REINFORCED CONCRETE BEAM
RGB - 1
Input Parameters :
Sup Mid
Standard Specs Moment Capacity Top Bot Shear Capacity
fc' = 21 Mpa Tension Bar, Dt = 3 3 bw = 200 mm fyt =
fy = 275 Mpa Tension Bar 2-L, Nb = 0 0 h = 500 mm Av =
b₁ = .85 Compression Bar, Dc = 2 2 Sb = 10 mm Stirrups Bar Ø
Es = 200 Gpa Main Bar dia, D = 16 Cc = 40 mm, Clear Covering
Moment, Mu = 54.6 53.2
CONDITION : Val = 0.65+0.25 (Ԑt - Ԑty/0.005 - Ԑty)
Ø = 0.65 , Ԑt ≤ Ԑty 3-16mmØ
Val , Ԑty ˂ Ԑt ˂ 0.005 -- -- --
0.90 , Ԑt ≥ 0.005
Location of d' & dt; Support Midspan
As1 = π D² Db /4 = 603.19 603.19
2L, As2 = π D² Nb /4 = 0.00 0.00
y = (As1 y1+As2 y2)/As = 0.00 0.00 2-16mmØ
d' = Cc + Sb + (D/2) + y = 58.00 58.00
dt = h - d' = 442.00 442.00
CHECKING : εt ≥ 0.004, Support Midspan
Cmax = 600 dt / fsmin +600 = 189.4 189.43
amax = β1 Cmax = 161.0 161.01 2-16mmØ
Asmax = 0.85f'c amax bw / fy = 2090.26 2090.26
a = (As fy- As' fy)/0.85 fc' b = 46.46 46.46
C= a/β1 = 54.66 54.66
fs' = 600 (C-d')/C = -36.62 -36.62
fs' = Compression Bars = Not Yield Not Yield -- -- --
fs = 600 (dt-C)/C = 4251.51 4251.51 3-16mmØ
fs = Tension Bars = Yield Yield
BEAM MOMENT CAPACITY; Ø = 0.9 CHECK SHEAR; Ø = 0.75
As fy =0.85fc' β1 C bw + As' fs'; Where, fs' = (600 C-d'/C) Vc = 0.17 √fc' bw dt = 69
Support Midspan Vsmax = 0.67 √fc' bw dt = 271
C= by quadratic = 56.69 56.69 Vs = (Vu/Ø ) - Vc = 31.13
a= β1 C = 48.19 48.19 Section is Adequate
fs' = 600 (C-d')/C = -13.84 -13.84 Av = 2 (π Sb²/4)= 157.1
fs = 600 (dt-C)/C = 4077.91 4077.91 Vs ≤ 0.33√f'c bw d, d/2
Mn = Cc[dt-(a/2)] + Cs (dt-d') = 69.76 69.76 Max S, w/c or 600mm otherwise
ever is
SUPPORT, ØMn = 62.78 > 54.56 Pass! lesser,mm Vs > 0.33√f'c bw d,
MIDSPAN, ØMn = 62.78 > 53.22 Pass! d/4 or 300mm
Therefore use 200x500with 5-16mmØ @ support and 5-16mmØ @ midspan Main Bars (Grade 40);
10mmØ 2 leg-stirrups: Sp. at 3@50, 10@90 and rest 200 O.C
359.99 359.99
C 56.69 56.69
Mn 69.76 69.76
INPUT ON BLUE COLORS ONLY
hear Capacity
fyt = 230 3
Av = 2 3
Stirrups Bar Ø Main Bar Spacing Calculator
Clear Covering Sup Main Bar, S = 36 > 25mm >
Mid Main Bar, S = 36 > 25mm >
200
S Dimensional Limits, 418.6.2.1 150
U bw ≥ max[.3h, 200mm] Ok! 200
P As
P Main Reinforcements Ratio Limits, 418.6.3.1 603.19 603.19 603.19
O Asmin < As > Asmax, Ok! 2210 2210 603.19
R Asmin < As > Asmax, Ok! 450.036364 450.036364
T 368.272447 368.272447
Main Reinforcements, 418.6.3.2 450.036364 450.036364
Mumin ≥ 0.25 Mumax Ok! fy Grade 2
230 33 3
275 40 4
M 2
I 3 3 415 60
D 2 2 0-16mmØ
S 2 2 0-16mmØ
P
A
N Add extra Stirrups to increase area of Shear resisting steel, Av
NSCP 2015 418.6.4
Beam mark Beam Length, Vu Vs Smax Req per
< 75.00 on critical m Seismic
KN 0 - 0.15m 75.00 31.13 533.8 50.00
< 271.42
