| Definitions Of Terms: |
|
|
|
|
|
All
forces in units 'kN' and 'm' |
|
|
|
All reinforcement details like area, spacing in 'mm' |
|
Neutral axis angle for resultant design moment is with respect to local major axis. |
|
|
|
|
| 1 |
βdns |
= |
Ratio to account for reduction of stiffness of columns due to
sustained axial loads |
2 |
δns |
= |
Moment magnification factor for frames not braced against sidesway
|
| 3 |
Δo |
= |
First-order relative deflection between the top and bottom of the story due to Vu in 'kN' |
4 |
∑Pu |
= |
Total factored vertical load in 'kN'. (Clause 6.6.4.4) |
5 |
δu |
= |
Design displacement in 'mm' |
| 6 |
λ |
= |
Modification factor reflecting the reduced mechanical properties Of
concrete |
| 7 |
ac |
= |
Coefficient defining the relative contribution Of concrete strength To
nominal wall shear strength |
| 8 |
Ach |
= |
Cross-sectional area of a structural member measured to the outside
edges of transverse reinforcement in 'sqmm' |
| 9 |
Acv |
= |
Gross area of concrete section bounded by web thickness And length of
section in the direction Of shear force considered in 'sqmm' |
| 10 |
Aj |
= |
Effective cross-sectional area within a joint In a plane parallel To plane Of reinforcement generating shear In the joint in 'sqmm' |
| 11 |
As |
= |
Area Of non-prestressed longitudinal tension reinforcement in 'sqmm' |
| 12 |
Avmin |
= |
Minimum area Of shear reinforcement within spacing 's' in 'sqmm' |
| 13 |
B |
= |
Width of column/ wall in 'mm' |
| 14 |
beff |
= |
Effective Width of column/ wall in 'mm' |
| 15 |
bc1 and dc1 |
= |
Cross-sectional dimension of member core measured to the outside edges
of the transverse reinforcement composing area Ash in 'mm' |
16 |
c |
= |
Distance from extreme compression fiber to neutral axis in 'mm' |
| 17 |
Cc |
= |
Clear cover to longitudinal reinforcement in 'mm' |
18 |
Cm |
= |
Factor relating actual moment diagram to an equivalent uniform moment diagram |
| 19 |
D |
= |
Depth / diameter of column in 'mm' |
| 20 |
deff |
= |
Effective Depth / diameter of column in 'mm' |
| 21 |
d |
= |
Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in 'mm' |
| 22 |
d' |
= |
Distance from extreme compression fiber to centroid of longitudinal compression reinforcement,'mm' |
| 23 |
Ec |
= |
Modulus of elasticity of concrete in 'N/sqmm' |
| 24 |
EI |
= |
Flexural stiffness of compression member in 'Nsqmm' |
| 25 |
f'c |
= |
Specified compressive strength of concrete cylinder in 'N/sqmm' |
| 26 |
fy |
= |
Specified yield strength of reinforcement in 'N/sqmm' |
| 27 |
fyt |
= |
Specified yield strength fy of transverse reinforcement in 'N/sqmm' |
28 |
hw |
= |
Height of entire wall from base to top of wall segment considered in 'mm' |
| 29 |
Icr |
= |
Moment of Inertia of concrete crack section |
| 30 |
k |
= |
Effective length factor for compression member |
| 31 |
lc |
= |
Length of compression member in a frame, measured center-to-center of the joints in the frame in 'mm' |
| 32 |
lg |
= |
