EX. US-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\US\US-18 Stress Calculation for Plate Elements.STD when you install the program.
Where:
- L = 1 ft
Fixed Supports at Joints 1, 2, 3, 4, 5, 9, 13
Load intensity = 1 psi (pound/in2) in negative global Y direction
UNIT KIP FEET
Defines the input units for the data that follows.
JOINT COORDINATES 1 0 0 0 4 3 0 0 REPEAT 3 0 0 1
UNIT INCH ELEMENT PROPERTIES 1 TO 9 THICK 1.0
Elements 1 to 9 have a thickness of 1.0 in.
DEFINE MATERIAL START ISOTROPIC CONCRETE E 3150 POISSON 0.17 DENSITY 8.7e-005 ALPHA 5e-006 DAMP 0.05 G 1346.15 TYPE CONCRETE STRENGTH FCU 4 END DEFINE MATERIAL CONSTANTS MATERIAL CONCRETE ALL
UNIT POUND LOAD 1 ELEMENT LOAD 1 TO 9 PRESSURE -1.0
A uniform pressure of 1 pound/sq. in 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.
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.
FINISH
The STAAD run is terminated.
Calculation of principal stresses for element 4
Calculations are presented for the top surface only.
SX = 0.0 lb/in2
SY = 0.0 lb/in2
SXY = 0.0 lb/in2
MX = 16.90 lb·in/in
MY = 85.81 lb·in/in
MXY = 36.43 lb·in/in
S = 1/6t2 = 1/6·12 = 0.1667 in3 (Section Modulus)
σx = SX + MX/S = 0.0 + 16.90/0.1667 = 101.38 psi
σy = SY + MY/S = 0.0 + 85.81/0.1667 = 514.75 psi
τxy = SXY + MXY/S = 0.0 + 36.43/0.1667 = 218.54 psi
SMax = (σx + σy)/2 + TMax = (101.38 + 514.75)/2 + 300.80 = 608.87 psi
SMin = (σx + σy)/2 - TMax = (101.38 + 514.75)/2 - 300.80 = 7.27 psi
Input File
STAAD SPACE SAMPLE CALCULATION FOR
* ELEMENT STRESSES
UNIT KIP FEET
JOINT COORDINATES
1 0 0 0 4 3 0 0
REPEAT 3 0 0 1
ELEMENT INCIDENCE
1 1 5 6 2 TO 3
REPEAT 2 3 4
UNIT INCH
ELEMENT PROPERTIES
1 TO 9 THICK 1.0
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 3150
POISSON 0.17
DENSITY 8.7e-005
ALPHA 5e-006
DAMP 0.05
G 1346.15
TYPE CONCRETE
STRENGTH FCU 4
END DEFINE MATERIAL
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORT
1 TO 4 5 9 13 FIXED
UNIT POUND
LOAD 1
ELEMENT LOAD
1 TO 9 PRESSURE -1.0
PERFORM ANALYSIS
PRINT SUPPORT REACTION
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= 9:37:25 * * * * 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 KIP FEET 4. JOINT COORDINATES 5. 1 0 0 0 4 3 0 0 6. REPEAT 3 0 0 1 7. ELEMENT INCIDENCE 8. 1 1 5 6 2 TO 3 9. REPEAT 2 3 4 10. UNIT INCH 11. ELEMENT PROPERTIES 12. 1 TO 9 THICK 1.0 13. DEFINE MATERIAL START 14. ISOTROPIC CONCRETE 15. E 3150 16. POISSON 0.17 17. DENSITY 8.7E-005 18. ALPHA 5E-006 19. DAMP 0.05 20. G 1346.15 21. TYPE CONCRETE 22. STRENGTH FCU 4 23. END DEFINE MATERIAL 24. CONSTANTS 25. MATERIAL CONCRETE ALL 26. SUPPORT 27. 1 TO 4 5 9 13 FIXED 28. UNIT POUND 29. LOAD 1 30. ELEMENT LOAD 31. 1 TO 9 PRESSURE -1.0 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 POUN INCH STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 -9.76 0.00 -12.51 0.00 12.51 2 1 0.00 70.14 0.00 -853.81 0.00 -16.81 3 1 0.00 301.41 0.00 -2821.43 0.00 95.50 4 1 0.00 281.33 0.00 -2127.22 0.00 -769.10 5 1 0.00 70.14 0.00 16.81 0.00 853.81 9 1 0.00 301.41 0.00 -95.50 0.00 2821.43 13 1 0.00 281.33 0.00 769.10 0.00 2127.22 ************** END OF LATEST ANALYSIS RESULT ************** 34. PRINT ELEMENT STRESSES LIST 4 ELEMENT STRESSES LIST 4 SAMPLE CALCULATION FOR -- PAGE NO. 4 * ELEMENT STRESSES 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 4 1 10.43 -9.94 16.90 85.81 36.43 605.39 605.39 0.00 0.00 0.00 608.99 608.99 TOP : SMAX= 608.99 SMIN= 7.25 TMAX= 300.87 ANGLE= 66.7 BOTT: SMAX= -7.25 SMIN= -608.99 TMAX= 300.87 ANGLE=-23.3 **** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES **** MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUM PRINCIPAL PRINCIPAL SHEAR VONMISES TRESCA STRESS STRESS STRESS STRESS STRESS 6.089873E+02 -6.089873E+02 3.008683E+02 6.053945E+02 6.089873E+02 PLATE NO. 4 4 4 4 4 CASE NO. 1 1 1 1 1 ********************END OF ELEMENT FORCES******************** 35. FINISH SAMPLE CALCULATION FOR -- PAGE NO. 5 * ELEMENT STRESSES *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 14,2023 TIME= 9:37:26 **** ************************************************************ * 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 * ************************************************************