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., 3^rd 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.

Locomotive axle model

Comparison

Table 1. Comparison of results
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