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

表 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
B_v	0	0	none
B_z	2,700	2,700	none
C_x	1,800	1,800	none
C_v	3,375	3,375	none
D_x	1,800	1,800	none
D_v	3,375	3,375	none

表 2. Comparison of results
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 2023\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