces. STAAD is capable to make a P-Delta effect without any problem, but in its TECHNICAL REFERENCE says:

 “A PDELTA ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification... Secondary effects will not be evaluated correctly for LOAD COMBINATIONS”

But the REPEAT LOAD specification says:

“RESPONSE SPECTRUM LOAD and TIME HISTORY LOAD should not be used in REPEAT LOAD. It is also not available for loads generated using the program's load generation facilities such as UBC LOAD Generation, WIND LOAD Generation, MOVING LOAD Generation, etc”

My question is:

How I can to combine several loads case including Time History or Response Spectrum load case, or any other load derivate from generation load facility, to make an appropriate P Delta analysis?

It’s necessary to model the totality of the mass of the structure in the same directions to avoid that the mass be canceled. That's why is extremely necessary to "combine" it effect in one way (positive) and in the other way (negative) with the rest of the common load case like dead, live and others. How I can do that and reach an appropriate P Delta effect analysis?

I give you an example where I've defined a seismic load case using the response spectrum analysis, you can see the error that STAAD give me back because I use response spectrum in a repeat load specification.

25. LOAD 1 LOADTYPE DEAD TITLE Dead

26. SELFWEIGHT Y -1

27. MEMBER LOAD

28. 2 UNI GY -1.5

29. LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live

30. MEMBER LOAD

31. 2 UNI GY -2

32. 2 CON GY -2 3

33. LOAD 3 LOADTYPE SEISMIC TITLE Seismic X

34. SELFWEIGHT X 1

35. SELFWEIGHT Y 1

36. MEMBER LOAD

37. 2 UNI GX 1.5

38. 2 UNI GY 1.5

39. 2 UNI GX 2

40. 2 UNI GY 2

41. 2 CON GX 2 3

42. 2 CON GY 2 3

43. SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN

44. ZIP 92887 SITE CLASS B TL 8.000

45. LOAD 4 LOADTYPE NONE TITLE Repeat Load

46. REPEAT LOAD

47. 1 1.0 2 1.0 3 1.0 **ERROR- CASE BEING FACTORED IS DYNAMIC. CASE= 3

48. PDELTA KG 15 ANALYSIS SMALLDELTA PRINT MODE SHAPES

Parents
  • A better choice of input is as follows:

                                Ensure that you have requested enough modes. The default 6 is often not enough.

    CUT OFF MODES 20

    LOAD 1 LOADTYPE DEAD TITLE Dead
    SELFWEIGHT Y -1
    MEMBER LOAD
    2 UNI GY -1.5

    LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live
    MEMBER LOAD
    2 UNI GY -2
    2 CON GY -2 3

                               Combine the static cases for PDELTA. For PDELTA the cases with both horizontal and vertical forces
                              will have more of the Pdelta effect.

    LOAD 4 LOADTYPE NONE TITLE Repeat Load
    REPEAT LOAD
    1 1.0 2 1.0

              To have the PDELTA effect in dynamic cases, place the case just before the PDELTA KG Analysis command.
              The dynamics will include the Kg matrix from the prior case (case 4).   | [K+Kg] - ω [M] | = 0

    LOAD 3 LOADTYPE SEISMIC TITLE Seismic X
    SELFWEIGHT X 1
    SELFWEIGHT Y 1
    MEMBER LOAD
    2 UNI GX 1.5
    2 UNI GY 1.5
    2 UNI GX 2
    2 UNI GY 2
    2 CON GX 2 3
    2 CON GY 2 3
    SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN
    ZIP 92887 SITE CLASS B TL 8.000

                          Combine the static and dynamic by using the LOAD COMBINATION command.
                          Create two cases: static + dynamic and static - dynamic   since RSA dynamic results can be + or - .
                          If there are 2 or more dynamic cases, you should combine those dynamic cases with SRSS option in
                          LOAD COMBINATION.

    LOAD COMBINATION 5 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 1.0

    LOAD COMBINATION 6 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 -1.0

                           The PDELTA KG command does not need iteration value or smalldelta. They are included.

    PDELTA KG ANALYSIS
    PRINT MODE SHAPES

    Answer Verified By: Sye 

Reply
  • A better choice of input is as follows:

                                Ensure that you have requested enough modes. The default 6 is often not enough.

    CUT OFF MODES 20

    LOAD 1 LOADTYPE DEAD TITLE Dead
    SELFWEIGHT Y -1
    MEMBER LOAD
    2 UNI GY -1.5

    LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live
    MEMBER LOAD
    2 UNI GY -2
    2 CON GY -2 3

                               Combine the static cases for PDELTA. For PDELTA the cases with both horizontal and vertical forces
                              will have more of the Pdelta effect.

    LOAD 4 LOADTYPE NONE TITLE Repeat Load
    REPEAT LOAD
    1 1.0 2 1.0

              To have the PDELTA effect in dynamic cases, place the case just before the PDELTA KG Analysis command.
              The dynamics will include the Kg matrix from the prior case (case 4).   | [K+Kg] - ω [M] | = 0

    LOAD 3 LOADTYPE SEISMIC TITLE Seismic X
    SELFWEIGHT X 1
    SELFWEIGHT Y 1
    MEMBER LOAD
    2 UNI GX 1.5
    2 UNI GY 1.5
    2 UNI GX 2
    2 UNI GY 2
    2 CON GX 2 3
    2 CON GY 2 3
    SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN
    ZIP 92887 SITE CLASS B TL 8.000

                          Combine the static and dynamic by using the LOAD COMBINATION command.
                          Create two cases: static + dynamic and static - dynamic   since RSA dynamic results can be + or - .
                          If there are 2 or more dynamic cases, you should combine those dynamic cases with SRSS option in
                          LOAD COMBINATION.

