V. Enclosed Zone Load - Panel with Opening
Validate the distributed member load calculations for enclosed zone panel members.
Details
A 6m × 6m floor is supported at the corners. A uniform load of 1 kN/m2 is applied
perpendicular to the floor. A square 2m × 2m opening in the center of the floor. The floor
framing is a series of 2m long W4x13 members on a 2m × 2m grid.
Determine the total member load on members along one exterior edge and one beam line along the opening.
Validation
Use yield line theory to determine the load paths of floor area subdivisions to each vertex. To match the sign output from STAAD.Pro, the global positive direction of Y is assumed for loads as well (i.e., loads acting with gravity are negative).
Members 1, 2, 3, and 5
These members receive load from only on one size of the beam (member 5 is loaded on one side due to the opening)
Tributary area for members 1, 2, 3, and 5
The green hatched area represents the tributary load for a member as determined by yield line theory.The area of each subdivision is ¼ of the 2m × 2m panel, or 1 m2.
Loaded at -1 kN/m2, the member load is thus -1 kN.
Members 4 and 6
These members receive load from both sides of the beam.
Tributary area for members 4 and 6
The tributary area of the interior members 4 and 6 –load on both sides– is 2 m2.
Thus, the total member load for these members is 2 kN.
Note: The STAAD.Pro output
provides results per member at each of 16 internal analysis points along the member.
Add the internal reported loads along the member for comparison.
| Member | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | -0.0078 | -0.0078 | -0.0078 | -0.0156 | -0.0078 | -0.0156 |
| 2 | -0.0234 | -0.0234 | -0.0234 | -0.0469 | -0.0234 | -0.0469 |
| 3 | -0.0391 | -0.0391 | -0.0391 | -0.0781 | -0.0391 | -0.0781 |
| 4 | -0.0547 | -0.0547 | -0.0547 | -0.1094 | -0.0547 | -0.1094 |
| 5 | -0.0703 | -0.0703 | -0.0703 | -0.1406 | -0.0703 | -0.1406 |
| 6 | -0.0859 | -0.0859 | -0.0859 | -0.1719 | -0.0859 | -0.1719 |
| 7 | -0.1016 | -0.1016 | -0.1016 | -0.2031 | -0.1016 | -0.2031 |
| 8 | -0.1172 | -0.1172 | -0.1172 | -0.2344 | -0.1172 | -0.2344 |
| 9 | -0.1172 | -0.1172 | -0.1172 | -0.2344 | -0.1172 | -0.2344 |
| 10 | -0.1016 | -0.1016 | -0.1016 | -0.2031 | -0.1016 | -0.2031 |
