What is P-Delta Analysis?

June 8, 2021
BLOG NEWS & TRENDS

OVERVIEW

The P-Delta analysis is a type of Geometric nonlinearity, which accounts for secondary structural behavior when axial and transverse loads are simultaneously applied to beam or wall elements. The P-Delta effect is more profound in tall building structures where high vertical axial forces act upon the laterally displaced structures caused by high lateral forces.

 

Virtually all design codes such as ACI 318 and AISC-LRFD specify that the P-Delta effect be included in structural analyses to account for more realistic member forces.

 

The P-Delta analysis feature in midas Gen & nGen is founded on the numerical analysis method adopted for Buckling analysis. Linear static analysis is performed first for a given loading condition. Then a new geometric stiffness matrix is formulated based on the member forces or stresses obtained from the first analysis. Thus, the geometric stiffness matrix is repeatedly modified and used to perform subsequent static analyses until the given convergence conditions are satisfied.

 

 

As shown in Figure 1, static loading conditions are also required to consider the P-Delta effect for dynamic analyses.

17_p delta analysis-1

Figure 1 Flow chart for P-Delta analysis in MIDAS/Gen

 

 

When a lateral load acts upon a column member, thereby resulting in moments and shear forces in the member, an additional tension force reduces the member forces. In contrast, another compression force increases the member forces.

 

Accordingly, tension forces acting on column members subjected to lateral loads increase the stiffness pertaining to lateral behaviors, while compression forces have an opposite effect on the column members.

 

 

 

Objective

 

 Compare the Analysis results with/without P-Delta

 

 

17_p delta analysis_objective

1. Define Material and Section

 

Define Material

 

 

17_p delta analysis_define material-11. select [Define>Material].

2. Select [EN] and [S235].

3. Click [OK].

Confirm from Model Tree Menu [Property>Material]

 

 

Define 1D Selection

 

17_p delta analysis_define material_1

1. select [ Define > 1D Selection ].

2. Select [ Material > S235].

3. Select Code : [ BS ].

         Type : [ Box ].

         List : [SHS 50*50*5.72 ].

4. Click [ Insert Template Section ].

5. Enter [ 5 ] to modify the width tw and tf > Press [ Enter ].

6. Click [ Apply ] & [ Close ].

          Confirm from Model Tree Menu [ Property > Section ].

 

 

 

 2. Create Columns

 

 

17_p delta analysis_create columns

1. Select [ Member > Column ].

2. Select [ SHS 50*50*5.72 (235) ].

3. Click at Datum Origin [ 0 ] > Enter [ 0, 0, 2.5] > Press [ Enter ] > Press [ Esc ] to finish.

 

 

 

 3. Copy Columns

 

 

17_p delta analysis_copy column

1. Select [ Member > Copy ].

2. Select the Column.

3. Select [X-axis ].

4. Enter [2@1.27] > Click [ Apply ].

5. Press [ Esc ] to finish.

   

 

4. Define Supports

Define Support - 1

 

 

17_p delta analysis_define supports

Apply supports

1. Go to [ Front ] view.

2. Select [ Boundary > Support ].

3. Select [ the ends of 3 columns ].

4. Select [ Fix ] > Select [ All DOF ].

5. Click [ OK ].

     Confirm [ Work Tree > Analysis > Support > Support - 1 ].

 

 

   

Define Support - 2

 

 17_p delta analysis_define supports._1

Apply supports

1. Select [ Boundary > Support ].

2. Select the [ top of 1st column ].

3. Check off [ Tx] & [Tz ].

4. Click [ Apply ].

 

Define Support - 3 & 4

 

17_p delta analysis_define supports._2

Apply supports

1. Select the [ top of 2nd column ].

2. Check on [ Tx ] & Check off [ Ry ].

3. Click [ Aplply ].

4. Select the [ top of 3rd column ].

5. Check off [ Tx ], [ Tz ], [ Ry ].

6. Click [ OK ].

     Confirm [ Work Tree > Analysis > Support > Support Set - 1 ].