2h 0.15 - 1m 50.00 (2.20) 7,553.1 96.00
> 2h > 1m 50.00 (2.20) 7,553.1 221.00
54.6 13.64075
53.2
(Grade 40);
110.5
96
AAV 150
2 AAV 221.00 221 50
3 AAAV 221.00 221 96
4 AAAAV 221.00 221 221
Av =
0.15
1.00 .5Vc 34.43 221 221
2Vc 137.73 221 221.0
Shear force 4Vc 275.47 110.5 533.8
Grade 40 ( ) with
Main Bars ;
5 5
- @ midspan @ stirrups :
x
Ø @ support and
Sup
Mid
b= 200 As fy = 165,876.09 As fy = 165,876.09
h= 500 5f'c B c b = 3034.5c B c b = 3,034.50
fc' = 21 A's = 402.123859659 A's = 402.12
fy = 275 As = 603.19 As = 603.19 b₁ =
b₁ = .85 d' = 58.00 d' = 58.00
Es = 200 442.0 442.00
dt = dt =
C= 56.692 C= 56.69
Asmax 1 1
2090.26 0 0 0 0 FALSE
2090.26 0 0 0 0 FALSE
0 #N/A 0 #N/A
dt = 442.0 442.00
C= 56.692 56.69
Thus, Not Ok!
f's -36.62
CP 2015 418.6.4 C= 56.692
Stirrups Spacing
Qty mm fs -600.00
3.00 50.00 Pass! First Stirrups Min of 50mm from Face of Support
0.85 0.9
10.00 90.00 Pass!
Rest 200.00 Pass!
Ø= 0.65 0.65
1.9613478 1.9613478
0.9 0.9
50.00
96.00
221.00
at o.c.
Must not Exceed
0.15 ⅓ √f'c bw d d/2 d/4
135.03 221 110.5
2
with 0 - extra
with 0- extra
0.9
REINFORCED CONCRETE BEAM
B-7
Input Parameters :
Sup Mid
Standard Specs Moment Capacity Top Bot Shear Capacity
fc' = 21 Mpa Tension Bar, Dt = 3 3 bw = 250 mm
fy = 275 Mpa Tension Bar 2-L, Nb = 0 0 h = 450 mm
b₁ = .85 Main Bar dia, D = 16 Sb = 10 mm
Es = 200 Gpa Moment, Mu = 107.0 30.0 Cc = 40 mm,
CONDITION ;
Val = 0.65+0.25(Ԑt - Ԑty/0.005 - Ԑty) ρ < ρmin, As is not Adequate for Beam Dim
Ø = 0.65 , Ԑt ≤ Ԑty if fs > fy, use fy 3-16mmØ
Val , Ԑty ˂ Ԑt ˂ 0.005 fs < fy, use fs -- -- --
0.90 , Ԑt ≥ 0.005
Location of d' & dt; Support Midspan
As1 = π D² Db /4 = 603.19 603.19
2L, As2 = π D² Nb /4 = 0.00 0.00
y = (As1 y1+As2 y2)/As = 0.00 0.00 2-16mm
d' = Cc + Sb + (D/2) + y = 58.00 58.00
dt = h - d' = 392.00 392.00
CHECKING ; Support Midspan
ρ= As / b dt = 0.0062 0.0062
ρmin = 1.4 / fy = 0.0051 0.0051 2-16mm
ρb = 0.85fc' β1 600/fy(600+fy) = 0.0378 0.0378
Therefore ρ < ρb ρ < ρb
Tension Steel Yield Yield
CHECK SHEAR ; Ø = 0.75
Vc = 0.17 √fc' bw dt = 76.35 < 0.00 -- -- --
Vsmax = 0.67 √fc' bw dt = 300.89 KN 3-16mm
Vs = (Vu/Ø ) - Vc = (76.35) < 300.89
Section is Adequate
Av = 4 (π Sb²/4) = 314.2
Vs ≤ 0.33√f'c bw d, d/2
Max S, w/c or 600mm otherwise
ever is
lesser,mm Vs > 0.33√f'c bw d,
d/4 or 300mm
BEAM MOMENT CAPACITY @ SUPPORT; Ø= 0.90 BEAM MOMENT CAPACITY @ MIDSPAN; Ø =
Direct Substitution Direct Substitution
----- ----- SUPPORT ----- ----- MIDSPAN
----- ----- = ----- ----- ----- = -----
----- ----- = ----- ----- ----- = -----
ω= ρ fy / fc' = 0.08 ω= ρ fy / fc' = 0.08
Mn = fc' ω bw dt² (1-0.59ω) = 61.93 Mn = fc' ω bw dt² (1-0.59ω) = 61.93
ØMn = 55.74 < 107.00 Fail! ØMn = 55.74 > 30.00 Pass!