| 11 | -0.0859 | -0.0859 | -0.0859 | -0.1719 | -0.0859 | -0.1719 |
| 12 | -0.0703 | -0.0703 | -0.0703 | -0.1406 | -0.0703 | -0.1406 |
| 13 | -0.0547 | -0.0547 | -0.0547 | -0.1094 | -0.0547 | -0.1094 |
| 14 | -0.0391 | -0.0391 | -0.0391 | -0.0781 | -0.0391 | -0.0781 |
| 15 | -0.0234 | -0.0234 | -0.0234 | -0.0469 | -0.0234 | -0.0469 |
| 16 | -0.0078 | -0.0078 | -0.0078 | -0.0156 | -0.0078 | -0.0156 |
| ∑ | -1.0 | -1.0 | -1.0 | -2.0 | -1.0 | -2.0 |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\06 Loading\Enclosed Zone Load\Enclosed Zone Load - Panel with Opening.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Apr-23
END JOB INFORMATION
*Enclosed Zone example with opening
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 2 0 0; 3 4 0 0; 4 6 0 0; 5 0 0 2; 6 2 0 2; 7 4 0 2; 8 6 0 2;
9 0 0 4; 10 2 0 4; 11 4 0 4; 12 6 0 4; 13 0 0 6; 14 2 0 6; 15 4 0 6; 16 6 0 6;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 5 6; 5 6 7; 6 7 8; 7 9 10; 8 10 11; 9 11 12; 10 13 14;
11 14 15; 12 15 16; 13 1 5; 14 2 6; 15 3 7; 16 4 8; 17 5 9; 18 6 10; 19 7 11;
20 8 12; 21 9 13; 22 10 14; 23 11 15; 24 12 16;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
G 7.88462e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 24 TABLE ST W4X13
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 13 16 FIXED
DEFINE ENCLOSED ZONE
ENCLOSED ZONE Z1
BOUNDARY 1 4 16 13
OPENING 6 10 11 7
END
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
ENCLOSED ZONE LOAD
Z1 LZ 1
PERFORM ANALYSIS PRINT LOAD DATA
FINISH
STAAD.Pro Output
LOADING 1 LOADTYPE DEAD TITLE LOAD CASE 1 ----------- MEMBER LOAD - UNIT KN METE MEMBER UDL L1 L2 CON L LIN1 LIN2 1 -0.0078 GY 0.08 1 -0.0234 GY 0.19 1 -0.0391 GY 0.32 1 -0.0547 GY 0.44 1 -0.0703 GY 0.56 1 -0.0859 GY 0.69 1 -0.1016 GY 0.81 1 -0.1172 GY 0.94 1 -0.1172 GY 1.06 1 -0.1016 GY 1.19 1 -0.0859 GY 1.31 1 -0.0703 GY 1.44 1 -0.0547 GY 1.56 1 -0.0391 GY 1.68 1 -0.0234 GY 1.81 1 -0.0078 GY 1.92 10 -0.0078 GY 0.08 10 -0.0234 GY 0.19 10 -0.0391 GY 0.32 10 -0.0547 GY 0.44 10 -0.0703 GY 0.56 10 -0.0859 GY 0.69 10 -0.1016 GY 0.81 10 -0.1172 GY 0.94 10 -0.1172 GY 1.06 10 -0.1016 GY 1.19 10 -0.0859 GY 1.31 10 -0.0703 GY 1.44 10 -0.0547 GY 1.56 10 -0.0391 GY 1.68 10 -0.0234 GY 1.81 10 -0.0078 