EX. UK-18 Stress Calculation for Plate Elements
This is an example which demonstrates the calculation of principal stresses on a finite element.
This problem is installed with the program by default to C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples\Sample Models\UK\UK-18 Stress Calculation for Plate Elements.STD when you install the program.
Where:
- L = 3 m
Fixed Supports at Joints 1, 2, 3, 4, 5, 9, 13
Load intensity = 2000 Kn/sq.m in - Y direction
UNIT METER KNS
Defines the input units for the data that follows.
JOINT COORDINATES 1 0 0 0 4 9 0 0 REPEAT 3 0 0 3
ELEMENT PROPERTIES 1 TO 9 THICK 0.25
Elements 1 to 9 have a thickness of 0.25 m.
UNIT MMS DEFINE MATERIAL START ISOTROPIC CONCRETE E 21.0 POISSON 0.17 DENSITY 2.36158e-008 ALPHA 5e-006 DAMP 0.05 G 9.25 TYPE CONCRETE STRENGTH FCU 0.0275 END DEFINE MATERIAL CONSTANTS MATERIAL CONCRETE ALL UNIT METER
LOAD 1 ELEMENT LOAD 1 TO 9 PRESSURE -2000.0
A uniform pressure of 2000 Kn/sq.m is applied on all the elements. In the absence of an explicit direction specification, the load is assumed to act along the local Z axis. The negative value indicates that the load acts opposite to the positive direction of the local Z.
PERFORM ANALYSIS
The above command instructs the program to proceed with the analysis.
PRINT SUPPORT REACTION
The above command is self-explanatory.
UNIT MMS PRINT ELEMENT STRESSES LIST 4
Element stresses at the centroid of the element are printed using the above command. The output includes membrane stresses, shear stresses, bending moments per unit width and principal stresses. The change of length unit from meter to mms indicates that the values will be printed in KN and MMs units.
FINISH
The STAAD run is terminated.
Calculation of principal stresses for element 4
Calculations are presented for the top surface only.
SX = 0.0 kN/mm2
SY = 0.0 kN/mm2
SXY = 0.0 kN/mm2
MX = 2,111.84 kN-mm/mm
MY = 10,726.22 kN-mm/m
MXY = 4,553.97 kN-mm/mm
S = 1/6t2 = 1/(6·2502) = 10,416.67mm2 (Section Modulus)
σx = SX + MX/S = 0.0 + 2,111.84/10,416.67 = 0.2027 kN/mm2
σy = SY + MY/S = 0.0 + 10,726.22/10,416.67 = 1.0297 kN/mm2
τxy = SXY + MXY/S = 0.0 + 4,553.97/10,416.67 = 0.4372 kN/mm2
SMax = (σx + σy)/2 + TMax = (0.2027 + 1.0297)/2 + 0.6018 = 1.218 kN/mm2
Say 1.22 kN/mm2
SMin = (σx + σy)/2 - TMax = (0.2027 + 1.0297)/2 - 0.6018 = 0.0144 kN/mm2
Say 0.01 kN/ mm2
Input File
STAAD SPACE SAMPLE CALCULATION FOR
* ELEMENT STRESSES
UNIT METER KNS
JOINT COORDINATES
1 0 0 0 4 9 0 0
REPEAT 3 0 0 3
ELEMENT INCIDENCE
1 1 5 6 2 TO 3
REPEAT 2 3 4
ELEMENT PROPERTIES
1 TO 9 THICK 0.25
UNIT MMS
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 21.0
POISSON 0.17
DENSITY 2.36158e-008
ALPHA 5e-006
DAMP 0.05
G 9.25
TYPE CONCRETE
STRENGTH FCU 0.0275
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
UNIT METER
SUPPORT
1 TO 4 5 9 13 FIXED
LOAD 1
ELEMENT LOAD
1 TO 9 PRESSURE -2000.0
PERFORM ANALYSIS
PRINT SUPPORT REACTION
UNIT MMS
PRINT ELEMENT STRESSES LIST 4
FINISH
STAAD Output File