Moment of inertia of gross concrete section about centroidal axis
neglecting reinforcement in 'mm4' |
| 33 |
lw |
= |
Length of entire wall in 'mm' |
| 34 |
lux |
= |
Un-supported length for compression member along D in 'mm' |
| 35 |
luy |
= |
Un-supported length for compression member along B in 'mm' |
| 36 |
MCap |
= |
Moment capacity of section for a given NA angle at design Pu in 'kNm
' |
| 37 |
Mcr |
= |
Cracking Moment |
| 38 |
MRes |
= |
Resultant design moment at a given load angle to local major axis in 'kNm
' |
39 |
Mc |
= |
Factored moment amplified for the effects of member curvature used for
design of compression member in 'kNm' |
| 40 |
Mm |
= |
Factored moment modified to account for effect of axial compression in 'kNm' |
| 41 |
Mmx |
= |
Factored moment along D of column modified to account for effect of axial compression in 'kNm' |
| 42 |
Mmy |
= |
Factored moment along D of column modified to account for effect of axial compression in 'kNm' |
| 43 |
Mur |
= |
Sqrt (Mmy^2 + Mmx^2) for circular column in 'kNm' |
44 |
Mux |
= |
Factored moment acting on a section along D in 'kNm' from Analysis (Momemt About Major Axis) |
| 45 |
Muy |
= |
Factored moment acting on a section along B in 'kNm' from Analysis (Momemt About Minor Axis) |
| 46 |
M1 |
= |
Smaller factored end moment on a compression member
in 'kNm' |
| 47 |
M1ns |
= |
Factored end moment on a compression member at the end at which M1
acts, due to loads that cause no appreciable sidesway
in 'kNm' |
| 48 |
M1s |
= |
Factored end moment on compression member at the end at which M1
acts, due to loads that cause appreciable sidesway
in 'kNm' |
| 49 |
M1sldr |
= |
Smaller factored end moment on a compression member due to
slenderness effect in 'kNm' |
| 50 |
M2 |
= |
Larger factored end moment on compression member in
'kNm' |
51 |
M2min |
= |
Minimum value of moment M2 as per minimum eccentricity of column |
| 52 |
M2ns |
= |
Factored end moment on compression member at the end at which M2
acts, due to loads that cause no appreciable sidesway in 'kNm' |
| 53 |
M2s |
= |
Factored end moment on compression member at the end at which M2
acts, due to loads that cause appreciable sidesway in 'kNm' |
| 54 |
M2sldr |
= |
Largest factored end moment on a compression member due to
slenderness effect in 'kNm' |
| 55 |
Mnb |
= |
Flexure Capacity for Beam |
| 56 |
Mnc |
= |
Flexure Capacity for Column |
| 57 |
Mnty |
= |
Nominal Flexure strength of column at top along depth in 'kNm' |
| 58 |
Mnby |
= |
Nominal Flexure strength of column at bottom along depth in 'kNm' |
| 59 |
Mntx |
= |
Nominal Flexure strength of column at top along width in 'kNm' |
| 60 |
Mnbx |
= |
Nominal Flexure strength of column at bottom along width in 'kNm' |
| 61 |
Nu |
= |
Factored axial force normal to cross section occurring simultaneously
with Vu in 'kN' |
62 |
Pc |
= |
Critical buckling load in 'kN' |
| 63 |
pt |
= |
Ratio of area of distributed transverse reinforcement to gross concrete
area perpendicular to that reinforcement |