GY 1.92 11 -0.0078 GY 0.08 11 -0.0234 GY 0.19 11 -0.0391 GY 0.32 11 -0.0547 GY 0.44 11 -0.0703 GY 0.56 11 -0.0859 GY 0.69 11 -0.1016 GY 0.81 11 -0.1172 GY 0.94 11 -0.1172 GY 1.06 11 -0.1016 GY 1.19 11 -0.0859 GY 1.31 11 -0.0703 GY 1.44 11 -0.0547 GY 1.56 11 -0.0391 GY 1.68 STAAD SPACE -- PAGE NO. 4 11 -0.0234 GY 1.81 11 -0.0078 GY 1.92 12 -0.0078 GY 0.08 12 -0.0234 GY 0.19 12 -0.0391 GY 0.32 12 -0.0547 GY 0.44 12 -0.0703 GY 0.56 12 -0.0859 GY 0.69 12 -0.1016 GY 0.81 12 -0.1172 GY 0.94 12 -0.1172 GY 1.06 12 -0.1016 GY 1.19 12 -0.0859 GY 1.31 12 -0.0703 GY 1.44 12 -0.0547 GY 1.56 12 -0.0391 GY 1.68 12 -0.0234 GY 1.81 12 -0.0078 GY 1.92 13 -0.0078 GY 0.08 13 -0.0234 GY 0.19 13 -0.0391 GY 0.32 13 -0.0547 GY 0.44 13 -0.0703 GY 0.56 13 -0.0859 GY 0.69 13 -0.1016 GY 0.81 13 -0.1172 GY 0.94 13 -0.1172 GY 1.06 13 -0.1016 GY 1.19 13 -0.0859 GY 1.31 13 -0.0703 GY 1.44 13 -0.0547 GY 1.56 13 -0.0391 GY 1.68 13 -0.0234 GY 1.81 13 -0.0078 GY 1.92 14 -0.0156 GY 0.08 14 -0.0469 GY 0.19 14 -0.0781 GY 0.32 14 -0.1094 GY 0.44 14 -0.1406 GY 0.56 14 -0.1719 GY 0.69 14 -0.2031 GY 0.81 14 -0.2344 GY 0.94 14 -0.2344 GY 1.06 14 -0.2031 GY 1.19 14 -0.1719 GY 1.31 14 -0.1406 GY 1.44 14 -0.1094 GY 1.56 14 -0.0781 GY 1.68 14 -0.0469 GY 1.81 14 -0.0156 GY 1.92 15 -0.0156 GY 0.08 15 -0.0469 GY 0.19 15 -0.0781 GY 0.32 15 -0.1094 GY 0.44 15 -0.1406 GY 0.56 15 -0.1719 GY 0.69 STAAD SPACE -- PAGE NO. 5 15 -0.2031 GY 0.81 15 -0.2344 GY 0.94 15 -0.2344 GY 1.06 15 -0.2031 GY 1.19 15 -0.1719 GY 1.31 15 -0.1406 GY 1.44 15 -0.1094 GY 1.56 15 -0.0781 GY 1.68 15 -0.0469 GY 1.81 15 -0.0156 GY 1.92 16 -0.0078 GY 0.08 16 -0.0234 GY 0.19 16 -0.0391 GY 0.32 16 -0.0547 GY 0.44 16 -0.0703 GY 0.56 16 -0.0859 GY 0.69 16 -0.1016 GY 0.81 16 -0.1172 GY 0.94 16 -0.1172 GY 1.06 16 -0.1016 GY 1.19 16 -0.0859 GY 1.31 16 -0.0703 GY 1.44 16 -0.0547 GY 1.56 16 -0.0391 GY 1.68 16 -0.0234 GY 1.81 16 -0.0078 GY 1.92 17 -0.0078 GY 0.08 17 -0.0234 GY 0.19 17 -0.0391 GY 0.32 17 -0.0547 GY 0.44 17 -0.0703 GY 0.56 17 -0.0859 GY 0.69 17 -0.1016 GY 0.81 17 -0.1172 GY 0.94 17 -0.1172 GY 1.06 17 -0.1016 GY 1.19 17 -0.0859 GY 1.31 17 -0.0703 GY 1.44 17 -0.0547 GY 1.56 17 -0.0391 GY 1.68 17 -0.0234 GY 1.81 17 -0.0078 GY 1.92 18 -0.0078 GY 0.08 18 -0.0234 GY 0.19 18 -0.0391 GY 0.32 18 -0.0547 GY 0.44 18 -0.0703 GY 0.56 18 -0.0859 GY 0.69 18 -0.1016 GY 0.81 18 -0.1172 GY 0.94 18 -0.1172 GY 1.06 18 -0.1016 GY 1.19 18 -0.0859 GY 1.31 18 -0.0703 GY 1.44 18 -0.0547 GY 1.56 18 -0.0391 GY 1.68 STAAD SPACE -- PAGE NO. 6 18 -0.0234 GY 1.81 18 -0.0078 GY 1.92 19 -0.0078 GY 0.08 19 -0.0234 GY 0.19 19 -0.0391 GY 0.32 19 -0.0547 GY 0.44 19 -0.0703 GY 0.56 19 -0.0859 GY 0.69 19 -0.1016 GY 0.81 19 -0.1172 GY 0.94 19 -0.1172 GY 1.06 19 -0.1016 GY 1.19 19 -0.0859 GY 1.31 19 -0.0703 GY 1.44 19 -0.0547 GY 1.56 19 -0.0391 GY 1.68 19 -0.0234 GY 1.81 19 -0.0078 GY 1.92 2 -0.0078 GY 0.08 2 -0.0234 GY 0.19 2 -0.0391 GY 0.32 2 -0.0547 GY 0.44 2 -0.0703 GY 0.56 2 -0.0859 GY 0.69 2 -0.1016 GY 0.81 2 -0.1172 GY 0.94 2 -0.1172 GY 1.06 2 -0.1016 GY 1.19 2 -0.0859 GY 1.31 2 -0.0703 GY 1.44 2 -0.0547 GY 1.56 2 -0.0391 GY 1.68 2 -0.0234 GY 1.81 2 -0.0078 GY 1.92 20 -0.0078 GY 0.08 20 -0.0234 GY 0.19 20 -0.0391 GY 0.32 20 -0.0547 GY 0.44 20 -0.0703 GY 0.56 20 -0.0859 GY 0.69 20 -0.1016 GY 0.81 20 -0.1172 GY 0.94 20 -0.1172 GY 1.06 20 -0.1016 GY 1.19 20 -0.0859 GY 1.31 20 -0.0703 GY 1.44 20 -0.0547 GY 1.56 20 -0.0391 GY 1.68 20 -0.0234 GY 1.81 20 -0.0078 GY 1.92 21 -0.0078 GY 0.08 21 -0.0234 GY 0.19 21 -0.0391 GY 0.32 21 -0.0547 GY 0.44 21 -0.0703 GY 0.56 21 -0.0859 GY 0.69 STAAD SPACE -- PAGE NO. 7 21 -0.1016 GY 0.81 21 -0.1172 GY 0.94 21 -0.1172 GY 1.06 21 -0.1016 GY 1.19 21 -0.0859 GY 1.31 21 -0.0703 GY 1.44 21 -0.0547 GY 1.56 21 -0.0391 GY 1.68 21 -0.0234 GY 1.81 21 -0.0078 GY 1.92 22 -0.0156 GY 0.08 22 -0.0469 GY 0.19 22 -0.0781 GY 0.32 22 -0.1094 GY 0.44 22 -0.1406 GY 0.56 22 -0.1719 GY 0.69 22 -0.2031 GY 0.81 22 -0.2344 GY 0.94 22 -0.2344 GY 1.06 22 -0.2031 GY 1.19 22 -0.1719 GY 1.31 22 -0.1406 GY 1.44 22 -0.1094 GY 1.56 22 -0.0781 GY 1.68 22 -0.0469 GY 1.81 22 -0.0156 GY 1.92 23 -0.0156 GY 0.08 23 -0.0469 GY 0.19 23 -0.0781 GY 0.32 23 -0.1094 GY 0.44 23 -0.1406 GY 0.56 23 -0.1719 GY 0.69 23 -0.2031 GY 0.81 23 -0.2344 GY 0.94 23 -0.2344 GY 1.06 23 -0.2031 GY 1.19 23 -0.1719 GY 1.31 23 -0.1406 GY 1.44 23 -0.1094 GY 1.56 23 -0.0781 GY 1.68 23 -0.0469 GY 1.81 23 -0.0156 GY 1.92 24 -0.0078 GY 0.08 24 -0.0234 GY 0.19 24 -0.0391 GY 0.32 24 -0.0547 GY 0.44 24 -0.0703 GY 0.56 24 -0.0859 GY 0.69 24 -0.1016 GY 0.81 24 -0.1172 GY 