 

 

5. Apply Loads

 

Apply Point Load

 

17_p delta analysis_apply point load Apply supports

 

Apply Point Load - 1

1. Select [ Load > Point Load ].

2. Select point > Enter [ 0.5 ]  in  'FX' > Enter [ -5 ] in 'FZ'.

3. Click [ Apply ].

 

Apply Point Load - 2 & 3

17_p delta analysis_apply point load_1

Apply Point Load - 2 & 3

1. Select point.

2. Enter [ 0 ] in 'FX' > Enter [ -10 ] in 'FZ' > Enter [ 10 ] in 'MY'.

3. Click [ Apply ].

4. Select point.

5. Enter [ 0 ] in 'FX' > Enter [ -10 ] in 'FZ' > Enter [ 10 ] in 'MY'.

6. Click [ OK ].

 

 

6. Perform Analysis

Analysis Settings

 

17_p delta analysis_perform analysis_analysis settings

Analysis Settings

1. Select [ Analysis > Analysis Settings ].

2. Select [ Mesh ] > Enter '7' in Division.

3. Click [ OK ].

 

 

Perform Analysis 

 

17_p delta analysis_Perform Analysis

Define Analysis Case & Run Analysis 

1. Select [ Analysis > Static/RS ].

2. Click [ Analysis Control ].

3. Check off [ P-Delta ] > Click [ OK ].

4. Click [ OK ].

5. Select [ Run Analysis ].

6. Click [ OK ].

 

 

7. Analysis Results

Confirm Analysis Results

 

17_p delta analysis_analysis result

Deformation

1. Click Indicator 1. [ Show/Hide Load Value ].

2. Select [ Deformation > Displacement-XYZ ].

3. Check on [ Value ] > Select [ Fixed > All ].

4. Check on [ Deform ] > Define Scale [ x1, x0.5, x2 ] > User [ 1000 ].

     Subtle deformation occurs at 2nd column since [ Ry ] was deselected at top support.

 

 

 

 

17_p delta analysis reaction_2

Reaction

1. Adjust the scale of [ Deform ].

2. Click Indicator 2. > Check off [ Support ].

3. Click the Yellow box > Select [ Reactions > Force-Z ].

        Reaction Force-Z and Load-Z are the same.

 

 

 

 

17_p delta analysis reaction_3

Reaction

1. Select [ Reactions > Moment-XYZ ].

      645 kN.MM = 0.5kN * 2500mm/2

 

 

 

17_p delta analysis reaction_4

Beam Forces

1. Select [ Beam > Force > Axial Force ].

2. Axial Force and Load-Z are the same.

3. Select [ Beam > Force > Bending Moment-y ].

 

       Check Bending moment-y induced by deformation.

 

17_p delta analysis reaction_5

 

8. Perform P-Delta Analysis

 


17_p delta analysis perform p-delta analysis_1

P-Delta Analysis Case

    1. Click the Yellow Box > Select [ Analysis for Design-1 ] > Right-click >

        Click [ Modify ].

    2. Click [ Analysis Control ].

    3. Select [ Consider P-Delta Effect > Static Load Set-1 ].

    4. Enter [ 30 ] in Number of Increments.

    5. Select [ Displacement ] > Check off [ Load > Work ].

    6. Click [ OK ] > [OK ] > [ YES ].

    7. Select [ Analysis > Run Analysis ].

 

 

9. P-Delta Analysis Result

Confirm Analysis Results

 

17_p delta analysis 09 confirm analysis results

Reactions

1. Select [ Reactions > Moment-XYZ ].

2. Select [ Value > Fixed > All ].

    Reaction moments have increased due to P-Delta Effect.

 

 

 

 

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About Author
Yeong-il Seo | Principal Structural Engineer

Young-il has over 13+ years of experience in building design, especially high-rise buildings with column reduction analysis, plant structures, pushover analysis, health monitoring, and vibration control projects. Since 2016, he is planning and providing technical supports for midas building products such as midas Gen, nGen, and Design+.

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