V. Single Column P-Delta Analysis

Determine the support forces at the base of the column.

Details

A 12 ft tall column with a fixed base and free end is subject to a 3 kip axial load and a 5 kip lateral load. The section is a W8x10 using steel with a modulus of elasticity of 29,000 ksi.

Validation

Moment at the base including P-Delta

M = H×L + P×Δ

where

H	=	the lateral load
L	=	the length of the column
P	=	the axial compression load
Δ	=	the displacement due to the lateral load at the free end of the column $\frac{H L^{3}}{3 E I} = \frac{5 \times {(144)}^{3}}{3 \times 29,000 \times 30.80} = 5.57 in$

Therefore, the moment is:

M = 5 (144) + 3 (5.57) = 736.72 in·kip

Results

Table 1.
Parameter	Reference	STAAD.Pro	Difference	Comment
Base moment (ft·kip)	736.72	736.72	none

STAAD Input

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\Verification Models\07 Nonlinear Analysis\Single Column P-Delta Analysis.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-May-08
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 12 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+006
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-006
DAMP 0.03
END DEFINE MATERIAL
SET SHEAR
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X10
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
PRINT MEMBER PROPERTIES ALL
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FX 5
LOAD 2 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -3
PERFORM ANALYSIS PRINT STATICS CHECK
CHANGE
LOAD 3 LOADTYPE None  VERTICAL 
REPEAT LOAD
1 1.0 2 1.0
PDELTA ANALYSIS LARGEDELTA PRINT STATICS CHECK
unit kips inches
PRINT JOINT DISPLACEMENTS ALL
PRINT MEMBER FORCES
FINISH

STAAD Output

   MEMBER END FORCES    STRUCTURE TYPE = SPACE
   -----------------
   ALL UNITS ARE -- KIPS INCH     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    3     1      3.00      5.12     0.00      0.00      0.00     736.72
                 2     -3.00     -5.12     0.00      0.00      0.00       0.00
   ************** END OF LATEST ANALYSIS RESULT **************