Definitions Of Terms: |
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All
forces in units kN and m |
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All reinforcement details like area, spacing are mm |
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Grade Of steel for 6 mm dia. bars is Fe250. It is irrespective of the grade of steel defined by user in column design. |
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Neutral axis angle for resultant design moment is with respect to local major axis. |
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1 |
β |
= |
Stiffness proportion factor at joint ( column stiffness/sum of stiffness of all members connected at joint) |
2 |
Δu |
= |
Elastically computed first order lateral deflection.(Relative deflections) |
3 |
ε1 |
= |
Strain at level considered, Calculated ignoring the stiffening of the concrete in tension zone |
4 |
εm |
= |
Average steel strain at level considered |
5 |
acr |
= |
Distance from the point considered to the surface of the nearest longitudinal bar |
6 |
Ag |
= |
Gross area of the column cross section |
7 |
Ak |
= |
Area of confined concrete core |
8 |
Ash |
= |
Area of link cross section |
9 |
b |
= |
Effective Width of Column in
mm |
10 |
B |
= |
Width / Smaller Dimension of Column in
mm |
11 |
d |
= |
Effective Depth of Column in
mm |
12 |
D |
= |
Depth / Larger Dimension of Column OR
Diameter of Circular Column in mm |
13 |
Dk |
= |
Diameter Of core measured to the outside of
circular link |
14 |
Ec |
= |
Modulus of elasticity of concrete
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15 |
Es |
= |
Modulus of elasticity of steel
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16 |
FcPerm |
= |
Permissible Stress in Concrete required in N/ (sqmm) |
17 |
Fst |
= |
Stress in steel |
18 |
FstPerm |
= |
Permissible Stress in Steel required in N/ (sqmm) |
19 |
Fck |
= |
Characteristic compressive strength of
concrete cube in N/sqmm |
20 |
Fy |
= |
Yield Stress Of Steel in N/sqmm |
21 |
h |
= |
Longer dimension of rectangular link
measured to its outer face |
22 |
Hu |
= |
Total lateral force acting within the story(Story shear) |
23 |
Hs |
= |
Height of the story (Floor height) |
24 |
k |
= |
Reduction factor for slenderness
moments |
25 |
Max |
= |
Additional moment due to slenderness about
major axis (Along D) |
26 |
May |
= |
Additional moment due to slenderness about
minor axis (Along B) |
27 |
Mminx |
= |
Moment due to minimum eccentricity along
D |
28 |
Mminy |
= |
Moment due to minimum eccentricity along
B |
29 |
Muv |
= |
Moment capacity of web portion of wall as per clause
9.4.2 and Annes A of IS 13920 - 2016 |
30 |
Mux |
= |
Factored moment Along D (Momemt About Major Axis) |
31 |
Muy |
= |
Factored moment Along B (Momemt About Minor Axis) |
32 |
MCap |
= |
Moment capacity of section for NA angle at design Pu
|
33 |
MRes |
= |
Resultant design moment at angle to local major axis
|
34 |
Pb |
= |
Axial capacity of column along B as defined in
39.7.1.1 |
35 |
Pd |
= |
Axial capacity of column along D as defined in
39.7.1.1 |
36 |
Pu |
= |
Factored axial force |
37 |
Puz |
= |
Axial load on column as defined in 39.6
|
38 |
Pu_Total |
= |
Sum of Axial loads on all column in the story (Gravity Load) |
39 |
Q |
= |
Stability Index (factor for checking sway/ non sway condition for a given story) |
40 |
S |
= |
Link Spacing |
41 |
Shear Strength Enhancement Factor |
= |
Multiplying factor for shear strength of
concrete as per 40.2.2 |
42 |
Vur |
= |
