V. Stress in a 2D Truss Model

Find the joint deflection and member stress due to a joint load in a plane truss.

Reference

Timoshenko, S., Strength of Materials, Part 1, D. Van Nostrand Co., Inc., 3^rd edition, 1956, page 10, problem 2.

Problem

Determine the vertical deflection at point A and the member stresses

A_X = 0.5 in²

E = 30E6 psi

P = 5000 lbf

L = 180 in.

angle = 30°

Model of two member truss

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
σ_A (psi)	10,000.	10,000.	none
δ_A (in)	0.12	0.12	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\02 Trusses\Stress in a 2D Truss Model.STD is typically installed with the program.

STAAD TRUSS : STRESS IN TRUSS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
*  THIS EXAMPLE IS TAKEN FROM 'STRENGTH OF MATERIALS'
*  (PART 1) BY TIMOSHENKO, PAGE 10 PROB 2.
*  THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH
*  AND STRESS =10000 PSI
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 155.885 -90 0; 3 311.769 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3;
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 0.5
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.15
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 3 PINNED
LOAD 1 VERT LOAD
JOINT LOAD
2 FY -5000
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS
PRINT MEMBER STRESSES
FINISH

STAAD Output

   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = TRUSS
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
      2    1    0.00000  -0.12000   0.00000   0.00000   0.00000   0.00000
      3    1    0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   ************** END OF LATEST ANALYSIS RESULT **************
    32. PRINT MEMBER STRESSES
  MEMBER   STRESSES                   
      : STRESS IN TRUSS                                        -- PAGE NO.    4
  MEMBER STRESSES
  ---------------
  ALL UNITS ARE POUN/SQ INCH
 MEMB   LD  SECT    AXIAL    BEND-Y     BEND-Z   COMBINED  SHEAR-Y  SHEAR-Z
      1    1   .0  10000.0 T      0.0       0.0   10000.0      0.0      0.0
              1.0  10000.0 T      0.0       0.0   10000.0      0.0      0.0
      2    1   .0  10000.0 T      0.0       0.0   10000.0      0.0      0.0
              1.0  10000.0 T      0.0       0.0   10000.0      0.0      0.0