V. Axial Force in a 2D Plane Frame 1

To find member forces due to joint loads in a plane truss.

Reference

Norris C.H., Wilbur J. B., Elementary Structural Analysis, 2nd Edition, McGraw – Hill, Inc., Page 159, Problem 4.3. (Original data is in US Customary Units)

Problem

Compute the bar forces in the bars a, b, c, d, e of the truss due to the loads shown.

Plane truss

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
a	-202.13	-202.13	none
b	-185.76	-190.28	2.4% (negligible)
c	-22.42	-23.42	4.5%
d	266.23	269.52	1.2% (negligible)
e	119.61	117.08	2.1% (negligible)

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\02 Trusses\Axial Force in a 2D Plane Frame 1.STD is typically installed with the program.

STAAD TRUSS :A PLANE TRUSS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR,
*            2nd EDITION, McGRAW-HILL BOOK COMPANY, PAGE 159,
*            PROBLEM 4.3 (ORIGINAL DATA IN US CUSTOMARY UNITS)
*
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 7.62 0 0; 3 7.62 9.144 0; 4 15.24 0 0; 5 15.24 4.572 0;
6 15.24 9.144 0; 7 22.86 0 0; 8 22.86 12.192 0; 9 30.48 0 0;
10 30.48 4.572 0; 11 30.48 9.144 0; 12 38.1 0 0; 13 38.1 9.144 0;
14 45.72 0 0;
MEMBER INCIDENCES
1 1 2; 2 1 5; 3 1 3; 4 2 3; 5 2 4; 6 5 3; 7 3 6; 8 4 7; 9 7 5; 10 6 8;
11 7 9; 12 7 10; 13 11 8; 14 9 12; 15 10 13; 16 11 13; 17 12 14;
18 14 10; 19 12 13; 20 14 13; 21 4 5; 22 5 6; 23 7 8; 24 9 10; 25 10 11;
MEMBER PROPERTY AMERICAN
1 TO 25 PRIS AX 0.00129032
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.06843e+08
POISSON 0.290909
END DEFINE MATERIAL
UNIT METER NEWTON
CONSTANTS
MATERIAL MATERIAL1 ALL
MEMBER TRUSS 
1 TO 25
SUPPORTS
1 PINNED
14 FIXED BUT FX
LOAD 1 VERTICAL JOINT LOADS
JOINT LOAD
2 9 FY -44482.2
4 7 FY -88964.4
12 FY -22241.1
PERFORM ANALYSIS
UNIT METER KN
PRINT MEMBER FORCES LIST 2 5 6 10 12
FINISH

STAAD Output

   MEMBER END FORCES    STRUCTURE TYPE = TRUSS
   -----------------
   ALL UNITS ARE -- KN   METE     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      2    1     1    190.28      0.00     0.00      0.00      0.00       0.00
                 5   -190.28      0.00     0.00      0.00      0.00       0.00
      5    1     2   -269.52      0.00     0.00      0.00      0.00       0.00
                 4    269.52      0.00     0.00      0.00      0.00       0.00
      6    1     5   -117.08      0.00     0.00      0.00      0.00       0.00
                 3    117.08      0.00     0.00      0.00      0.00       0.00
     10    1     6    202.12      0.00     0.00      0.00      0.00       0.00
                 8   -202.12      0.00     0.00      0.00      0.00       0.00
     12    1     7     23.42      0.00     0.00      0.00      0.00       0.00
                10    -23.42      0.00     0.00      0.00      0.00       0.00