| 64 |
Pω |
= |
Ratio of As to B x d |
| 65 |
Q |
= |
Stability index for storey |
| 66 |
r |
= |
Radius of gyration of cross section of a compression member in 'mm' |
| 67 |
Vc |
= |
Nominal shear strength provided by concrete in 'kN' |
| 68 |
Vj |
= |
Shear Force acting at the joint in 'kN' |
| 69 |
Vn |
= |
Nominal shear strength in 'kN' |
| 70 |
Vn' |
= |
Nominal shear strength at joint in 'kN' |
| 71 |
Vs |
= |
nominal shear strength provided by shear reinforcement in 'kN' |
| 72 |
Vs permissible |
= |
Maximum nominal shear strength provided by shear reinforcement in 'kN' |
| 73 |
Vur |
= |
Factored resultant shear force acting on the column in 'kN' |
| 74 |
Vus |
= |
Factored horizontal shear in a storey in 'kN' |
| 75 |
Vux |
= |
Factored shear at section along B in 'kN' (From Analysis) |
| 76 |
Vux1 |
= |
Shear induced due to column flexural capacity along width,'kN' |
| 77 |
Vux2 |
= |
Shear due to enhanced earthquake factor along width, 'kN' |
| 78 |
Vuy |
= |
Factored shear at section along D in 'kN' (From Analysis) |
| 79 |
Vuy1 |
= |
Shear induced due to column flexural capacity along depth, 'kN' |
| 80 |
Vuy2 |
= |
Shear due to enhanced earthquake factor along depth, 'kN' |
| 81 |
y |
= |
Neutral axis depth. |
| 82 |
β |
= |
It is a Neutral Axis angle corresponding to load angle to find out MCap |
| 83 |
So |
= |
Center to center spacing of transverse reinforcement within the length lo in 'mm' |
| 84 |
lo |
= |
Length, measured from joint face along axis of member, over which special transverse reinforcement must be provided in 'mm' |
| Code References: |
|
|
|
|
| ACI 318M - 14 |
|
|
|
|
| Sr.No |
Element |
|
Clause / table |
| 1 |
Minimum area of longitudinal reinforcement for column |
: |
18.7.4 |
| 2 |
Maximum area of longitudinal reinforcement for column |
: |
18.7.4 |
| 3 |
Minimum longitudinal and transverse reinforcement for wall |
: |
18.10.2.1 |
| 4 |
Minimum diameter of transverse ties |
: |
25.7.2 |
| 5 |
Minimum spacing of transverse ties |
: |
25.7.2 |
| 6 |
Maximum spacing of longitudinal and transverse reinforcement for wall |
: |
18.10.2.1 |
| 7 |
Applicability of boundary element |
: |
18.10.6 |
| 8 |
Area and spacing of special confining reinforcement |
: |
18.7.5 |
| 9 |
Slenderness Moments |
: |
6.2.5 |
| 10 |
Shear Strength provided by concrete for column |
: |
22.5.5 |
| 11 |
Design of shear for non-ductile wall |
: |
11.5.4 |
| 12 |
Design of shear for ductile wall |
: |
18.10.4.1 |
| 13 |
Minimum Flexural Strength of Columns |
: |
18.7.3 |
| 14 |
Shear Check at Column Joint |
: |
18.8.4.1 |
| 15 |
Shear Strength of Column |
: |
18.3.3, 18.4 & 18.6.5 |
| 16 |
fs,perm |
: |
10.6.4 |
| 17 |
fc,perm |
: |
10.2.7.1 |
| 18 |
Wcr |
: |
Eq 4.2(a) |
| Sway Calculation (Stability Index) |
| Level |
Load Combination
Analysis |
Storey Height (m) |
Gravity Load P (kN) |
Relative Displacements (mm) |
Storey Shear (kN) |
Stability Index (Q) |
Sway Condition |
| A |
B |
C |
D |
B x C / (A x D) |
| 0 m to 4.2 m |