Factored resultant shear force acting on the
column |
43 |
Vux |
= |
Factored shear force Along B |
44 |
Vuy |
= |
Factored shear force Along D |
45 |
Wcr |
= |
Surface Crack Width |
46 |
WcrPerm |
= |
Permissible Crack Width required in mm |
47 |
β |
= |
It is a Neutral Axis angle corresponding to load angle to find out MCap |
Code References: |
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IS 456 |
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ELEMENT |
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CLAUSE / table |
1 |
Max area of reinforcement |
: |
26.5.3.1-a & b |
2 |
Min area of reinforcement |
: |
26.5.3.1-a & b |
3 |
Min number of bars |
: |
26.5.3.1-c |
4 |
Minimum Eccentricity Calc |
: |
25.4 & 39.2 |
5 |
Effective Length |
: |
25.2 |
6 |
Slenderness Moments |
: |
25.3 & 39.7 |
7 |
Design for axial loads |
: |
39.3 |
8 |
Design for axial loads And uniaxial bending |
: |
39.5 |
9 |
Design for axial loads And Biaxial bending |
: |
39.6 |
10 |
Design of horizontal links |
: |
26.5.3.2 |
11 |
Design shear strength |
: |
40.2 |
12 |
Stiffness Proportion Factor, β |
: |
E-1 |
13 |
Stability(Index, Q) |
: |
E -2 |
14 |
Crack width calculation |
: |
3.8 |
15 |
Multiplying factor to Beam Stiffness for effective length calculation |
: |
SP 24 1983 APPENDIX D |
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IS 13920 - 2016 |
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ELEMENT |
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CLAUSE / table |
1 |
Spacing of special confining reinforcement |
: |
10.4 and 7.6 |
2 |
C/s area of special confining reinforcement |
: |
7.6.1 |
3 |
Applicability of boundary element |
: |
10.4.1 |
4 |
Muv-Moment Capacity of Web |
: |
Annex |
5 |
Additional Compressive Force in BE |
: |
10.4.2 |
6 |
Check for BE in tension and compression |
: |
10.4.2.1 and 10.4.3 |
7 |
Shear include due to Beam |
: |
7.5 |
8 |
Minimum Flexural Strength of Column |
: |
7.2 |
9 |
Shear Check at Column Joint |
: |
9.1 |
10 |
Length of wall to thickness ratio |
: |
10.1.3 |
11 |
Type of wall & Minimum reinforcement |
: |
10.1.4 |
12 |
Largest diameter of longitudinal steel bar |
: |
10.1.8 |
13 |
Shear reinforcement in RC wall |
: |
10.2.3 |
14 |
Special confinement reinforcement in Boundary Element |
: |
10.4.4 |
15 |
Minimum vertical reinforcement across horizontal construction joint |
: |
10.7 |
Sway Calculation (Stability Index) |
Level |
Load Name |
Storey Height (m) |
Gravity Load P (kN) |
Relative Displacements (mm) |
Storey Shear (kN) |
Stability Index |
Sway Condition |
A |
B |
C |
D |
B x C / (A x D) |
0 m to 4.2 m |
LOAD 3: LOAD CASE 3 EQ-X |
4.2 |
58589.743 |
1.11 |
1754.701 |
0.009 |
Non Sway |
4.2 m to 7.858 m |
LOAD 3: LOAD CASE 3 EQ-X |
3.658 |
51324.946 |
1.366 |
1690.676 |
0.011 |
Non Sway |
7.858 m to 12.058 m |
LOAD 3: LOAD CASE 3 EQ-X |
4.2 |
31795.793 |
1.677 |
1450.58 |
0.009 |
Non Sway |
12.058 m to 16.258 m |
LOAD 3: LOAD CASE 3 EQ-X |
4.2 |
13873.803 |
1.302 |
1015.406 |
0.004 |
Non Sway |
Level |
Load Name |
Storey Height (m) |
Gravity Load P (kN) |
Relative Displacements (mm) |
Storey Shear (kN) |
Stability Index |
Sway Condition |
A |
B |
C |
D |
B x C / (A x D) |
0 m to 4.2 m |
LOAD 4: LOAD CASE 4 EQ-Y |
4.2 |
58589.743 |
0.986 |
1754.701 |
0.008 |
Non Sway |
4.2 m to 7.858 m |
LOAD 4: LOAD CASE 4 EQ-Y |
3.658 |
51324.946 |
1.303 |
1690.676 |
0.011 |
Non Sway |
7.858 m to 12.058 m |
LOAD 4: LOAD CASE 4 EQ-Y |
4.2 |
31795.793 |
1.698 |
1450.58 |
0.009 |
Non Sway |
12.058 m to 16.258 m |
LOAD 4: LOAD CASE 4 EQ-Y |
