# V. 2D Frame 2 Step P-Delta Displacement

To verify P-Delta analysis for a ten story plane frame.

## Reference

Naeim, F., The Seismic Design Handbook, Van Nostrand Reinhold, 1989.

## Problem

Find the lateral displacement of the 10th story after two iterations of P-Delta analysis.

 E = 29,000 ksi

## Comparison

Table 1. Comparison of results
Displacement in X dir. at top (Node 41), Î´ (in) 8.508 8.65347 1.7%

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\07 Nonlinear Analysis\2D Frame 2 Step P-Delta Displacement.STD is typically installed with the program.

``````STAAD PLANE : 2-ITERATION PDELTA ANALYSIS OF A 10 STOREY PLANE FRAME
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
INPUT WIDTH 72
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 20 0 0; 3 40 0 0; 4 60 0 0; 5 0 15 0; 6 20 15 0; 7 40 15 0;
8 60 15 0; 9 0 27 0; 10 20 27 0; 11 40 27 0; 12 60 27 0; 13 0 39 0;
14 20 39 0; 15 40 39 0; 16 60 39 0; 17 0 51 0; 18 20 51 0; 19 40 51 0;
20 60 51 0; 21 0 63 0; 22 20 63 0; 23 40 63 0; 24 60 63 0; 25 0 75 0;
26 20 75 0; 27 40 75 0; 28 60 75 0; 29 0 87 0; 30 20 87 0; 31 40 87 0;
32 60 87 0; 33 0 99 0; 34 20 99 0; 35 40 99 0; 36 60 99 0; 37 0 111 0;
38 20 111 0; 39 40 111 0; 40 60 111 0; 41 0 123 0; 42 20 123 0;
43 40 123 0; 44 60 123 0;
MEMBER INCIDENCES
1 1 5; 2 2 6; 3 3 7; 4 4 8; 5 5 6; 6 6 7; 7 7 8; 8 5 9; 9 6 10; 10 7 11;
11 8 12; 12 9 10; 13 10 11; 14 11 12; 15 9 13; 16 10 14; 17 11 15;
18 12 16; 19 13 14; 20 14 15; 21 15 16; 22 13 17; 23 14 18; 24 15 19;
25 16 20; 26 17 18; 27 18 19; 28 19 20; 29 17 21; 30 18 22; 31 19 23;
32 20 24; 33 21 22; 34 22 23; 35 23 24; 36 21 25; 37 22 26; 38 23 27;
39 24 28; 40 25 26; 41 26 27; 42 27 28; 43 25 29; 44 26 30; 45 27 31;
46 28 32; 47 29 30; 48 30 31; 49 31 32; 50 29 33; 51 30 34; 52 31 35;
53 32 36; 54 33 34; 55 34 35; 56 35 36; 57 33 37; 58 34 38; 59 35 39;
60 36 40; 61 37 38; 62 38 39; 63 39 40; 64 37 41; 65 38 42; 66 39 43;
67 40 44; 68 41 42; 69 42 43; 70 43 44;
MEMBER PROPERTY AMERICAN
61 TO 63 68 TO 70 TABLE ST W16X40
47 TO 49 54 TO 56 TABLE ST W21X44
33 TO 35 40 TO 42 TABLE ST W21X50
5 TO 7 12 TO 14 19 TO 21 26 TO 28 TABLE ST W24X55
1 4 8 11 TABLE ST W14X109
15 18 22 25 TABLE ST W14X82
29 32 36 39 TABLE ST W14X68
43 46 50 53 TABLE ST W14X53
57 60 64 67 TABLE ST W14X43
2 3 9 10 TABLE ST W14X159
16 17 23 24 TABLE ST W14X109
30 31 37 38 TABLE ST W14X90
44 45 51 52 TABLE ST W14X68
58 59 65 66 TABLE ST W14X48
DEFINE MATERIAL START
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT INCHES KIP
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 TO 4 FIXED
UNIT FEET KIP
SELFWEIGHT Y -1
5 FX 2.97
9 FX 5.34
13 FX 7.71
17 FX 10.08
21 FX 12.45
25 FX 14.83
29 FX 17.2
33 FX 19.57
37 FX 21.94
41 FX 30.22
68 TO 70 UNI GY -3
5 TO 7 12 TO 14 19 TO 21 26 TO 28 33 TO 35 40 TO 42 47 TO 49 -
54 TO 56 61 TO 63 UNI GY -3.6
PDELTA 2 ANALYSIS SMALLDELTA
PRINT SUPPORT REACTION
PRINT JOINT DISPLACEMENTS LIST 5 9 13 17 21 25 29 33 37 41
FINISH
``````

```   SUPPORT REACTIONS -UNIT KIP  FEET    STRUCTURE TYPE = PLANE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
1    1    -24.00    167.66      0.00      0.00      0.00    266.10
2    1    -44.43    728.95      0.00      0.00      0.00    450.70
3    1    -44.18    735.97      0.00      0.00      0.00    450.22
4    1    -29.70    562.02      0.00      0.00      0.00    299.68
************** END OF LATEST ANALYSIS RESULT **************
77. PRINT JOINT DISPLACEMENTS LIST 5 9 13 17 21 25 29 33 37 41
JOINT    DISPLACE LIST     5
: 2-ITERATION PDELTA ANALYSIS OF A 10 STOREY PLANE FRAME -- PAGE NO.    5
JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = PLANE
------------------
JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
5    1    0.82891  -0.03236   0.00000   0.00000   0.00000  -0.00489
9    1    1.67612  -0.05711   0.00000   0.00000   0.00000  -0.00505
13    1    2.62313  -0.08857   0.00000   0.00000   0.00000  -0.00526
17    1    3.53893  -0.11821   0.00000   0.00000   0.00000  -0.00526
21    1    4.53306  -0.15114   0.00000   0.00000   0.00000  -0.00599
25    1    5.50759  -0.18037   0.00000   0.00000   0.00000  -0.00583
29    1    6.48197  -0.21244   0.00000   0.00000   0.00000  -0.00576
33    1    7.32004  -0.23784   0.00000   0.00000   0.00000  -0.00526
37    1    8.09379  -0.25973   0.00000   0.00000   0.00000  -0.00516
41    1    8.65347  -0.26998   0.00000   0.00000   0.00000  -0.00483
```