V. Bent Beam Thermal Loading

To find member forces and moments due to a temperature load on a Zee shaped plane bent.

Reference

Seeley, F.B., and Smith, J.O., Advanced Mechanics of Materials, 2nd Edition, John Wiley and Sons, 1955, Pages 494-497.

Problem

Calculate reactions and maximum moments in the structure due to a temperature increase of 430 ºF. Do not consider shear deformation.

E = 26,400 ksi

α = 7.26744 x 10^-6 in/in/ºF

OD = 12 in

ID = 10.255 in

Frame subject to temperature change

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
Horizontal reaction (lbs)	8,980	8,949.43	negligible
Vertical reaction (lbs)	7,756	7,729.42	negligible
Moment at supports (in·lb)	783,750	781,127.75	negligible
Moment at node 2 (in·lb)	1,077,656	1,073,932.12	negligible

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Bent Beam Thermal Loading.STD is typically installed with the program.

STAAD PLANE :A FIXED-FIXED ZEE SHAPED PLANE BENT BEAM
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: Seeley, F.B., and Smith, J.O., Advanced Mechanics of Materials, 
*            2nd Edition, John Wiley and Sons, 1955, Pages 494-497
*
SET SHEAR
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 240 0 0; 3 240 240 0; 4 480 240 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
MEMBER PROPERTY AMERICAN
1 TO 3 TABLE ST PIPE OD 12 ID 10.255
PRINT MEMBER PROPERTIES
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.64e+07
POISSON 0.3
ALPHA 7.26744e-06
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
* DONOT PROVIDE POISSON'S RATIO, NO SHEAR DEFORMATION CONSIDERED
SUPPORTS
1 4 FIXED
LOAD 1
TEMPERATURE LOAD
1 TO 3 TEMP 430
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES LIST 1
FINISH

STAAD Output

   SUPPORT REACTIONS -UNIT POUN INCH    STRUCTURE TYPE = PLANE
   -----------------
 JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
      1    1   8949.43   7729.42      0.00      0.00      0.00 781127.94
      4    1  -8949.43  -7729.42      0.00      0.00      0.00 781127.94
   ************** END OF LATEST ANALYSIS RESULT **************
    34. PRINT MEMBER FORCES LIST 1
  MEMBER   FORCES   LIST     1        
      :A FIXED-FIXED ZEE SHAPED PLANE BENT BEAM                -- PAGE NO.    5
   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    1     1   8949.43   7729.42     0.00      0.00      0.00  781127.94
                 2  -8949.43  -7729.42     0.00      0.00      0.00 1073932.12