V. IS 1893 2016 Torsion Irregularity

Verify part 1 of the torsional irregularity check per the IS 1893 2016 Part 1 specifications.

Details

A three story building is modelled with floor diaphragms defined at each floor level.

A 1 kip (4.4482 kN) load is applied to each diaphragm in both the global X and Z directions. In STAAD.Pro, this is modelled using an analytical node in each diaphragm. This is used to obtain the displacements in the nodes of the diaphragm.

Structure diagram

Nodes 17, 18, and 19 are the master nodes in each diaphragm.

Validation

As per Cl. 7.8.2, the design eccentricity, e_di, is computed as the a constant times the dynamic eccentricity plus or minus the accidental eccentricity:

e_{d i} = | \begin{array}{l} 1.5 e_{s i} + 0.05 b_{i} & (Case
		  1) \\ 1.0 e_{s i} - 0.05 b_{i} & (Case
		  2) \end{array}

where

e_si	=	the static eccentricity at floor i, which is the distance between the center of rigidity and the center of mass at that level
b_i	=	the floor plan dimension at floor i, perpendicular to the direction of force = 5 m for this example in both direction at all floors

Also, to perform a torsion irregularity check unit load should be applied at edi considering design eccentricity. Hence, in addition to unit load F = 1 kip (4.45 kN), a moment M = F × (lever arm) is also applied at the center of mass.

The displacements induced because of the applied loads on the master nodes for the nodes situated on the extremities of each diaphragm is taken from the STAAD.Pro output for each lateral direction.

X direction

By inspection, the center of rigidity (as reported by STAAD.Pro) and the center of mass are located at the same point at each floor. Therefore, e_si = 0.

Table 1. X Direction: Case 1 (`ACC` = +0.05, `DEC` = 1.5)
Diaphragm	Master Node	Accidental Eccentricity (0.05b_i)	Design Eccentricity (e _di = 1.5e_si+0.05b_i)	F_x Applied at C.M.	M_y Applied at CM (F_x×(e_di-e_si)
1	17	0.25	0.25	4.45	1.11
2	18	0.25	0.25	4.45	1.11
3	19	0.25	0.25	4.45	1.11

Table 2. X Direction: Case 2 (`ACC` = -0.05, `DEC` = 1.0)
Diaphragm	Master Node	Accidental Eccentricity (-0.05b_i)	Design Eccentricity (e _di = 1.0e_si-0.05b_i)	F_x Applied at C.M.	M_y Applied at CM (F_x×(e_di-e_si)
1	17	-0.25	-0.25	4.45	-1.11
2	18	-0.25	-0.25	4.45	-1.11
3	19	-0.25	-0.25	4.45	-1.11

The displacements induced because of the applied loads centers of mass for the nodes situated on the extremities of each diaphragm are taken from the STAAD.Pro output for each lateral direction.

Table 3. X Direction: Case 1 Checks
Diaphragm	Master Node	Primary LC Number	Diaphragm Extremities		Displacements (mm)		Δmax/Δmin	Status
Diaphragm	Master Node	Primary LC Number	Extreme Node 1	Extreme Node 2	Δx Extreme Node 1	Δx Extreme Node 2	Δmax/Δmin	Status
1	17	1	2 or 3	6 or 7	0.466	0.498	1.07	OK
2	18	2	9 or 10	11 or 12	2.399	2.487	1.04	OK
3	19	3	13 or 14	15 or 16	6.016	6.164	1.02	OK

Table 4. X Direction: Case 2 Checks
Diaphragm	Master Node	Primary LC Number	Diaphragm Extremities		Displacements (mm)		Δmax/Δmin	Status
Diaphragm	Master Node	Primary LC Number	Extreme Node 1	Extreme Node 2	Δx Extreme Node 1	Δx Extreme Node 2	Δmax/Δmin	Status
1	17	4	2 or 3	6 or 7	0.498	0.466	1.07	OK
2	18	5	9 or 10	11 or 12	2.487	2.399	1.04	OK
3	19	6	13 or 14	15 or 16	6.164	6.016	1.02	OK

Z direction checks

Table 5. Z Direction: Case 1 (`ACC` = +0.05, `DEC` = 1.5)
Diaphragm	Master Node	C.R. (from output file)	e_si (m) (C.M. - C.R.)	Dynamic Eccentricity (1.5e_si)	Accidental Eccentricity (0.05b_i)	Design Eccentricity (e _di = 1.5e_si+0.05b_i)	F_x Applied at C.M.	M_y Applied at CM (F_x×(e_di-e_si)
1	17	0.247	1.239 - 0.247 = 0.992	1.488	0.25	1.738	4.45	3.32
2	18	0.319	1.239 - 0.319 = 0.92	1.380	0.25	1.630	4.45	3.16
3	19	0.372	1.313 - 0.372 = 0.941	1.412	0.25	1.662	4.45	3.20

