V. Axial Force on a Cable

To find member force due to a member load in a plane articulate structure.

Reference

Kinney, J. S.,Indeterminate Structural Analysis, Addison - Wesley Publishing Co., 1957, p.275, Problem 6 - 19.(Original data is in US Customary Units)

Problem

Find the tensile stress in the cable. The cross - sectional area of the cable is 967.74 mm² with an E of 137.895 GPa. The timber beam 1-3 is 304.8 mm x 304.8 mm in section, with E = 11.03161 GPa. Each member of the steel cantilever truss has a cross - sectional area of 2,580.64 mm², and E of 206.8427 GPa.

Plane articulate truss

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
Cable, 3-4	22.7	22.58	0.6% (negligible)

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\02 Trusses\Axial Force on a Cable.STD is typically installed with the program.

STAAD PLANE :A PLANE ARTICULATE STRUCTURE
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: INDETERMINATE STRURAL ANALYSIS, KINNEY, 1957,
*            ADISON-WESLEY PUBLISHING COMPANY, PAGE 275, PROBLEM 6-19.
*
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 3.048 0 0; 3 4.572 0 0; 4 4.572 2.4384 0; 5 6.4008 4.8768 0;
6 6.4008 2.4384 0; 7 8.2296 4.8768 0; 8 8.2296 2.4384 0;
9 10.0586 4.8768 0; 10 10.0586 2.4384 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 6; 5 6 8; 6 8 10; 7 4 5; 8 6 5; 9 6 7; 10 8 7;
11 8 9; 12 5 7; 13 7 9;
MEMBER PROPERTY AMERICAN
1 2 PRIS YD 0.3048 ZD 0.3048
3 PRIS AX 0.00096774 IZ 4.16231e-07
4 TO 13 PRIS AX 0.00258064 IZ 4.16231e-07
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1.10316e+07
POISSON 0.22857
ISOTROPIC MATERIAL2
E 1.37895e+08
POISSON 0.261539
ISOTROPIC MATERIAL3
E 2.06843e+08
POISSON 0.290909
END DEFINE MATERIAL
UNIT METER NEWTON
CONSTANTS
MATERIAL MATERIAL1 MEMB 1 2
MATERIAL MATERIAL2 MEMB 3
MATERIAL MATERIAL3 MEMB 4 TO 13
MEMBER RELEASE
3 TO 13 START MZ
SUPPORTS
1 9 10 FIXED
LOAD 1
JOINT LOAD
2 FY -44482.2
PERFORM ANALYSIS
UNIT METER KN
PRINT MEMBER FORCES LIST 3
FINISH

STAAD Output

   MEMBER END FORCES    STRUCTURE TYPE = PLANE
   -----------------
   ALL UNITS ARE -- KN   METE     (LOCAL )
  MEMBER  LOAD  JT     AXIAL   SHEAR-Y  SHEAR-Z   TORSION     MOM-Y      MOM-Z
      3    1     3    -22.58     -0.00     0.00      0.00      0.00       0.00
                 4     22.58      0.00     0.00      0.00      0.00       0.00