12 |
4.2 |
82606.79 |
0.98 |
1804.72 |
0.011 |
Non Sway |
| 4.2 m to 7.858 m |
10 |
3.66 |
60641.35 |
1.26 |
1740.7 |
0.012 |
Non Sway |
| 7.858 m to 12.058 m |
10 |
4.2 |
38449.91 |
1.52 |
1500.6 |
0.009 |
Non Sway |
| 12.058 m to 16.258 m |
10 |
4.2 |
17397.06 |
1.12 |
1050.42 |
0.004 |
Non Sway |
| Level |
Load Combination
Analysis |
Storey Height (m) |
Gravity Load P (kN) |
Relative Displacements (mm) |
Storey Shear (kN) |
Stability Index (Q) |
Sway Condition |
| A |
B |
C |
D |
B x C / (A x D) |
| 0 m to 4.2 m |
13 |
4.2 |
82606.79 |
0.85 |
1804.72 |
0.009 |
Non Sway |
| 4.2 m to 7.858 m |
11 |
3.66 |
60641.35 |
0.85 |
1740.7 |
0.008 |
Non Sway |
| 7.858 m to 12.058 m |
13 |
4.2 |
38449.91 |
1.68 |
1500.6 |
0.01 |
Non Sway |
| 12.058 m to 16.258 m |
11 |
4.2 |
17397.06 |
0.32 |
1050.42 |
0.001 |
Non Sway |
| General Data |
| Column No. |
: |
C22 |
| Level |
: |
0 m To 4.2 m |
|
| Frame Type |
= |
Lateral |
|
| Response Modification Coefficient |
= |
3 |
|
| Design Code |
= |
ACI 318M - 14 |
|
| Grade Of Concrete (f'c) |
= |
C25 |
N/sqmm |
| Grade Of Steel (Main) |
= |
Fy550 |
N/sqmm |
| Grade Of Steel (Shear) |
= |
Fy550 |
N/sqmm |
| Grade Of Steel - Flexural Design |
= |
Fy420 |
N/sqmm |
| Grade Of Steel - Shear Design |
= |
Fy420 |
N/sqmm |
| Consider Ductile |
= |
Yes |
| Type of Frame |
= |
Special |
|
| Column B |
= |
600 |
mm |
| Column D |
= |
900 |
mm |
| Clear Cover, Cc |
= |
50 |
mm |
| Clear Floor Height @ lux |
= |
3400 |
mm |
| Clear Floor Height @ luy |
= |
3400 |
mm |
| No Of Floors |
= |
1 |
|
| No Of Columns In Group |
= |
1 |
|
| Strength Reduction Factor φ (Shear) |
= |
0.6 |
|
|
|
|
|
| Flexural Design (Analysis Forces) |
|
| Analysis Reference No. |
= |
1801 |
|
| Critical Analysis Load Combination |
: |
10 |
| Load Combination |
= |
[6] : 1.2 (LOAD 1: LOAD CASE 1) +0.5 (LOAD 2: LOAD CASE 2) +(LOAD 3: LOAD CASE 3 EQ-X) |
|
| Critical Location |
= |
Bottom Joint |
|
| Put |
= |
4062.4 |
kN |
| Muxt |
= |
-128.43 |
kNm |
| Muyt |
= |
4.27 |
kNm |
| Vuxt |
= |
1.74 |
kN |
| Vuyt |
= |
82.53 |
kN |
| Pub |
= |
4130.47 |
kN |
| Muxb |
= |
302.13 |
kNm |
| Muyb |
= |
-3.03 |
kNm |
| Vuxb |
= |
1.74 |
kN |
| Vuyb |
= |
922.87 |
kN |
| Slenderness Check |
|
| Column Is Braced Along D |
|
|
|
| Slenderness Check along D |
|
|
|
| k |
= |
0.83 |
|
| r |
= |
259.81 |
mm |
| Kluy /r |
= |
10.86 |
|
| M1 |
= |
-128.43 |
kNm |
| M2 |
= |
302.13 |
kNm |
| Min (40, 34 - 12 x (M1/M2)) |
= |
39.1 |
|
|
10.86 < 39.1, Column not slender along D |
| Column Is Braced Along B |
|
|
|
| Slenderness Check along B |
|
|
|
| k |
= |
0.8 |
|
| r |
= |
173.2 |
mm |
| Klux /r |
= |
15.7 |
|
| M1 |
= |
-3.03 |
kNm |
| M2 |
= |
4.27 |
kNm |
| Min (40, 34 - 12 x (M1/M2)) |
= |
40 |
|
|
15.7 < 40, Column not slender along B |
| Design Of Links |
| Links in the zone where special confining links are not
required |
| Normal Links |
|
|
|
| |
|
| Maximum Longitudinal Diameter |
= |
Dia Of Rebar |
|
| Rebar Number of bundled bar, D1 |
= |
19 |
|