4.2 |
13873.803 |
1.449 |
1015.406 |
0.005 |
Non Sway |
General Data |
Wall No. |
: |
C7 |
Frame Type |
= |
Ductile |
Level |
: |
4.2 m To 7.858 m |
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Design Code |
= |
IS 456 - 2000 + IS 13920 - 2016 |
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Grade Of Concrete |
= |
M25 |
N/sqmm |
Grade Of Steel |
= |
Fe415 |
N/sqmm |
Wall B |
= |
300 |
mm |
Wall D |
= |
1500 |
mm |
Clear Cover |
= |
50 |
mm |
Clear Floor Height @ B |
= |
2858 |
mm |
Clear Floor Height @ D |
= |
2858 |
mm |
No Of Floors |
= |
1 |
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No Of Walls In Group |
= |
1 |
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Wall Type |
: |
UnBraced |
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Minimum eccentricity check |
: |
One Axis at a Time |
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Code defined D/B ratio |
: |
4 |
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D/B Ratio |
: |
5 >= 4 Hence, Design as Wall |
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Flexural Design (Analysis Forces) |
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Analysis Reference No. |
= |
611 |
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Critical Analysis Load Combination |
: |
19 |
Load Combination |
= |
[9] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y) |
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Critical Location |
= |
Top Joint |
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Pu |
= |
2261.28 |
kN |
Mux |
= |
-12.08 |
kNm |
Muy |
= |
158.44 |
kNm |
Vux |
= |
82.43 |
kN |
Vuy |
= |
1.05 |
kN |
Check For Requirement Of Boundary Element |
Check For Maximum Compressive Stress |
Having maxstress in between level's (4.2 m - 16.258 m) |
At level (4.2 m) |
Load Combination |
= |
[7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X) |
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Maximum Stress |
= |
11.34 |
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0.2 x Fck |
= |
5 |
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Maximum Stress in Wall > 0.2 x Fck |
Hence Boundary Element is applicable |
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At level (7.858 m) |
Load Combination |
= |
[7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X) |
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Maximum Stress |
= |
7.55 |
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0.15 x Fck |
= |
3.75 |
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Maximum Stress in Wall > 0.15 x Fck |
Hence Boundary Element is applicable |
Effective Length Calculation |
Calculation Along Major Axis Of Column |
Joint |
Column Stiffness |
Beam Sizes |
Beam Stiffness |
Beta |
Beam 1 (Length x Width x Depth) |
Beam 2 (Length x Width x Depth) |
Beam 1 |
Beam 2 |
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N-m x 10^6 |
mm |
mm |
N-m x 10^6 |
N-m x 10^6 |
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Bottom |
2306.588 |
8000 x 450 x 800 |
8000 x 450 x 800 |
240 |
240 |
0.9 |
Top |
2306.588 |
8000 x 450 x 800 |
8000 x 450 x 800 |
240 |
240 |
0.9 |
Sway Condition (as per Stability Index) |
= |
Non Sway |
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Effective Length Factor along Major Axis |
= |
0.92 |
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Calculation Along Minor Axis Of Column |
Joint |
Column Stiffness |
Beam Sizes |
Beam Stiffness |
Beta |
Beam 1 (Length x Width x Depth) |
Beam 2 (Length x Width x Depth) |