PAGE NO. 1 **************************************************** * * * STAAD.Pro 2023 * * Version 23.00.02.*** * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 14, 2023 * * Time= 9:35:11 * * * * Licensed to: Bentley Systems Inc * **************************************************** 1. STAAD SPACE SAMPLE CALCULATION FOR INPUT FILE: D:\Documentation\STAAD.Pro\_Automated_Py\output\2023-12-14\SPro_Output_Input_Files\Sample .. .STD 2. * ELEMENT STRESSES 3. UNIT METER KNS 4. JOINT COORDINATES 5. 1 0 0 0 4 9 0 0 6. REPEAT 3 0 0 3 7. ELEMENT INCIDENCE 8. 1 1 5 6 2 TO 3 9. REPEAT 2 3 4 10. ELEMENT PROPERTIES 11. 1 TO 9 THICK 0.25 12. UNIT MMS 13. DEFINE MATERIAL START 14. ISOTROPIC CONCRETE 15. E 21.0 16. POISSON 0.17 17. DENSITY 2.36158E-008 18. ALPHA 5E-006 19. DAMP 0.05 20. G 9.25 21. TYPE CONCRETE 22. STRENGTH FCU 0.0275 23. END DEFINE MATERIAL 24. CONSTANTS 25. MATERIAL CONCRETE ALL 26. UNIT METER 27. SUPPORT 28. 1 TO 4 5 9 13 FIXED 29. LOAD 1 30. ELEMENT LOAD 31. 1 TO 9 PRESSURE -2000.0 32. PERFORM ANALYSIS SAMPLE CALCULATION FOR -- PAGE NO. 2 * ELEMENT STRESSES P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 16 NUMBER OF MEMBERS 0 NUMBER OF PLATES 9 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 7 Using 64-bit analysis engine. SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 54 TOTAL LOAD COMBINATION CASES = 0 SO FAR. 33. PRINT SUPPORT REACTION SUPPORT REACTION SAMPLE CALCULATION FOR -- PAGE NO. 3 * ELEMENT STRESSES SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 -1291.48 0.00 -348.06 0.00 348.06 2 1 0.00 8700.82 0.00 -26485.08 0.00 -384.11 3 1 0.00 37742.16 0.00 -87763.47 0.00 3265.14 4 1 0.00 35202.76 0.00 -66094.57 0.00 -23952.47 5 1 0.00 8700.82 0.00 384.11 0.00 26485.08 9 1 0.00 37742.16 0.00 -3265.14 0.00 87763.47 13 1 0.00 35202.76 0.00 23952.47 0.00 66094.57 ************** END OF LATEST ANALYSIS RESULT ************** 34. UNIT MMS 35. PRINT ELEMENT STRESSES LIST 4 ELEMENT STRESSES LIST 4 SAMPLE CALCULATION FOR -- PAGE NO. 4 * ELEMENT STRESSES ELEMENT STRESSES FORCE,LENGTH UNITS= KNS MMS ---------------- STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH ELEMENT LOAD SQX SQY MX MY MXY VONT VONB SX SY SXY TRESCAT TRESCAB 4 1 0.02 -0.02 2080.05 10634.76 4648.47 1.21 1.21 0.00 0.00 0.00 1.22 1.22 TOP : SMAX= 1.22 SMIN= 0.00 TMAX= 0.61 ANGLE= 66.3 BOTT: SMAX= -0.00 SMIN= -1.22 TMAX= 0.61 ANGLE=-23.7 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 1.216739E+00 -1.216739E+00 6.064286E-01 1.214803E+00 1.216739E+00 PLATE NO. 4 4 4 4 4 CASE NO. 1 1 1 1 1 ********************END OF ELEMENT FORCES******************** 36. FINISH SAMPLE CALCULATION FOR -- PAGE NO. 5 * ELEMENT STRESSES *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 14,2023 TIME= 9:35:11 **** ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://www.bentley.com/en/support/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright (c) Bentley Systems, Inc. * * http://www.bentley.com * ************************************************************