Therfore use, 250x450 with 5-16mmØ @ support and 5-16mmØ @ midspan Main Bars (Grade 40);
10mmØ 4 leg-stirrups: Sp. at 1@50, 9@90 and rest 150 O.C, BOTH ENDS.
ω= ρ fy / fc' = 0.081 0.081
ØMn = fc' ω bw dt² (1-0.59ω) = 61.93 61.93
As fs [dt-(a/2)] 275 275
fs = 600 (dt-C)/C 952.19 952.19
Solve fs, From Strain Diagram, [ΣFh = 0], T = C
0.003 = C (fs / Es) / (d-C); Where fs = 600 (dt-C)/C > >
As fy = 0.85fc' β1 C bw ρ > ρmin ρ > ρmin
C= by quadratic 151.53 151.53 ρ < ρb ρ < ρb
a= β1 C 128.80 128.80
359.99 359.99
C 151.53 151.53
Mn 54.34 54.34
54.34 54.34
INPUT ON BLUE COLORS ONLY
Shear Capacity
fyt = 230
Av = 4
Stirrups Bar Ø Main Bar Spacing Calculator
Clear Covering Sup Main Bar, S = 61 > 25mm >
Mid Main Bar, S = 61 > 25mm >
200
S Dimensional Limits, 418.6.2.1 135
U bw ≥ max[.3h, 200mm] Ok! 200
P
P Main Reinforcements Ratio Limits, 418.6.3.1 Sup
O Asmin < As > Asmax, Ok! Support Mid
R Asmin < As > Asmax, Ok! Midspan d'
T 0.75
Main Reinforcements, 418.6.3.2 0.75
Mumin ≥ 0.25 Mumax Ok fy Grade
230 33
275 40
M
I 415 60
D 26.75 107.0
S 30.0
P
A
N Add extra Stirrups to increase area of Shear resisting steel, Av
NSCP 2015 418.6.4
Beam mark Beam Length, Vu Vs Smax
on critical m
0 - 0.05m - (76.35) 388.0
2h 0.05 - 0.9m - (76.35) 388.0
Mid > 0.9m - (76.35) 388.0
0.90
1
0 0
MIDSPAN 0 0
----- 0 #N/A
-----
0.08
61.93
Pass! d/4 98
96
n Bars (Grade 40); 150
DS. AAAAV 196.00 196 50
2 AAV 196.00 196 96
3 AAAV 196.00 196 196
4 AAAAV
Av =
0.05
0.90 .5Vc 38.17 196
2.25 2Vc 152.69 196
Shear force 4Vc 305.4 98
Grade 40 ( ) with
RS ONLY Main Bars ;
5 5
- @ midspan @ stirrups :
x
Ø @ support and
Sup
Mid
b= 250 As fy = 165,876.09 As fy = 165,876.09
3 h= 4505f'c B c b = 3793.125c B c b = 3,793.12
3 fc' = 21 A's = A's =
2450 2450 fy = 275 As = 603.19 As = 603.19
603.19 603.19 b₁ = .85 d' = 58.00 d' = 58.00
sup mid Es = 200 392.0 392.00
408.26583 408.26583 dt = dt =
498.90909 498.90909 C= 151.528 C= 151.53
498.90909 498.90909
As Asmax
603.19 ρ < ρb 0
603.19 ρ < ρb 0
1.5 2 0.75 2
0.75 2 0.75 2
2 < Yield dt = 392.0 392.00
3 < Yield C= 151.528 151.53
4 0.005091
Thus, Not Ok!
0-16mmØ
0-16mm
f's #REF!
NSCP 2015 418.6.4 C= #REF!
Req per Stirrups Spacing
Seismic Qty mm (unit) fs #REF!
50.00 1.00 50.00 Pass! First Stirrups Min of 50mm from Face of Support
0.85 0.81
96.00 9.00 90.00 Fail!
196.00 Rest 150.00 Pass!
1
0 FALSE
0 FALSE
0 #N/A Ø= 0.65
0.8835132
0.9
50.00
96.00
196.00
196
196.0
388.0
at
Must not Exceed
0.05 ⅓ √f'c bw d d/2
149.70 196
2
with 2
with 2- extra
with 2- extra
b₁ = 0.9
0.65
0.8835132
0.9
o.c.
d/4
98
- extra