Beam 1 |
Beam 2 |
|
N-m x 10^6 |
mm |
mm |
N-m x 10^6 |
N-m x 10^6 |
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Bottom |
92.264 |
8900 x 450 x 800 |
5710 x 450 x 800 |
215.73 |
336.252 |
0.238 |
Top |
92.264 |
8900 x 450 x 800 |
5710 x 450 x 800 |
215.73 |
336.252 |
0.238 |
Sway Condition (as per Stability Index) |
= |
Non Sway |
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Effective Length Factor along Minor axis |
= |
0.57 |
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Minimum Eccentricity Check |
Since Axial Force is compressive, Min. Eccentricity check to be performed |
Most critical case is with Min. Eccentricity check in
Y-direction |
Minimum Eccentricity Along B : |
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Minimum Eccentricity |
= |
Unsupported Length / 500 + B / 30 |
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= |
15.72 |
mm |
Mminy |
= |
Pu x Minimum Eccentricity |
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= |
45.23 |
kNm |
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Slenderness Check |
Max Slenderness Ratio(L/B) |
= |
9.53 |
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< |
60 |
(Hence Ok) |
Column Is Unbraced Along D |
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Slenderness Check Along D: |
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Effective Length Factor |
= |
0.92 |
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Slenderness Ratio |
= |
Effective Length / D |
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= |
1.75, Wall not Slender Along D |
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Column Is Unbraced Along B |
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Slenderness Check Along B: |
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Effective Length Factor |
= |
0.57 |
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Slenderness Ratio |
= |
Effective Length / B |
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= |
5.43, Wall not Slender Along B |
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Calculation of Design Moment |
Direction |
Manalysis |
Mmin (Abs) |
Mdesign |
Mslndx (Abs) |
Mdesign-final |
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A |
B |
C |
E |
F |
Major Axis - Mux |
-12.08 |
--- |
-12.08 |
0 |
-12.08 |
Minor Axis - Muy
|
158.44 |
45.23 |
158.44 |
0 |
158.44 |
Where
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A |
= |
Moments directly from analysis |
B |
= |
Moments due to minimum eccentricity |
C |
= |
Maximum of analysis moment and min.
eccentricity = Max (A,B) |
E |
= |
Moment due to slenderness effect |
F |
= |
Final design Moment =
Max(C- Top Bottom , D- Top Bottom) + E |
Final Critical Design Forces |
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Pu |
= |
2261.28 |
kN |
Mux |
= |
-12.08 |
kNm |
Muy |
= |
158.44 |
kNm |
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Minimum % steel |
User defined pt min1 |
= |
0.25 |
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Vertical reinforcement as per type of wall |
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hw |
= |
3658 |
mm |
Lw |
= |
1500 |
mm |
hw/Lw |
= |
2.44 |
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Type of wall |
= |
2.44 > 2, hence, Slender wall |
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tw |
= |
300 |
mm |
Ph |
= |
0.0025 |
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Pvweb |
= |
0.0025 |
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Ptv min2 |