0.94 24 -0.1172 GY 1.06 24 -0.1016 GY 1.19 24 -0.0859 GY 1.31 24 -0.0703 GY 1.44 24 -0.0547 GY 1.56 24 -0.0391 GY 1.68 STAAD SPACE -- PAGE NO. 8 24 -0.0234 GY 1.81 24 -0.0078 GY 1.92 3 -0.0078 GY 0.08 3 -0.0234 GY 0.19 3 -0.0391 GY 0.32 3 -0.0547 GY 0.44 3 -0.0703 GY 0.56 3 -0.0859 GY 0.69 3 -0.1016 GY 0.81 3 -0.1172 GY 0.94 3 -0.1172 GY 1.06 3 -0.1016 GY 1.19 3 -0.0859 GY 1.31 3 -0.0703 GY 1.44 3 -0.0547 GY 1.56 3 -0.0391 GY 1.68 3 -0.0234 GY 1.81 3 -0.0078 GY 1.92 4 -0.0156 GY 0.08 4 -0.0469 GY 0.19 4 -0.0781 GY 0.32 4 -0.1094 GY 0.44 4 -0.1406 GY 0.56 4 -0.1719 GY 0.69 4 -0.2031 GY 0.81 4 -0.2344 GY 0.94 4 -0.2344 GY 1.06 4 -0.2031 GY 1.19 4 -0.1719 GY 1.31 4 -0.1406 GY 1.44 4 -0.1094 GY 1.56 4 -0.0781 GY 1.68 4 -0.0469 GY 1.81 4 -0.0156 GY 1.92 5 -0.0078 GY 0.08 5 -0.0234 GY 0.19 5 -0.0391 GY 0.32 5 -0.0547 GY 0.44 5 -0.0703 GY 0.56 5 -0.0859 GY 0.69 5 -0.1016 GY 0.81 5 -0.1172 GY 0.94 5 -0.1172 GY 1.06 5 -0.1016 GY 1.19 5 -0.0859 GY 1.31 5 -0.0703 GY 1.44 5 -0.0547 GY 1.56 5 -0.0391 GY 1.68 5 -0.0234 GY 1.81 5 -0.0078 GY 1.92 6 -0.0156 GY 0.08 6 -0.0469 GY 0.19 6 -0.0781 GY 0.32 6 -0.1094 GY 0.44 6 -0.1406 GY 0.56 6 -0.1719 GY 0.69 STAAD SPACE -- PAGE NO. 9 6 -0.2031 GY 0.81 6 -0.2344 GY 0.94 6 -0.2344 GY 1.06 6 -0.2031 GY 1.19 6 -0.1719 GY 1.31 6 -0.1406 GY 1.44 6 -0.1094 GY 1.56 6 -0.0781 GY 1.68 6 -0.0469 GY 1.81 6 -0.0156 GY 1.92 7 -0.0156 GY 0.08 7 -0.0469 GY 0.19 7 -0.0781 GY 0.32 7 -0.1094 GY 0.44 7 -0.1406 GY 0.56 7 -0.1719 GY 0.69 7 -0.2031 GY 0.81 7 -0.2344 GY 0.94 7 -0.2344 GY 1.06 7 -0.2031 GY 1.19 7 -0.1719 GY 1.31 7 -0.1406 GY 1.44 7 -0.1094 GY 1.56 7 -0.0781 GY 1.68 7 -0.0469 GY 1.81 7 -0.0156 GY 1.92 8 -0.0078 GY 0.08 8 -0.0234 GY 0.19 8 -0.0391 GY 0.32 8 -0.0547 GY 0.44 8 -0.0703 GY 0.56 8 -0.0859 GY 0.69 8 -0.1016 GY 0.81 8 -0.1172 GY 0.94 8 -0.1172 GY 1.06 8 -0.1016 GY 1.19 8 -0.0859 GY 1.31 8 -0.0703 GY 1.44 8 -0.0547 GY 1.56 8 -0.0391 GY 1.68 8 -0.0234 GY 1.81 8 -0.0078 GY 1.92 9 -0.0156 GY 0.08 9 -0.0469 GY 0.19 9 -0.0781 GY 0.32 9 -0.1094 GY 0.44 9 -0.1406 GY 0.56 9 -0.1719 GY 0.69 9 -0.2031 GY 0.81 9 -0.2344 GY 0.94 9 -0.2344 GY 1.06 9 -0.2031 GY 1.19 9 -0.1719 GY 1.31 9 -0.1406 GY 1.44 9 -0.1094 GY 1.56 9 -0.0781 GY 1.68 STAAD SPACE -- PAGE NO. 10 9 -0.0469 GY 1.81 9 -0.0156 GY 1.92