Table 6. Z Direction: Case 2 (`ACC` = -0.05, `DEC` = 1.0)
Diaphragm	Master Node	C.R. (from output file)	e_si (m) (C.M. - C.R.)	Dynamic Eccentricity (1.0e_si)	Accidental Eccentricity (-0.05b_i)	Design Eccentricity (e _di = 1.0e_si-0.05b_i)	F_x Applied at C.M.	M_y Applied at CM (F_x×(e_di-e_si)
1	17	0.247	1.239 - 0.247 = 0.992	0.992	-0.25	0.742	4.45	-1.11
2	18	0.319	1.239 - 0.319 = 0.92	0.920	-0.25	0.670	4.45	-1.11
3	19	0.372	1.313 - 0.372 = 0.941	0.941	-0.25	0.691	4.45	-1.11

Table 7. Z Direction: Case 1 Checks
Diaphragm	Master Node	Primary LC Number	Diaphragm Extremities		Displacements (mm)		Δmax/Δmin	Status
Diaphragm	Master Node	Primary LC Number	Extreme Node 1	Extreme Node 2	Δz Extreme Node 1	Δz Extreme Node 2	Δmax/Δmin	Status
1	17	7	2 or 6	3 or 7	0.238	0.27	1.13	OK
2	18	8	9 or 11	10 or 12	0.935	1.009	1.08	OK
3	19	9	13 or 15	14 or 16	1.916	2.046	1.07	OK

Table 8. Z Direction: Case 2 Checks
Diaphragm	Master Node	Primary LC Number	Diaphragm Extremities		Displacements (mm)		Δmax/Δmin	Status
Diaphragm	Master Node	Primary LC Number	Extreme Node 1	Extreme Node 2	Δz Extreme Node 1	Δz Extreme Node 2	Δmax/Δmin	Status
1	17	10	2 or 6	3 or 7	0.232	0.392	1.69	FAIL
2	18	11	9 or 11	10 or 12	0.913	1.325	1.45	OK
3	19	12	13 or 15	14 or 16	1.873	2.578	1.38	OK

Results

Table 9. Comparison of results (max/min displacement ratios and check results)
Result Type	Floor	Reference	STAAD.Pro	Difference
X Direction; Case 1	1	OK (1.07)	OK (1.0690)	negligible
	2	OK (1.04)	OK (1.0367)	negligible
	3	OK (1.02)	OK (1.0246)	negligible
X Direction; Case 2	1	OK (1.07)	OK (1.0690)	negligible
	2	OK (1.04)	OK (1.0367)	negligible
	3	OK (1.02)	OK (1.0246)	negligible
Z Direction; Case 1	1	OK (1.13)	OK (1.1327)	negligible
	2	OK (1.08)	OK (1.0791)	negligible
	3	OK (1.07)	OK (1.0680)	negligible
Z Direction; Case 2	1	Fail (1.69)	Fail (1.6887)	negligible
	2	OK (1.45)	OK (1.4515)	negligible
	3	OK (1.38)	OK (1.3764)	negligible