= |
0.52 |
% |
Ptmin |
= |
Max ( 0.25 , 0.52 ) |
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= |
0.52 |
% |
Resultant Moment (Combined Action) |
Moment Capacity Check |
Pt Calculated |
= |
1.03 |
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Reinforcement Provided |
= |
20-T16 + 8-T10 |
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Load Angle |
= |
Tan-1(Muy/Mux) |
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= |
85.64 |
deg |
MRes |
= |
158.9 |
kNm |
MCap |
= |
286.96 |
kNm |
Capacity Ratio |
= |
MRes/ MCap |
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= |
0.55 <= 1 |
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Check For Boundary Element |
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Calculation of vertical reinforcement in BE zone |
A |
= |
450000 |
sqmm |
Z |
= |
112500000 |
mm^3 |
Maximum Compressive Force in BE |
Most Favouring Pu |
= |
[7] : 1.5 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 3: LOAD CASE 3 EQ-X) |
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P |
= |
2370.99 |
kN |
M |
= |
-257.13 |
kN-m |
P/A |
= |
5.27 |
N/sqmm |
M/Z |
= |
-2.29 |
N/sqmm |
Stress Slope,S1 |
= |
((P/A + M/Z) - (P/A - M/Z)) / Lw |
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|
= |
-3.05 |
N/sqmm |
Stress - 1 |
= |
(P/A + M/Z) - S1 X (BE length) / 2 |
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|
= |
3.55 |
N/sqmm |
Stress - 2 |
= |
(P/A - M/Z) + S1 X (BE length) / 2 |
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|
= |
6.98 |
N/sqmm |
Maximum compressive force |
= |
Maximum (Stress-1, Stress-2) x BE length |
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|
= |
785.6 |
KN |
Pt required |
= |
0 |
% |
Maximum Tensile Force in BE |
Most Un-favouring Pu |
= |
0.8 DL--1.5 EQ |
|
P |
= |
1265.43 |
kN |
M |
= |
-255.6 |
kN-m |
P/A |
= |
2.81 |
N/sqmm |
M/Z |
= |
-2.27 |
N/sqmm |
Stress Slope,S1 |
= |
((P/A + M/Z) - (P/A - M/Z)) / Lw |
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|
= |
-3.03 |
N/sqmm |
Stress - 1 |
= |
(P/A + M/Z) - S1 X (BE length) / 2 |
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|
= |
1.11 |
N/sqmm |
Stress- 2 |
= |
(P/A - M/Z) + S1 X (BE length) / 2 |
|
|
= |
4.52 |
N/sqmm |
Maximum Tensile force |
= |
Minimum (Stress-1, Stress-2) x BE length |
|
|
= |
124.66 |
KN |
Pt required |
= |
0 |
% |
Design pt in BE |
Minimum pt |
= |
0.8 |
% |
Pt required in BE |
= |
Maximum (0,0,0.8) |
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|
= |
0.8 |
% |
Check For Compression Capacity Of BE |
PT provided in BE |
= |
1.79 |
|
Ast provided in BE |
= |
2010.62 |
mm2 |
Capacity of BE in compression |
= |
0.4 x Fck x Aconcrete + 0.67 x Fy x Ast |
|
= |
1664.79 |
kN |
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|
1664.79 > 785.6 |
|
|
1664.79 Hence OK |
Check For Tension Capacity Of BE |
PT provided in BE |
= |
1.79 |
% |
Ast provided in BE |
= |
2010.62 |
mm2 |
Capacity of BE in Tension |
= |
0.87 x Fy x Ast |
|
= |
727.06 |
kN |
|
|
727.06 > 124.66 |
|
|
727.06 Hence OK |
Wall Configuration |
|
Boundary Element |
Mid |
Boundary Element |
Length (mm) |
375 |
750 |
375 |
Reinforcement |
10-T16 |
8-T10 |
10-T16 |
Ast provided |
2010.62 |
628.32 |
2010.62 |
Pt as % of entire wall |
0.45 % |
0.14 % |
0.45 % |
Pt as % of zone |
1.79 % |
0.28 % |
1.79 % |
|
Shear Design (Analysis Forces) |
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|
Design for shear along D |
|
|
|
Critical Analysis Load Combination |
: |
20 |
Critical Load Combination |
= |
