V. Forces on a Propped Cantilever 1
To find the deflection and member forces due to an applied load on a propped cantilever beam with a compression only support.
Reference
Hand calculation using the following reference:
Manual of Steel Construction, Load and Resistance Factor Design, Second Edition, American Institute of Steel Construction, 1998, pp. 4-194, 4-197.
Problem
- P = +0.5 lbs (up), and
- P = -0.5 lbs (down)
-
E = 10(10)6
-
width = 0.6 in
-
depth = 0.3 in
-
L = 4 ft
Propped cantilever member with a compression only support
Load Case 1
General solution equations found on p.2-121 of the reference. In this case, the "propped" end carries no load as the support cannot carry tension. Thus, the member acts like a pure cantilever.
At the rigid support, M = 14.4 in·lb.
By inspection, fixed end shear is equal to load value = 0.50 lb.
Comparison
Load Case | Result Type | Theory | STAAD.Pro | Difference |
---|---|---|---|---|
LC 1 | Moment at fixed end (in·lb) | -14.4 | -14.4 | none |
Shear at fixed end (lb) | 0.50 | 0.50 | none | |
Deflection at load (.in) | 0.295 | 0.295 | none | |
LC 2 | Moment at fixed end (in·lb) | 4.032 | 4.03 | none |
Shear at fixed end (lb) | 0.284 | 0.28 | 1.4% | |
Deflection at load (.in) | -0.040 | -.0401 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Forces on a Propped Cantilever 1.STDis typically installed with the program.
STAAD PLANE :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*********************************************
* The end support is to be defined as a *
* compression only support. A dummy member,*
* #7, is set as compression only to model *
* this. *
*********************************************
SET NL 2
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 9.6 0 0; 3 19.2 0 0; 4 28.8 0 0; 5 38.4 0 0; 6 48 0 0;
7 48 -4 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7;
MEMBER PROPERTY AMERICAN
1 TO 5 PRIS YD 0.3 ZD 0.6
6 PRIS YD 40
MEMBER COMPRESSION
6
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1e+07
POISSON 0.33
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
7 FIXED
*7 PINNED
LOAD 1 UPWARD
JOINT LOAD
4 FY 0.5
PERFORM ANALYSIS
PRINT MEMBER FORCES LIST 1 TO 5
PRINT JOINT DISPLACEMENTS LIST 1 TO 6
PRINT SUPPORT REACTION
CHANGE
LOAD 2 DOWNWARD
JOINT LOAD
4 FY -0.5
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES LIST 1 TO 5
PRINT JOINT DISPLACEMENTS LIST 1 TO 6
FINISH
STAAD Output
ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 0.00 -0.50 0.00 0.00 0.00 -14.40 2 0.00 0.50 0.00 0.00 0.00 9.60 2 1 2 0.00 -0.50 0.00 0.00 0.00 -9.60 3 0.00 0.50 0.00 0.00 0.00 4.80 3 1 3 0.00 -0.50 0.00 0.00 0.00 -4.80 4 0.00 0.50 0.00 0.00 0.00 0.00 4 1 4 0.00 -0.00 0.00 0.00 0.00 -0.00 5 0.00 0.00 0.00 0.00 0.00 0.00 5 1 5 0.00 0.00 0.00 0.00 0.00 0.00 6 0.00 -0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 39. PRINT JOINT DISPLACEMENTS LIST 1 TO 6 JOINT DISPLACE LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- 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 0.00000 0.00000 0.00000 0.00000 0.00000 2 1 0.00000 0.04370 0.00000 0.00000 0.00000 0.00853 3 1 0.00000 0.15293 0.00000 0.00000 0.00000 0.01365 4 1 0.00000 0.29494 0.00000 0.00000 0.00000 0.01536 5 1 0.00000 0.44239 0.00000 0.00000 0.00000 0.01536 6 1 0.00000 0.58985 0.00000 0.00000 0.00000 0.01536 ************** END OF LATEST ANALYSIS RESULT ************** 40. PRINT SUPPORT REACTION SUPPORT REACTION :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 5 SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 -0.50 0.00 0.00 0.00 -14.40 7 1 0.00 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 41. CHANGE 42. LOAD 2 DOWNWARD 43. JOINT LOAD 44. 4 FY -0.5 45. PERFORM ANALYSIS **NOTE-Tension/Compression converged after 1 iterations, Case= 2 46. PRINT SUPPORT REACTION SUPPORT REACTION :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 6 SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 2 0.00 0.28 0.00 0.00 0.00 4.03 7 2 0.00 0.22 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 47. PRINT MEMBER FORCES LIST 1 TO 5 MEMBER FORCES LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 7 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 2 1 0.00 0.28 0.00 0.00 0.00 4.03 2 0.00 -0.28 0.00 0.00 0.00 -1.31 2 2 2 0.00 0.28 0.00 0.00 0.00 1.31 3 0.00 -0.28 0.00 0.00 0.00 1.42 3 2 3 0.00 0.28 0.00 0.00 0.00 -1.42 4 0.00 -0.28 0.00 0.00 0.00 4.15 4 2 4 0.00 -0.22 0.00 0.00 0.00 -4.15 5 0.00 0.22 0.00 0.00 0.00 2.07 5 2 5 0.00 -0.22 0.00 0.00 0.00 -2.07 6 0.00 0.22 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 48. PRINT JOINT DISPLACEMENTS LIST 1 TO 6 JOINT DISPLACE LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 8 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 2 0.00000 -0.01066 0.00000 0.00000 0.00000 -0.00190 3 2 0.00000 -0.03024 0.00000 0.00000 0.00000 -0.00186 4 2 0.00000 -0.04012 0.00000 0.00000 0.00000 0.00012 5 2 0.00000 -0.02714 0.00000 0.00000 0.00000 0.00233 6 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00307