V. Deflections in a 2D Truss Model

Find the joint deflection due to joint loads in a plane truss.

Reference

McCormac, J. C., Structural Analysis, Intext Educational Publishers, 3^rd edition, 1975, page 271, example 18 - 2.

Problem

Determine the vertical deflection at point 5 of plane truss structure shown in the figure.

Plane truss model

P = 20 kip

L = 15 ft

Truss width = 4 spaces at 15 ft = 60 ft

Truss height = 15 ft

A_{X 1-4} = 1 in², A_{X 5-6} = 2 in², A_{X 7-8} =1.5 in²,

A_{X 9-11} _B = 3 in² ^P, A_{X 12-13} = 4 in²

E = 30E3 ksi

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
δ₅ (in.)	2.63	2.63033	negligible

STAAD Input

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

STAAD TRUSS : DEFLECTION IN TRUSS
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
*  REFERENCE 'STRUCTURAL ANALYSIS' BY JACK McCORMACK, PAGE
*  271 EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 15 0 0; 3 30 0 0; 4 45 0 0; 5 60 0 0; 6 15 7.5 0; 7 30 15 0;
8 45 7.5 0;
MEMBER INCIDENCES
1 2 6; 2 3 4; 3 4 8; 4 4 5; 5 1 2; 6 2 3; 7 3 6; 8 3 8; 9 3 7; 10 1 6;
11 5 8; 12 6 7; 13 7 8;
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 TO 4 PRIS AX 1
5 6 PRIS AX 2
7 8 PRIS AX 1.5
9 TO 11 PRIS AX 3
12 13 PRIS AX 4
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 30000
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 PINNED
3 FIXED BUT FX MZ
LOAD 1 VERTICAL LOAD
JOINT LOAD
2 4 5 FY -20
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS
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   -0.12000   0.18000   0.00000   0.00000   0.00000   0.00000
      3    1   -0.24000   0.00000   0.00000   0.00000   0.00000   0.00000
      4    1   -0.48000  -0.89516   0.00000   0.00000   0.00000   0.00000
      5    1   -0.72000  -2.63033   0.00000   0.00000   0.00000   0.00000
      6    1   -0.00820   0.24000   0.00000   0.00000   0.00000   0.00000
      7    1    0.29758  -0.12000   0.00000   0.00000   0.00000   0.00000
      8    1    0.06578  -0.83516   0.00000   0.00000   0.00000   0.00000