V. Axial Forces on a 3D Space Model
To find support reactions and member forces due to a joint load in a space truss.
Reference
Beer F. P., and Johnston, E. R., Vector Mechanics for Engineers - Statics, 4th Edition, McGraw – Hill, Inc., p.216, Problem 6.20.
Problem
The space truss is supported by the six reactions shown. If a horizontal 2,700 N load is applied at A, determine the reactions and the force in each member.
Space truss
Comparison
| Result Type | Theory | STAAD.Pro | Difference |
|---|---|---|---|
| Bv | 0 | 0 | none |
| Bz | 2,700 | 2,700 | none |
| Cx | 1,800 | 1,800 | none |
| Cv | 3,375 | 3,375 | none |
| Dx | 1,800 | 1,800 | none |
| Dv | 3,375 | 3,375 | none |
| Result Type | Theory | STAAD.Pro | Difference |
|---|---|---|---|
| AB | 0 | 0 | none |
| AC | 4,275 | 4,275 | none |
| AD | 4,275 | 4,275 | none |
| BC | 4,270 | 4,269 | negligible |
| CD | 0 | 0 | none |
| BD | 4,270 | 4,269 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\02 Trusses\Axial Forces on a 3D Space Model.STD is typically installed with the program.
STAAD TRUSS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: VECTOR MECHANICS FOR ENGINEERS - STATICS, BEER AND
* JOHNSTON, 4th EDITION, McGRAW-HILL BOOK CO.,
* PAGE 216, PROBLEM 6.20.
*
UNIT METER NEWTON
JOINT COORDINATES
1 1 0 0.6; 2 1 0 -0.6; 3 -0.8 0 0; 4 0 1.5 0;
MEMBER INCIDENCES
1 1 4; 2 2 4; 3 3 4; 4 1 2; 5 2 3; 6 3 1;
MEMBER PROPERTY AMERICAN
1 TO 6 PRIS AX 0.001
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2e+11
POISSON 0.29542
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
MEMBER TRUSS
1 TO 6
SUPPORTS
1 FIXED BUT FZ
2 FIXED BUT FZ
3 FIXED BUT FX
LOAD 1 HORIZONTAL LOAD
JOINT LOAD
4 FZ 2700
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES
FINISH
STAAD Output
SUPPORT REACTION STAAD TRUSS -- PAGE NO. 3 SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = TRUSS ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 1800.00 3375.00 0.00 0.00 0.00 0.00 2 1 -1800.00 -3375.00 0.00 0.00 0.00 0.00 3 1 0.00 0.00 -2700.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 35. PRINT MEMBER FORCES MEMBER FORCES STAAD TRUSS -- PAGE NO. 4 MEMBER END FORCES STRUCTURE TYPE = TRUSS ----------------- ALL UNITS ARE -- NEWT METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 4275.00 0.00 0.00 0.00 0.00 0.00 4 -4275.00 0.00 0.00 0.00 0.00 0.00 2 1 2 -4275.00 0.00 0.00 0.00 0.00 0.00 4 4275.00 0.00 0.00 0.00 0.00 0.00 3 1 3 -0.00 0.00 0.00 0.00 0.00 0.00 4 0.00 0.00 0.00 0.00 0.00 0.00 4 1 1 0.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 0.00 5 1 2 4269.07 0.00 0.00 0.00 0.00 0.00 3 -4269.07 0.00 0.00 0.00 0.00 0.00 6 1 3 -4269.07 0.00 0.00 0.00 0.00 0.00 1 4269.07 0.00 0.00 0.00 0.00 0.00