    LOAD COMBINATION 5 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 1.0

    LOAD COMBINATION 6 LOADTYPE NONE TITLE LOAD COMB
    4 1.0 3 -1.0

                           The PDELTA KG command does not need iteration value or smalldelta. They are included.

    PDELTA KG ANALYSIS
    PRINT MODE SHAPES

    Answer Verified By: Sye 

Children
  • Raycxxx,

    According to your reply, it seems that the repeat load command can be replaced by putting the Load 1 and Load 2 in one load case (if the factors are unity in this case). The commands can be reduced to as follows:

    LOAD 1 Dead + Live
    * * Dead Load
    SELFWEIGHT Y -1
    MEMBER LOAD
    2 UNI GY -1.5
    * * Live Load
    2 UNI GY -2
    2 CON GY -2 3

    Then Load 4 for repeat load is not necessary. Am I correct?

    My another question is that you mentioned "For PDELTA the cases with both horizontal and vertical forces will have more of the Pdelta effect." However, you only use REPEAT LOAD for vertical loads; the horizontal loads (seismic) is inclued later using LOAD COMBINATION. The veritcal and horizontal loads are not "combined" together as what you mentioned.

    Second,  when you use response sectrum analysis together with P-delta effect. Does the modal superposition take into account the geometric nonlinearity?

    Thanks,
    Paul

  • STAAD.Pro developers please answer the queries of PaulY.

    Thank you.

  • *********************** P D E L T A  with Response Spectrum and Load Combinations

    *******************************

    ******************************* Enter static cases

    LOAD 1 LOADTYPE DEAD TITLE Dead

    SELFWEIGHT Y -1

    MEMBER LOAD

    2 UNI GY -1.5

    ************************ Keep entering cases until all entered

    *******************

    LOAD 2 LOADTYPE LIVE REDUCIBLE TITLE Live

    MEMBER LOAD

    2 UNI GY -2

    2 CON GY -2 3

    PERFORM ANALYSIS

    CHANGE

    ***************** Enter static case for computing member axial forces to be used only for member Kg matrices

    ***************** Alternatively all static loads could be entered into this one case

    ***************** or use repeat load to replicate the cases here.

    LOAD 3 LOADTYPE DEAD+LIVE

    repeat load

    1 1.0 2 1.0

    ***************** Case for modes and response spectrum (just before first dynamic case)

    LOAD 4 LOADTYPE SEISMIC TITLE Seismic X

    ***************** Enter all 3D masses to be considered times g here

    ***************** Solve X direction

    SELFWEIGHT X 1

    SELFWEIGHT Y 1

    SELFWEIGHT Z 1

    MEMBER LOAD

    2 UNI GX 1.5

    2 UNI GY 1.5

    2 UNI GZ 1.5

    2 UNI GX 2

    2 UNI GY 2

    2 UNI GZ 2

    2 CON GX 2 3

    2 CON GY 2 3

    2 CON GZ 2 3

    SPECTRUM CQC IBC 2006 X 1 ACC DAMP 0.05 LIN

    ZIP 92887 SITE CLASS B TL 8.000

    *******************************

    PDELTA KG ANALYSIS

    CHANGE

    **************** Solve Z direction

    LOAD 5 LOADTYPE SEISMIC TITLE Seismic Z

    SPECTRUM CQC IBC 2006 Z 1 ACC DAMP 0.05 LIN

    ZIP 92887 SITE CLASS B TL 8.000

    ******************* Combine first two static cases algebraically

    ******************* then SRSS the two directions of RSA and add to static

    LOAD COMB SRSS  6 LOADTYPE NONE TITLE SRSS Combination Load

    -1 1.0 -2 1.0 4 1.0 5 1.0 1.0

    ******************* Combine first two static cases algebraically

    ******************* then SRSS the two directions of RSA and subtract from static

    LOAD COMB SRSS  7 LOADTYPE NONE TITLE SRSS Combination Load

    -1 1.0 -2 1.0 4 1.0 5 1.0 -1.0

    PERFORM ANALYSIS

    Answer Verified By: Sye 

  • Hello RayC,

    The TECHNICAL REFERENCE states the same thing for the BUCKLING and DIRECT Analysis - namely:

    “A BUCKLING/DIRECT ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification... Secondary effects will not be evaluated correctly for LOAD COMBINATIONS”

    Does this workaround method that you described for the P-Delta work also for the two other types of analysis mentioned above?

    I would much appreciate if you could give me an answer at your earliest convenience!

    Kind Regards,

    Skerdi
  • The method Ray suggested is only an approximate way of accounting for second order effect in a dynamic load case. If you are asking whether a load combination where static part is combined algebraically and is SRSS-d with the dynamic part, is going to work for BUCKLING or DIRECT ANALYSIS, I would say No.