[10] : 0.9 (LOAD 1: LOAD CASE 1) +1.5 (LOAD 3: LOAD CASE 3 EQ-X) |
|
Design shear force, Vuy |
= |
120.5658 |
kN |
Pu |
= |
1382.45 |
kN |
|
= |
0.3349 |
N/sqmm |
Pt (20% of vertical reinforcement) |
= |
0.207 |
% |
Design shear strength, Tc |
= |
0.3356 |
N/sqmm |
Shear Strength Enhancement Factor |
= |
1 + 3 x Pu / ( B x D x Fck) |
|
|
= |
1.3687 |
|
Shear Strength Enhancement Factor (max) |
= |
1.5 |
|
Shear Strength Enhancement Factor |
= |
1.3687 |
|
Enhanced shear strength, Tc-e |
= |
0.4593 |
N/sqmm |
Design shear check |
= |
Tvy < Tc x Enhancement factor |
|
Link for Shear Design along D are not required |
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Design for shear along B |
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|
Critical Analysis Load Combination |
: |
23 |
Critical Load Combination |
= |
[13] : 0.9 (LOAD 1: LOAD CASE 1) -1.5 (LOAD 4: LOAD CASE 4 EQ-Y) |
|
Design shear force, Vux |
= |
73.5342 |
kN |
Pu |
= |
1338.35 |
kN |
Design shear stress, Tvx |
= |
Vux / (B x 0.8 xD) |
kN |
|
= |
0.2043 |
N/sqmm |
Pt (20% of vertical reinforcement) |
= |
0.207 |
% |
Design shear strength, Tc |
= |
0.3356 |
N/sqmm |
Shear Strength Enhancement Factor |
= |
1 + 3 x Pu / (B x D x Fck) |
|
|
= |
1.3569 |
|
Shear Strength Enhancement Factor (max) |
= |
1.5 |
|
Shear Strength Enhancement Factor |
= |
1.3569 |
|
Enhanced shear strength, Tc-e |
= |
0.4553 |
N/sqmm |
Design shear check |
= |
Tvx < Tc x Enhancement factor |
|
Link for Shear Design along B are not required |
|
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Design Of Links |
Main Links |
|
|
|
Links in the zone where special confining links are not
required |
Normal Links |
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|
Horizontal reinforcement as per type of wall |
|
|
|
hw |
= |
3658 |
mm |
Lw |
= |
1500 |
mm |
hw/Lw |
= |
2.44 |
|
Type of wall |
= |
2.44 > 2, hence, Slender wall |
|
tw |
= |
300 |
mm |
Ph |
= |
0.0025 |
|
Pvweb |
= |
0.0025 |
|
Pth min |
= |
0.52 |
% |
Diameter of main horizontal steel |
= |
8 |
mm |
Thus, Spacing |
= |
125 |
mm |
Spacing of horizontal reinforcement is
minimum of following |
|
|
|
D / 5 |
= |
300 |
mm |
3 x B |
= |
900 |
mm |
Maximum |
= |
450 |
mm |
|
|
|
|
Spacing considered |
= |
125 |
mm |
|
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|
|
Special confining reinforcement as per IS
13920 - 2016 |
|
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Min. Lateral dimension of column, B |
= |
300 |
mm |
B/3 |
= |
100 |
mm |
6 X Smallest Longitudinal Bar Dia |
= |
60 |
mm |
Spacing |
= |
150 |
mm |
Hence Link spacing, Sv |
= |
100 |
mm |
Hoop dimension, h |
|
116.33 |
|
Area of special confining link, Ash |
= |
0.05 x Sv x h x (Fck/Fy) |
|
|
= |
35.04 |
sqmm |
Diameter of special confining link |
= |
8 |
mm |
|
= |
> Max. longitudinal bar dia / 4 |
|
|
= |
4 |
mm |
Area of horizontal steel provided |
= |
Area of bar provided x 1000 x 2 / spacing |
|
|
= |
1005.4 |
(sqmm)/ m height |
|
= |
0.3351 |
% |
|
= |
> min. steel required 0.25% |
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Special confining links to be provided along full height in BE. |
Note: Ductile Design Of Links Is Applicable Only For Boundary Elements |
|
Required |
Provided |
|
Normal Design |
Shear Design |
Ductile Design |
Normal Zone |
Ductile Zone |
Link Dia. |
8 |
--- |
8 |
8 |
8 |
Spacing |
125 |
--- |
100 |
125 |
100 |
Secondary Links: |
|
In Boundary element |
T8@100c/c |
In Mid-zone |
T8@125c/c |
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