| Diameter of bundled bar, D1 |
= |
19.1 |
mm |
| Bundled Rebar |
= |
No |
|
| Minimum diameter of link |
>= |
9.5 |
mm |
| Provided Link Rebar Number |
= |
10 |
|
| Provided Diameter of link |
= |
9.5 |
mm |
| |
|
| Criterion for spacing of normal links |
|
|
|
| Min. Longitudinal Bar dia X 16 |
= |
254.4 |
mm |
| 48 x diameter of links |
= |
456 |
mm |
| Min. Dimension of column |
= |
600 |
mm |
| |
|
| Spacing Criteria as per Vs & 0.33*Sqrt (f'c)*Aeff |
|
|
|
| Along D |
|
| Vs |
= |
326.63 |
kN |
| 0.33*Sqrt (f'c)*Aeff |
= |
832.05 |
kN |
| Check |
Vs <= 0.33*Sqrt (f'c)*B*d |
|
|
| d/2 |
= |
420.22 |
mm |
| 600 |
= |
600 |
mm |
| |
|
| Provided spacing |
= |
250 |
mm |
| |
|
| Provided spacing |
= |
250 |
mm |
| |
|
|
|
| Criterion for spacing of Ductile links / Links at Beam column Joint: |
|
|
|
| fyt |
= |
420 |
N/sqmm |
| Along D |
|
|
|
| Av/s min-1 |
= |
0.062 x Sqrt(f'c) x B x 1000 / fyt |
|
|
= |
442.86 |
sqmm/m |
| Av/s min-2 |
|
0.35 x B x 1000 / fyt |
|
|
= |
500 |
sqmm/m |
| Av/s min |
= |
Max ( Av/s min-1, Av/s min-2) |
|
|
= |
500 |
sqmm/m |
| |
|
| Along B |
|
|
|
| Av/s min-1 |
= |
0.062 x Sqrt(f'c) x D x 1000 / fyt |
|
|
= |
664.29 |
sqmm/m |
| Av/s min-2 |
|
0.35 x B x 1000 / fyt |
|
|
= |
750 |
sqmm/m |
| Av/s min |
= |
Max ( Av/s min-1, Av/s min-2) |
|
|
= |
750 |
sqmm/m |
| Criterion for spacing of Ductile links: |
|
|
|
| Min. Longitudinal Bar dia x 6 |
= |
95.4 |
mm |
| B / 4 |
= |
150 |
mm |
| So |
= |
150 |
mm |
| Max 150 mm |
= |
150 |
mm |
| Provided Spacing |
= |
75 |
mm |
| |
|
|
|
| Special confining reinforcement as per ACI
|
|
|
|
| Load Combination |
= |
[2] : 1.2 (LOAD 1: LOAD CASE 1) +1.6 (LOAD 2: LOAD CASE 2) |
|
| Pu |
= |
5405.69 |
kN |
| Check for Ash |
|
|
|
| 0.3 x Ag x f'c |
= |
4050 |
kN |
|
Pu > 0.3 x Ag x f'c |
|
|
| f'c |
= |
25 |
N/sqmm |
|
f'c <= 70 |
|
|
| Along D |
| No of bars along D |
= |
5 |
|
| S1 |
= |
75 |
mm |
| Pu |
= |
5405.69 |
kN |
| Ag |
= |
540000 |
sqmm |
| bc1 |
= |
519 |
mm |
| Ach |
= |
425061 |
sqmm |
| AshD1 |
= |
143.53 |
sqmm |
| AshD2 |
= |
159.24 |
sqmm |
| AshD3 |
= |
200.01 |
sqmm |
| AshD (Max (AshD1, AshD2, AshD3)) |
= |
200.01 |
sqmm |
| AshD Provided |
= |
354.41 |
sqmm |
| Along B |
| No of bars along B |
= |
7 |
|
| S1 |
= |
75 |
mm |
| Pu |
= |
5405.69 |
kN |
| Ag |
= |
540000 |
sqmm |
| dc1 |
= |
819 |
mm |
| Ach |
= |
425061 |
sqmm |
| AshB1 |
= |
226.5 |
sqmm |
| AshB2 |
= |
251.28 |
sqmm |
| AshB3 |
= |
315.62 |
sqmm |
| AshB (Max (AshB1, AshB2, AshB3)) |
= |
315.62 |
sqmm |
| AshB Provided |
= |
496.18 |
sqmm |
|
|
|
|
|
|
|
|
| Provided Links |
= |
#10@75 |
c/c |
| |
|
| Numbers of legs provided along D |
= |
5 |
|
| Av/s provided along D |
= |
4725.33 |
sqmm/m |
| Numbers of legs provided along B |
= |
7 |
|
| Av/s provided along B |
= |
6615.47 |
sqmm/m |
| |
|
Hence, OK |
|
| |
|
| Length of Confining Zone |
|
|
|
| Column maximum dimension |
= |
900 |
mm |
| Clear height /6 |
= |
566.7 |
mm |
Min. 450 mm |
= |
450 |
mm |
| Zone length |
= |
900 |
mm |