V. Stresses in a Circular Beam
Find deflections and stress at the center of a locomotive axle.
Reference
Timoshenko, S., Strength of Materials, Part- 1, D. Van Nostrand Co., 3rd edition, 1956.
p. 94, problems 1, 2.
Problem
Determine the maximum stress in a locomotive axle (as shown in the figure) as well as the deflection at the middle of the axle.
Diameter = 10 in. |
P = 26,000 lbf |
E = 30×(10)6 psi |
L1 = 13.5 in., L2 = 59 in. |
Comparison
Result Type | Theory | STAAD.Pro | Difference |
---|---|---|---|
σ (psi), Node 3 | 3,575.* | 3,575.3 | negligible |
δ (in.), Node 3 | 0.01040 | 0.01037 | negligible |
* The value is recalculated.
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Stresses in a Circular Beam.STD is typically installed with the program.
STAAD PLANE : STRESSES IN A CIRCULAR BEAM
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE 'STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO
* PAGE 97 PROBLEM NO. 1 AND 2. ANSWERS ARE 3580 FOR MAX. STRESS
* AND 0.104 INCH FOR MAX. DEFLECTION.
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 13.5 0 0; 3 43 0 0; 4 72.5 0 0; 5 86 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5;
MEMBER PROPERTY AMERICAN
1 TO 4 TABLE ST PIPE OD 10 ID 0
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
2 4 PINNED
LOAD 1
JOINT LOAD
1 5 FY -26000
PERFORM ANALYSIS
PRINT MEMBER STRESSES
PRINT JOINT DISPLACEMENTS
FINISH
STAAD Output
MEMBER STRESSES --------------- ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 0.0 0.0 0.0 0.0 441.4 0.0 1.0 0.0 C 0.0 3575.3 3575.3 441.4 0.0 2 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.0 1.0 0.0 C 0.0 3575.3 3575.3 0.0 0.0 3 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.0 1.0 0.0 C 0.0 3575.3 3575.3 0.0 0.0 4 1 .0 0.0 0.0 3575.3 3575.3 441.4 0.0 1.0 0.0 C 0.0 0.0 0.0 441.4 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 31. PRINT JOINT DISPLACEMENTS JOINT DISPLACE : STRESSES IN A CIRCULAR BEAM -- PAGE NO. 4 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 -0.01138 0.00000 0.00000 0.00000 0.00086 2 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00070 3 1 0.00000 0.01037 0.00000 0.00000 0.00000 0.00000 4 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00070 5 1 0.00000 -0.01138 0.00000 0.00000 0.00000 -0.00086