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\06 Loading\IS 1893\IS 1893 2016 Torsion Irregularity.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0; 3 5 5 0; 4 5 0 0; 5 0 0 5; 6 0 5 5; 7 5 5 5; 8 5 0 5;
9 0 10 0; 10 5 10 0; 11 0 10 5; 12 5 10 5; 13 0 15 0; 14 5 15 0; 15 0 15 5;
16 5 15 5; 17 1.239 5 2.5; 18 1.239 10 2.5; 19 1.313 15 2.5
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 6; 5 3 7; 6 5 6; 7 6 7; 8 7 8; 9 2 9; 10 3 10;
11 6 11; 12 7 12; 13 9 10; 14 9 11; 15 10 12; 16 11 12; 17 9 13; 18 10 14;
19 11 15; 20 12 16; 21 13 14; 22 13 15; 23 14 16; 24 15 16;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
2 3 5 7 8 10 12 13 15 16 18 20 21 23 24 PRIS YD 0.35 ZD 0.25
MEMBER PROPERTY AMERICAN
1 4 6 9 11 14 17 19 22 PRIS YD 0.5 ZD 0.65
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 4 5 8 FIXED
*MEMBER CRACKED CODE IS1893 2016
*1 3 6 8 TO 12 17 TO 20 REDUCTION RIY 0.7 RIZ 0.7
*2 4 5 7 13 TO 16 21 TO 24 REDUCTION RIY 0.35 RIZ 0.35
MEMBER CRACKED 
1 3 6 8 TO 12 17 TO 20 REDUCTION RIY 0.7 RIZ 0.7
2 4 5 7 13 TO 16 21 TO 24 REDUCTION RIY 0.35 RIZ 0.35
DEFINE REFERENCE LOADS
LOAD R1 LOADTYPE Mass  TITLE REF LOAD CASE 1
SELFWEIGHT X 1 
SELFWEIGHT Y 1 
SELFWEIGHT Z 1 
END DEFINE REFERENCE LOADS
FLOOR DIAPHRAGM
DIA 1 TYPE RIG HEI 5
DIA 2 TYPE RIG HEI 10
DIA 3 TYPE RIG HEI 15
CHECK IRREGULARITIES CODE IS1893 2016
DEFINE IS1893 2016 LOAD
ZONE 0.36 RF 5 I 1.2 SS 1 ST 5 DM 0.05
LOAD 1 LOADTYPE None  TITLE Diaphragm 1 Case 1 X Dir
JOINT LOAD
17 FX 4.4482 MY 1.11205
LOAD 2 LOADTYPE None  TITLE Diaphragm 2 Case 1 X Dir
JOINT LOAD
18 FX 4.4482 MY 1.11205
LOAD 3 LOADTYPE None  TITLE Diaphragm 3 Case 1 X Dir
JOINT LOAD
19 FX 4.4482 MY 1.11205
LOAD 4 LOADTYPE None  TITLE Diaphragm 1 Case 2 X Dir
JOINT LOAD
17 FX 4.4482 MY -1.11205
LOAD 5 LOADTYPE None  TITLE Diaphragm 2 Case 2 X Dir
JOINT LOAD
18 FX 4.4482 MY -1.11205
LOAD 6 LOADTYPE None  TITLE Diaphragm 3 Case 2 X Dir
JOINT LOAD
19 FX 4.4482 MY -1.11205
LOAD 7 LOADTYPE None  TITLE Diaphragm 1 Case 1 Z Dir
JOINT LOAD
17 FZ 4.4482 MY 3.3183572
LOAD 8 LOADTYPE None  TITLE Diaphragm 2 Case 1 Z Dir
JOINT LOAD
18 FZ 4.4482 MY 3.158222
LOAD 9 LOADTYPE None  TITLE Diaphragm 3 Case 1 Z Dir
JOINT LOAD
19 FZ 4.4482 MY 3.2049281
LOAD 10 LOADTYPE None  TITLE Diaphragm 1 Case 2 Z Dir
JOINT LOAD
17 FZ 4.4482 MY -1.11205
LOAD 11 LOADTYPE None  TITLE Diaphragm 2 Case 2 Z Dir
JOINT LOAD
18 FZ 4.4482 MY -1.11205
LOAD 12 LOADTYPE None  TITLE Diaphragm 3 Case 2 Z Dir
JOINT LOAD
19 FZ 4.4482 MY -1.11205
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PRINT DIA CR
FINISH

STAAD.Pro Output

 Using edi = 1.5esi + 0.05bi
 ---------------------------
 Dia.   Extreme Points of Dia in X        Extreme Points of Dia in Z
       Node    Disp.    Node    Disp.    Node    Disp.     Node    Disp.
               (mm)             (mm)             (mm)              (mm)
 ------------------------------------------------------------------------
    1      7   0.49839      2   0.46623      3   0.26987      2   0.23826
    2     12   2.48706      9   2.39897     10   1.00866      9   0.93470
    3     16   6.16371     13   6.01568     14   2.04634     13   1.91601
 Using edi = esi - 0.05bi
 ------------------------
 Dia.   Extreme Points of Dia in X        Extreme Points of Dia in Z
       Node    Disp.    Node    Disp.    Node    Disp.     Node    Disp.
               (mm)             (mm)             (mm)              (mm)
 ------------------------------------------------------------------------
    1      7   0.46623      2   0.49839      3   0.39164      2   0.23192
    2     12   2.39897      9   2.48706     10   1.32531      9   0.91311
    3     16   6.01568     13   6.16371     14   2.57825     13   1.87322
             Using edi = 1.5esi + 0.05bi
             ---------------------------
             Diaphragm  D X-max/min  D Z-max/min Status
             --------------------------------------
                   1     1.0690   1.1327        OK    
                   2     1.0367   1.0791        OK    
                   3     1.0246   1.0680        OK    
             Using edi = esi - 0.05bi
             ------------------------
             Diaphragm  D X-max/min  D Z-max/min Status
             --------------------------------------
                   1     1.0690   1.6887       FAIL   
                   2     1.0367   1.4514        OK    
                   3     1.0246   1.3764        OK    
 --GEOMETRY IRREGULARITY CHECKS 
 Re-Entrant Corner Check.
 (Ref: Table 5 (ii)   - Ratio Limit: 0.15 )
 ------------------------------------------
   ***NOTE: No Irregular Re-Entrant Nodes found in the diaphragm.
   ***NOTE: No Irregular Re-Entrant Nodes found in the diaphragm.
   ***NOTE: No Irregular Re-Entrant Nodes found in the diaphragm.
 --MASS IRREGULARITY CHECKS 
 Mass Irregularity Check
 Ref: Table 6 (ii)   - Ratio Limit: 1.50
 ---------------------------------------