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

## Comparison

Table 1. Comparison of results
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

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
1 TO 3 TEMP 430
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES LIST 1
FINISH
``````

```   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
```