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".
Symmetric portal frame
Calculations
From the reference:
Comparison
Table 1. Comparison of results
Result Type |
|
Theory |
STAAD.Pro
|
Difference |
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 |
STAAD Output
: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
28. LOAD 1 MID SPAN
29. JOINT LOAD
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 **************