V. Beam on Elastic Foundation
To find deflection and stress at the center due to a uniform, static load on a simply supported beam on elastic foundation.
Reference
Hand calculation using the following reference:
Peterson, F.E., Elastic Analysis for Structural Engineering (EASE2), Example Problem Manual, Engineering Analysis Corporation, Berkeley, CA, 1981.
Problem
Find the vertical deflection and bending stress at the center of the beam.
- beam width, b = 1.0 in.
- beam depth, h = 7.114 in.
| E = 30×(10)6 psi |
| L = 240 in. |
| wu = 43.3 lb/in. |
One-half beam for mathematical model
Comparison
| Result | Theory | STAAD.Pro | Difference |
|---|---|---|---|
| Bending stress, σ (psi) | 18,052 | 18,053.29 | none |
| Vertical deflection (in.) | 1.0453 | 1.04549 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Beam on Elastic Foundation.STDis typically installed with the program.
STAAD SPACE :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: PETERSON, EASE2, EXAMPLE PROBLEM MANUAL
*
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 0 7.114 0; 3 0 0 6; 4 0 7.114 6; 5 0 0 12; 6 0 7.114 12;
7 0 0 18; 8 0 7.114 18; 9 0 0 24; 10 0 7.114 24; 11 0 0 30;
12 0 7.114 30; 13 0 0 36; 14 0 7.114 36; 15 0 0 42; 16 0 7.114 42;
17 0 0 48; 18 0 7.114 48; 19 0 0 54; 20 0 7.114 54; 21 0 0 60;
22 0 7.114 60; 23 0 0 66; 24 0 7.114 66; 25 0 0 72; 26 0 7.114 72;
27 0 0 78; 28 0 7.114 78; 29 0 0 84; 30 0 7.114 84; 31 0 0 90;
32 0 7.114 90; 33 0 0 96; 34 0 7.114 96; 35 0 0 102; 36 0 7.114 102;
37 0 0 108; 38 0 7.114 108; 39 0 0 114; 40 0 7.114 114; 41 0 0 120;
42 0 7.114 120;
ELEMENT INCIDENCES SHELL
1 1 2 4 3; 2 3 4 6 5; 3 5 6 8 7; 4 7 8 10 9; 5 9 10 12 11;
6 11 12 14 13; 7 13 14 16 15; 8 15 16 18 17; 9 17 18 20 19;
10 19 20 22 21; 11 21 22 24 23; 12 23 24 26 25; 13 25 26 28 27;
14 27 28 30 29; 15 29 30 32 31; 16 31 32 34 33; 17 33 34 36 35;
18 35 36 38 37; 19 37 38 40 39; 20 39 40 42 41;
ELEMENT PROPERTY
1 TO 20 THICKNESS 1
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED BUT KFY 78.125
41 FIXED BUT FZ MX
2 FIXED BUT FY
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 -
39 FIXED BUT FZ MX KFY 156.25
LOAD 1 UNIFORM LOAD OF 43.4 LBS/IN
JOINT LOAD
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 FY 260.4
2 42 FY 130.2
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 1 2
PRINT ELEMENT JOINT STRESSES LIST 1 2
FINISH
STAAD Output
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 1.04548 0.00000 0.00000 0.00000 0.00000 2 1 0.00000 1.04549 0.00000 0.00000 0.00000 0.00000 ************** END OF LATEST ANALYSIS RESULT ************** 47. PRINT ELEMENT JOINT STRESSES LIST 1 2 ELEMENT JOINT STRESSES LIST :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION -- PAGE NO. 4 ELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH ---------------- STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH ELEMENT LOAD SQX SQY MX MY MXY VONT VONB SX SY SXY TRESCAT TRESCAB 1 1 0.00 0.00 0.00 0.00 0.00 37.23 37.23 35.30 -0.00 -6.82 37.85 37.85 TOP : SMAX= 36.57 SMIN= -1.27 TMAX= 18.92 ANGLE=-10.6 BOTT: SMAX= 36.57 SMIN= -1.27 TMAX= 18.92 ANGLE=-10.6 JOINT 0.00 0.00 0.00 0.00 0.00 1 18071.09 18071.09 35.32 -18053.40 -6.80 TOP : SMAX= 35.32 SMIN= -18053.41 TMAX= 9044.36 ANGLE= -0.0 BOTT: SMAX= 35.32 SMIN= -18053.41 TMAX= 9044.36 ANGLE= -0.0 JOINT 0.00 0.00 0.00 0.00 0.00 2 18035.75 18035.75 35.32 18053.38 -6.84 TOP : SMAX= 18053.38 SMIN= 35.31 TMAX= 9009.03 ANGLE=-90.0 BOTT: SMAX= 18053.38 SMIN= 35.31 TMAX= 9009.03 ANGLE=-90.0 JOINT 0.00 0.00 0.00 0.00 0.00 4 18035.79 18035.79 35.29 18053.40 -6.84 TOP : SMAX= 18053.41 SMIN= 35.28 TMAX= 9009.06 ANGLE=-90.0 BOTT: SMAX= 18053.41 SMIN= 35.28 TMAX= 9009.06 ANGLE=-90.0 JOINT 0.00 0.00 0.00 0.00 0.00 3 18071.05 18071.05 35.29 -18053.38 -6.80 TOP : SMAX= 35.29 SMIN= -18053.38 TMAX= 9044.33 ANGLE= -0.0 BOTT: SMAX= 35.29 SMIN= -18053.38 TMAX= 9044.33 ANGLE= -0.0 2 1 0.00 0.00 0.00 0.00 0.00 50.05 50.05 35.22 -0.00 -20.53 54.10 54.10 TOP : SMAX= 44.66 SMIN= -9.44 TMAX= 27.05 ANGLE=-24.7 BOTT: SMAX= 44.66 SMIN= -9.44 TMAX= 27.05 ANGLE=-24.7 JOINT 0.00 0.00 0.00 0.00 0.00 3 18001.93 18001.93 35.27 -17984.23 -20.48 TOP : SMAX= 35.29 SMIN= -17984.25 TMAX= 9009.77 ANGLE= -0.1 BOTT: SMAX= 35.29 SMIN= -17984.25 TMAX= 9009.77 ANGLE= -0.1 JOINT 0.00 0.00 0.00 0.00 0.00 4 17966.57 17966.57 35.27 17984.15 -20.58 TOP : SMAX= 17984.17 SMIN= 35.25 TMAX= 8974.46 ANGLE=-89.9 BOTT: SMAX= 17984.17 SMIN= 35.25 TMAX= 8974.46 ANGLE=-89.9 JOINT 0.00 0.00 0.00 0.00 0.00 6 17966.71 17966.71 35.17 17984.23 -20.58 TOP : SMAX= 17984.25 SMIN= 35.15 TMAX= 8974.55 ANGLE=-89.9 BOTT: SMAX= 17984.25 SMIN= 35.15 TMAX= 8974.55 ANGLE=-89.9 JOINT 0.00 0.00 0.00 0.00 0.00 5 18001.79 18001.79 35.17 -17984.15 -20.48 TOP : SMAX= 35.20 SMIN= -17984.17 TMAX= 9009.68 ANGLE= -0.1 BOTT: SMAX= 35.20 SMIN= -17984.17 TMAX= 9009.68 ANGLE= -0.1 :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION -- PAGE NO. 5 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 1.805341E+04 -1.805341E+04 9.044362E+03 5.004878E+01 5.409544E+01 PLATE NO. 1 1 1 2 2 CASE NO. 1 1 1 1 1 ********************END OF ELEMENT FORCES********************