V. Deflection and Reactions in a Beam
To find the deflection and support reactions due to a trapezoidally varying load applied on part of the span of a pinned-fixed beam.
Reference
Hand calculation using the following reference:
Roark's Formulas for Stress and Strain, Warren C. Young, 6th edition, McGraw-Hill, Table 3, Case (2c), p.103
Problem
The beam in the following geometric, load, and section properties: a = 3 m, b =4.5 m, wa = 4 KN/m, wl = 7 KN/m, IZ=5,000 cm4 , E = 200 KN/mm2 .
Beam with partial, trapezoidal load
Comparison
Result Type | Theory | STAAD.Pro | Difference |
---|---|---|---|
Rotation at A, OA (radians) | 0.0020 | 0.0020 | none |
Vertical reaction at A, RA (kN) | 3.2886 | 3.2886 | none |
Vertical reaction at B, RB (kN) | 21.461 | 21.461 | none |
Moment at B, MB (kN·m) | 25.9605 | 25.9605 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Deflection and Reactions in a Beam.STD is typically installed with the program.
STAAD PLANE REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE : ROARK'S FORMULAS FOR STRESS & STRAIN
* WARREN C. YOUNG, 6TH EDITION, MCGRAW-HILL
*
* TABLE 3, CASE (2C), LOAD ON PARTIAL SPAN
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 0; 3 7.5 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3;
UNIT CM KN
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 50 IZ 5000
UNIT METER NEWTON
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2e+11
POISSON 0.3
END DEFINE MATERIAL
UNIT METER KN
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 PINNED
3 FIXED
LOAD 1
MEMBER LOAD
2 TRAP GY -4 -7
LOAD 2
MEMBER LOAD
2 UNI GY -4
2 LIN GY 0 -3
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS
UNIT METER NEWTON
PRINT SUPPORT REACTION
FINISH
STAAD Output
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020 2 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020 2 1 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006 2 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006 3 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 40. UNIT METER NEWTON 41. PRINT SUPPORT REACTION SUPPORT REACTION REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 4 SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 3288.60 0.00 0.00 0.00 0.00 2 0.00 3288.60 0.00 0.00 0.00 0.00 3 1 0.00 21461.40 0.00 0.00 0.00 -25960.51 2 0.00 21461.40 0.00 0.00 0.00 -25960.51