04 RC Beam.pdf
description
Transcript of 04 RC Beam.pdf
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Page 1
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Page 2
Bending Moment in RC Beam
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Page 3
Bending Moment in RC Beam
N.A = Nutral Axis. D
kd
d jd
d-kd
As
Ac
C
T
kd/3
b fc
fs
M
C = T
M = C jd = T jd
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Page 4
Bending Moment in RC Beam
N.A = Nutral Axis. D
kd
d jd
d-kd
As
Ac
C
T
kd/3
b fc
fs
M
k = 11+
fs
nfc
; n = EsEc
jd = d kd3 j=1k3
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Page 5
Bending Moment in RC Beam
N.A = Nutral Axis. D
kd
d jd
d-kd
As
Ac
C
T
kd/3
b fc
fs
M
C = T, T = fs As and C = 12 fc b kd
M = T jd = fs As jd
As = Mfsjd
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Page 6
Concrete
W/C fC 28-day (ksc)
0.35 420 335
0.40 350 280
0.50 280 225
0.60 225 180
0.70 175 140
0.80 140 115
28 Ec ...
Ec = w1.5 4270 fC Where;
w = concrete density (t/m3)
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Page 7
Steel bar
Steel bar
(fc) ksc
(fc) ksc
Round bar (RB)
6-9 mm 2500 4100
> 12 mm 2400 4100
Deformed bar (DB)
SD24 2400 4900
SD30 3000 4900
SD35 3500 5700
SD40 4000 5700
28 Es ... Es = 2.04 106 kg/cm2
6-9mm 6-9mm [email protected] [email protected] 2 [email protected] [email protected] 10-DB24 # [email protected]
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General Condition of RC beam
1. (d)
2. (L/360) L/20 L/23 L/26 L/10
3. 2.5 1.23
4. 0.0025 0.0015
5.
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Page 9
Steel spacing and covering
Z
Z
2.5 cm
X
X X 1.34 X 2.5 Z 2 Z 3 15 Z 4 15
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Page 10
N.A = Nutral Axis.
kd
d jd
d-kd
Ac
C
T
kd/3
b fc
fs
k = 11+
fs
nfc
; n = EsEc
As = Mfsjd
As
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Page 11
Diameter Type
weight (kg/m)
o (cm)
Number of reinforced steel (bar)
1 2 3 4 5 6 7 8 9
mm In As (cm2)
6 1/4
RB
0.222 1.885 0.283 0.565 0.848 1.131 1.414 1.696 1.978 2.262 2.544
9 3/8 0.499 2.828 0.636 1.272 1.909 2.545 3.182 3.820 4.455 5.090 5.726
12 1/2 0.888 3.770 1.131 2.262 3.393 4.526 5.650 6.785 7.915 9.045 10.180
15 5/8 1.390 4.710 1.767 3.534 5.295 7.065 8.830 10.600 12.360 14.140 15.900
19 3/4 2.230 5.965 2.835 5.670 8.500 11.340 14.170 17.020 19.850 22.680 25.500
22 7/8 2.980 6.905 3.801 7.602 11.400 15.200 19.000 22.800 26.600 30.400 34.200
25 1 3.850 7.850 4.909 9.818 14.730 19.640 24.530 29.450 34.380 39.280 44.200
28 1 1/8 4.830 8.790 6.158 12.320 18.480 24.630 30.800 36.960 43.120 49.280 55.420
12 1/2
DB
0.888 3.771 1.130 2.260 3.390 4.520 5.650 6.780 7.910 9.040 10.170
16 5/8 1.580 5.029 2.010 4.020 6.030 8.040 10.050 12.060 14.070 16.080 18.090
19 3/4 2.230 5.971 2.840 5.680 8.520 11.360 14.200 17.040 19.880 22.720 23.560
20 3/4 2.470 6.290 3.140 6.280 9.420 12.560 15.700 18.840 21.980 25.120 28.260
22 7/8 2.980 6.910 3.800 7.600 11.400 15.200 19.000 22.800 26.600 30.400 34.200
