V. 3D Frame Max Forces

Find the maximum axial force and moment due to load and moment applied at a joint in a Space frame.

Reference

Weaver Jr., W., Computer Programs for Structural Analysis, page 146, problem 8.

Problem

Determine the maximum axial force and moment in the space structure.

F = 2 kip, P = 1 kip, M = 120 in·kip

L = 120 in.

E = 30E3 ksi,

AX = 11 in²

IX = 83 in⁴

IY = 56 in⁴

IZ = 56 in⁴

Space frame model

Comparison

表 1. Comparison of results
Result Type	Theory	Advanced Analysis
F_Max (kips)	1.47	1.47
M_Y, _Max (in·kip)	84.04	84.04
M_Z, _Max (in·kip)	95.319	95.32

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\03 Frames\3D Frame Max Forces.STD is typically installed with the program.

STAAD SPACE : 3D FRAME MAX FORCES
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
*
* REFERENCE 'COMPUTER PROGRAMS FOR STRUCTURAL ANALYSIS'
* BY WILLIAM WEAVER JR. PAGE 146 STRUCTURE NO. 8.
* ANSWER - MAX AXIAL FORCE= 1.47 (MEMB 3)
* MAX BEND-Y= 84.04, MAX BEND-Z= 95.319 (BOTH MEMB 3)
*
UNIT INCHES KIP
JOINT COORDINATES
1 0 120 0; 2 240 120 0; 3 0 0 0; 4 360 0 120;
MEMBER INCIDENCES
1 1 2; 2 3 1; 3 2 4;
MEMBER PROPERTY AMERICAN
1 TO 3 PRIS AX 11 IX 83 IY 56 IZ 56
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 30000
POISSON 0.25
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
3 4 FIXED
LOAD 1 JOINT LOAD
JOINT LOAD
1 FX 2
2 FY -1
2 MZ -120
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    1    0.22267   0.00016  -0.17182  -0.00255   0.00217  -0.00213
      2    1    0.22202  -0.48119  -0.70161  -0.00802   0.00101  -0.00435
      3    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
      4    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
      : 3D FRAME MAX FORCES                                    -- PAGE NO.    4 
   SUPPORT REACTIONS -UNIT KIP  INCH    STRUCTURE TYPE = SPACE
   -----------------
 JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
      3    1     -1.10     -0.43      0.22     48.78    -17.97     96.12
      4    1     -0.90      1.43     -0.22    123.08     47.25    -11.72
      : 3D FRAME MAX FORCES                                    -- PAGE NO.    5 
   MEMBER END FORCES    STRUCTURE TYPE = SPACE
   -----------------
   ALL UNITS ARE -- KIP  INCH     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      1    1     1      0.90     -0.43     0.22     22.71    -17.97     -36.37
                 2     -0.90      0.43    -0.22    -22.71    -34.18     -67.36
      2    1     3     -0.43      1.10     0.22    -17.97    -48.78      96.12
                 1      0.43     -1.10    -0.22     17.97     22.71      36.37
      3    1     2      1.47     -0.71    -0.48    -37.02     15.69     -53.28
                 4     -1.47      0.71     0.48     37.02     84.04     -95.32 
   ************** END OF LATEST ANALYSIS RESULT **************
    34. FINISH