# V. Column Buckling Factor

Determine the buckling factor for a pinned-pinned column subject to an axial load.

## Details

A 30 ft tall column with pinned ends is subject to a 160 kip axial load. The section is a W10x45 with a modulus of elasticity of 29,730 ksi.

## Validation

Critical elastic buckling capacity:

Pcr = π2EI/ℓ2

Pcr = π2(29,730)(248)/(30×12)2 = 561.5 k

Buckling factor: Pcr/P = 561.5 / 160 = 3.509

## Results

Table 1.
Buckling factor 3.509 3.50976562 negligible

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\Column Buckling Factor.std is typically installed with the program.

``````STAAD PLANE : BUCKLING FACTOR FOR PINNED-PINNED COLUMN WITH AN AXIAL LOAD
SET SHEAR
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0 5 0 30 0;
MEMBER INCIDENCES
1 1 2 4
UNIT KIP INCH
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29730
POISSON 0.3
DENSITY 0.286E-3
ALPHA 6e-006
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 4 TABLE ST W10X45
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
5 FIXED BUT FY MX MY MZ
5 FY -160
PERFORM BUCKLING ANALYSIS MAXSTEP 20
FINISH
``````

```    BUCKLING ITERATIONS FOR CASE NO.     1
ITERATION   BUCKLING FACTOR      UPPER BOUND        LOWER BOUND
0        1.00000000E+00     0.00000000E+00     0.00000000E+00
1        2.00000000E+00     1.01000000E+10     1.00000000E+00
2        4.00000000E+00     1.01000000E+10     2.00000000E+00
3        3.00000000E+00     4.00000000E+00     2.00000000E+00
4        3.50000000E+00     4.00000000E+00     3.00000000E+00
5        3.75000000E+00     4.00000000E+00     3.50000000E+00
6        3.62500000E+00     3.75000000E+00     3.50000000E+00
7        3.56250000E+00     3.62500000E+00     3.50000000E+00
8        3.53125000E+00     3.56250000E+00     3.50000000E+00
9        3.51562500E+00     3.53125000E+00     3.50000000E+00
10        3.50781250E+00     3.51562500E+00     3.50000000E+00
11        3.51171875E+00     3.51562500E+00     3.50781250E+00
12        3.50976562E+00     3.51171875E+00     3.50781250E+00
13        3.50976562E+00     3.51171875E+00     3.50976562E+00
CONVERGED
```