25 1 3.850 7.857 4.910 9.820 14.700 19.600 24.500 29.400 34.400 39.300 44.200
28 1 1/8 4.830 8.800 6.160 12.320 18.480 24.640 30.800 36.960 43.120 49.280 55.440
32 1 1/4 6.310 10.060 8.040 16.080 24.120 32.160 40.200 48.240 56.280 64.320 72.360
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Example 1 Bending RC Beam
. 0.20x0.40 3000 kg.m n = 11, fc = 210 ksc, fy = 2400 ksc
. fc = 0.45f c = 0.45*210 = 94.5 ksc fs = 0.50fy = 0.50*2400 = 1200 ksc k jd k = 1
1+fs
nfc
= 11+
12001194.5
= 0.4642
j = 1 k
3 = 1 0.4642
3 = 0.8453
2.5 cm => d = 40-5 = 35 cm jd = 0.8453*0.35 = 0.2958 m As = M
fsjd = 3000
12000.2958 = 8.45 cm2
Design 3-RB19 As = 8.50 cm2
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Example 1 Bending RC Beam
. 0.20x0.40 3000 kg.m n = 11, fc = 210 ksc, fy = 2400 ksc
Design 3-RB19 As = 8.52 cm2
d = 35 cm
covering = 2.5 cm
covering = 2.5 cm
20- (2*2.5) = 15 cm
x
x = 15 (31.9) 2
= 4.65 cm > 2.5 cm O.K.
diameter 2.5 cm
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C + Cs = T1 + T2
12 fc bkd + A
s fs = As1 fs + As2 fs
N.A = Nutral Axis. d-d
jd
Ac
C
T1
kd/3
b fc
As
Ast=As1+As2
Cs
T2
+ As1 As2
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T1 C
M1 = Rbd2
R = 12 fc k j
As1=M1fsjd
N.A = Nutral Axis. d-d
jd
Ac
C
T1
kd/3
b fc
As
Ast=As1+As2
Cs
T2
+ As1 As2
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T2 Cs
M2 = MM1 = As f s d d = As2 fs (d d
)
As2 =M2
fs(dd)
N.A = Nutral Axis. d-d
jd
Ac
C
T1
kd/3
b fc
As
Ast=As1+As2
Cs
T2
+ As1 As2
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Page 17
Ast = As1 + As2 = M1
fs jd+
M2fs(d d)
N.A = Nutral Axis. d-d
jd
Ac
C
T1
kd/3
b fc
As
Ast=As1+As2
Cs
T2
+ As1 As2
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Page 18
Cs=T2, Asf s = As1fs
f s = fsk(d d )1k
. f s f s = 2fsk(d d )
1k
As = 12As2
1k
kd
d
As = M2fs(dd)
N.A = Nutral Axis. d-d
jd
Ac
C
T1
kd/3
b fc
As
Ast=As1+As2
Cs
T2
+ As1 As2
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Page 19
. 1.
2. k, j, R, As
3. M 1 =Rbd2 M
M1
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Example 2 Bending RC Beam
. 0.25x0.60 16,500 kg.m n = 8, fc = 250 ksc, fy = 3,000 ksc
. fc = 0.45f c = 0.45*250 = 112.5 ksc fs = 0.50fy = 0.50*3000 = 1500 ksc k jd k = 1
1+fs
nfc
= 11+
15008112.5
= 0.375
j = 1 k
3 = 1 0.375
3 = 0.875
R = 12 fc kj =1
2 112.5 0.375 0.875 = 18.45 ksc
d = 60-5 = 55 cm d= 5 cm f s = 2fskd d
1k = 2 1500 0.3755 55
10.375 = 1364 ksc
M1 = Rbd2 =18.45 0.25 552 = 13,953 kg.m
As1 =M1fsjd
= 13,95315000.8750.55
= 19.33 cm2
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Example 2 Bending RC Beam
. 0.25x0.60 16,500 kg.m n = 8, fc = 250 ksc, fy = 3,000 ksc
M1=13,953 kg.m < M=16,500 kg.m 2 = M 1 = 16,500 13,953 = 2,547 kg.m
As2 =M2
fs(dd) =
2,547
1,500(0.550.05) = 3.40 cm2
As = M2fs(dd)
=2,547
1,364(0.550.05) = 3.73 cm2 ==>
Ast = As1 + As2 = 19.33 + 3.40 = 22.73 cm
2 ==>
Design Design 2-RB16 As = 4.020 cm2
Design 3-DB32 As = 24.120 cm2 (x) = (25-(2*3)-(3*3.2))/2 = 4.7 cm > 2.5 cm O.K.
