# V. 2D Portal Reactions 1

To find section properties, member forces and support reactions for a 1x1 bay plane frame with members of rectangular section.

## Reference

Timoshenko, S., Strength of Materials, Part I, Elementary Theory and Problems, 2nd Edition, Van Nostrand Company, 1940, Pages 188-191,

## Problem

The frame supports a concentrated load at middle of the horizontal member. Verify the internally calculated section properties, support reactions and bending moments at the ends of the horizontal member. Columns are square 2" x 2"; beams are rectangular with b = 2" and h = 4".

 P = 1,000 lb

 h = 100 in.

 l = 120 in.

 E = 30×(10)6 psi

## Calculations

From the reference:

$M = P l 8 1 1 + 2 3 h l I b I c = 1 , 000 ( 120 ) 8 1 1 + 2 3 100 120 10.67 1.333 = 2 , 754 in-lb$

## Comparison

Table 1. Comparison of results
Column Cross Section Ax (in.2) 4.0 4.0 none
Ix (in.4) 2.25 2.25 none
Iy (in.4) 1.333 1.33 none
Iz (in.4) 1.333 1.33 none
Beam Cross Section Ax (in.2) 8.0 8.0 none
Ix (in.4) 7.324 7.32 none
Iy (in.4) 2.667 2.67 none
Iz (in.4) 10.667 10.67 none
Ry (lb)   500 500 none
Rx (lb)   27.55 27.54 none
M(in·lb)   2,754.97 2,754.35 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\03 Frames\2D Portal Reactions 1.STD is typically installed with the program.

STAAD PLANE :A 1X1 BAY PLANE FRAME OF RECTANGULAR SECTION
START JOB INFORMATION
ENGINEER DATE 17-Sep-18
END JOB INFORMATION
*
* REFERENCE: TIMOSHENKO, S., STRENGTH OF MATERIALS, PART 1,
*           2ND EDITION, D. VAN NOSTRAND CO., 1940,
*           PAGES 188 THRU 191.
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 0 100 0; 3 60 100 0; 4 120 100 0; 5 120 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5;
MEMBER PROPERTY AMERICAN
1 4 PRIS YD 2 ZD 2
2 3 PRIS YD 4 ZD 2
PRINT MEMBER PROPERTIES
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 5 PINNED
3 FY 1000
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES LIST 2 3
FINISH

:A 1X1 BAY PLANE FRAME OF RECTANGULAR SECTION            -- PAGE NO.    2
MEMBER PROPERTIES. UNIT - INCH
-----------------
MEMB   PROFILE              AX/          IZ/          IY/        IX/
AY           AZ           SZ         SY
1  PRISMATIC              4.00         1.33         1.33       2.25
3.40         3.40         1.33       1.33
2  PRISMATIC              8.00        10.67         2.67       7.32
6.80         6.80         5.33       2.67
3  PRISMATIC              8.00        10.67         2.67       7.32
6.80         6.80         5.33       2.67
4  PRISMATIC              4.00         1.33         1.33       2.25
3.40         3.40         1.33       1.33
************ END OF DATA FROM INTERNAL STORAGE ************
19. DEFINE MATERIAL START
20. ISOTROPIC MATERIAL1
21. E 3E+07
22. POISSON 0.290909
23. END DEFINE MATERIAL
24. CONSTANTS
25. MATERIAL MATERIAL1 ALL
26. SUPPORTS
27. 1 5 PINNED
30. 3 FY 1000
31. PERFORM ANALYSIS
P R O B L E M   S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS          5  NUMBER OF MEMBERS       4
NUMBER OF PLATES          0  NUMBER OF SOLIDS        0
NUMBER OF SURFACES        0  NUMBER OF SUPPORTS      2
Using 64-bit analysis engine.
SOLVER USED IS THE IN-CORE ADVANCED MATH SOLVER
TOTAL      PRIMARY LOAD CASES =     1, TOTAL DEGREES OF FREEDOM =      11
:A 1X1 BAY PLANE FRAME OF RECTANGULAR SECTION            -- PAGE NO.    3
TOTAL LOAD COMBINATION  CASES =     0  SO FAR.
32. PRINT SUPPORT REACTION
SUPPORT  REACTION
:A 1X1 BAY PLANE FRAME OF RECTANGULAR SECTION            -- PAGE NO.    4
SUPPORT REACTIONS -UNIT POUN INCH    STRUCTURE TYPE = PLANE
-----------------
JOINT  LOAD   FORCE-X   FORCE-Y   FORCE-Z     MOM-X     MOM-Y     MOM Z
1    1    -27.54   -500.00      0.00      0.00      0.00      0.00
5    1     27.54   -500.00      0.00      0.00      0.00      0.00
************** END OF LATEST ANALYSIS RESULT **************
33. PRINT MEMBER FORCES LIST 2 3
MEMBER   FORCES   LIST     2
:A 1X1 BAY PLANE FRAME OF RECTANGULAR SECTION            -- 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
2    1     2    -27.54   -500.00     0.00      0.00      0.00   -2754.35
3     27.54    500.00     0.00      0.00      0.00  -27245.65
3    1     3    -27.54    500.00     0.00      0.00      0.00   27245.65
4     27.54   -500.00     0.00      0.00      0.00    2754.35
************** END OF LATEST ANALYSIS RESULT **************