V. Axially Loaded Column

To find support reactions due to an axial load applied at two locations on a column with both ends pinned.

Reference

Hand calculation using the following reference:

Timoshenko, S., Strength of Materials, Part I, D. Van Nostrand Co., Inc., 3rd Edition, 1956. Page 26, Problem 10.

Problem

Find the support reactions at the end joints 1 and 4.

E = 30×(10)⁶ psi

F₁ = 1,000 lbs

F₂ = 500 lbs

L = 3 in.

Pinned-pinned column with axial loads

Comparison

Table 1. Comparison of results
Result	Theory	STAAD.Pro	Difference
Reaction at Node 1 (lb)	600	600	none
Reaction at Node 4 (lb)	900	900	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Axially Loaded Column.STDis typically installed with the program.

STAAD PLANE :A PINNED-PINNED COLUMN
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: Timoshenko, Strength of Materials, Part 1
*            Problem 10, Page 26
*
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 48 72 0; 2 48 76 0; 3 48 79 0; 4 48 82 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
MEMBER PROPERTY AMERICAN
1 TO 3 PRIS AX 1 IZ 0.0001
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 4 PINNED
LOAD 1 AXIAL LOAD
JOINT LOAD
3 FY -1000
2 FY -500
PERFORM ANALYSIS
PRINT SUPPORT REACTION
FINISH

STAAD Output

   SUPPORT REACTIONS -UNIT POUN INCH    STRUCTURE TYPE = PLANE
   -----------------
 JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
      1    1      0.00    600.00      0.00      0.00      0.00      0.00
      4    1      0.00    900.00      0.00      0.00      0.00      0.00