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N.A.
H
H
N.A. V
V
H
V
T
H V
T
T2 = V2 + H2
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Shearing Stress ()
= Vbd V = bd
. 1.32 f c ksc
=0.29 f c ksc Vc = 0.29 f c bd kg Vc ==> (Stirrup)
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V = V Vc V = AVfV sin
= 90 Av = 2As of stirup fv = fs
V = Avfvds
V = 2Asfsds
(s ) ()
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1. d
2 0.30 m
2. (V) 1.32 f c ksc
3. Av = 2As > 0.0015bs
4. V > 0.795 f c ksc d
4
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Example 3 Shearing RC Beam
. 0.15x0.40 4.00 m 2,000 kg/m n = 11, fc = 250 ksc, fy = 2400 ksc
. fc = 0.45f c = 0.45*250 = 112.5 ksc fs = 0.50fy = 0.50*2400 = 1200 ksc
= 0.29 f c = 0.29 250 = 4.58 ksc Loading Analysis = = 4.58*15*30 = 2,061 kg V = V Vc = 4,000-2,061 = 1,939 kg Design [email protected] resist shear 1,970 kg
2000 kg/m
4000 kg 4000 kg
V=4000 kg
V=-4000 kg M=+4000 kg.m
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
. fc = 0.45f c = 0.45*250 = 112.5 ksc fs = 0.50fy = 0.50*2400 = 1200 ksc
= 0.29 f c = 0.29 250 = 4.58 ksc
820 kg/m
1640 kg 3954 kg
917 kg/m 480 kg
4.00 m 2.00 m
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
V=2314 kg V=1640 kg
M=-1093 kg M=-2794 kg
M=+547 kg
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
k jd k = 1
1+fs
nfc
= 11+
120010112.5
= 0.4839 j = 1 k3 = 1 0.4839
3 = 0.8387
d = 40-5 = 35 cm d= 5 cm jd = 0.8387*0.35 = 0.2935 m R = 1
2 fc kj =1
2 112.5 0.4839 0.8387 = 22.83 ksc
f s = 2fskd d 1k
= 2 1200 0.48395 35 10.4839
= 1,586 ksc
M1 = Rbd2 =22.83 0.20 352 = 5,593 kg.m
M=-1,093, +547, -2,794 kg.m M1 = 5,593 kg.m M < M1 O.K. Design 2-DB12 (As=2.260 cm2)
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
1) M=-1,093 kg.m As = M
fsjd = 1093
12000.2935 = 3.10 cm2
Design 3-DB12 (As = 3.390 cm2) 2) M= +547 kg.m As = M
fsjd = 547
12000.2935 = 1.55 cm2
Design 2-DB12 (As = 2.260 cm2) 3) M= -2,794 kg.m As = M
fsjd = 2794
12000.2935 = 7.93 cm2
Design 2-DB12 + 2-DB19 (As = 7.940 cm2)
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
V= 1,640 2,314 kg = = 4.58*20*40 = 3,664 kg 1) V= 1,640 kg V < V Design [email protected] 2) V= 2,314 kg V < V Design [email protected]
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Example 4 RC Beam Design
. A-A 0.20x0.40 n = 10, fc = 250 ksc, fy = 2400 ksc
3-DB12 2-DB12 + 2-DB19
2-DB12
3-DB12
2-RB6
2-DB12
2-DB12
2-RB6
2-DB12
2-DB19
2-DB12