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SUMMARY OF STRUCTURAL CALCULATION OF FLUME Class III roadClear width : 0.00 m (max)
Clear height : 0.00 m (max)
1 Design Dimensions and Bar Arrangements Without operation deck slab
Type of flume (width and height) B6.5 x H4.0Clear width m 6.50Clear height m 4.00Height of fillet m 0.20
Thickness Side wall Top cm 30.0Bottom cm 60.0
Bottom slab cm 60.0
Cover of reinforcement barSide wall Outside cm 7.0
Inside cm 7.0Bottom slab Lower cm 7.0
Upper cm 7.0
Bar arrangement (dia - spacing per unit width of 1.0 m)Side wall Lower outside Tensile bar mm D16@125
Distribution bar mm D13@250Lower inside Compressive bar mm D13@250
Distribution bar mm D13@250
Upper outside Tensile bar mm D16@250Distribution bar mm D13@250
Upper inside Compressive bar mm D13@250Distribution bar mm D13@250
Bottom slab Lower edge Tensile bar mm D16@125Distribution bar mm D13@250
Upper edge Compressive bar mm D16@250Distribution bar mm D13@250
Lower middle Tensile/comp. bar mm D16@250Distribution bar mm D13@250
Upper middle Tensile/comp. bar mm D16@250Distribution bar mm D13@250
Fillet Fillet bar mm D13@250
2 Design ParametersUnit Weight Reinforced Concrete 2.4
Backfill soil (wet) 1.8
(submerged) 1.0
Live Load Class of road Class III (BM50)Truck load at rear wheel P= 5.0 tf/mImpact coefficient Ci = 0.3
Pedestrian load wq= 0.0
Concrete Design Strength 175
(K175) Allowable Compressive Stress 60
Allowable Shearing Stress 5.5
Reinforcement Bar Allowable Tensile Stress 1,850
Yielding Point of Reinforcement Bar 3,200
Young's Modulus Ratio n= 24
Cohesion C = 0.0Internal friction angle 25.0 degree
c= tf/m3
s= tf/m3
s'= tf/m3
tf/cm2
ck= kgf/cm2
ca= kgf/cm2
a= kgf/cm2
sa= kgf/cm2
(U32, deformed bar) sy= kgf/cm2
Soil Properties tf/m2
=
5 - 10
STRUCTURAL CALCULATION OF FLUME TYPE: B6.5m x H4.0m
1. Design Dimensions and ParametersBasic Parameters
Kah: Horizontal coefficient of active earth pressure 0.367
we: Converted distribution loads 1.00
Unit weight of water 1.00
Unit weight of soil (wet) 1.80
Unit weight of soil (saturated) 2.00
Unit weight of reinforced concrete 2.40
Concrete design strength 175
Allowable compressive stress of concrete 60
Allowable tensile stress of reinforcement bar 1850
Allowable shearing stress of concrete 5.5
Yielding point of reinforcement bar 3200n: Young's modulus ratio 24Fa: Safety factor against uplift 1.2
Basic DimensionsH: Height of flume 4.00 mB: Width of flume 6.50 mHf: Height of fillet 0.20 m
0.07 m t1: Thickness of wall at top 0.30 m0.07 m t2: Thickness of wall at bottom 0.60 m
Minimum thickness t3: Thickness of invert (bottom slab) 0.60 mSingle bar 0.15 m t4: Thickness of wall at 1/2 H 0.45 mDouble bar 0.20 m BT: Gross width of fflume 7.70 m
HT: Gross height of flume 4.60 mL: Unit length of flume 1.00 m
Coefficient of Active Earth Pressureground surface angle 0.0 degree = 0.0000 radianinternal friction angle 25.0 degree = 0.4363 radian
16.7 degree = 0.2909 radianwall angle 4.3 degree = 0.0749 radian
c : cohesion of soil (not to be considered) 0.0 t/m2kh : seismic coefficient (not to be considered) 0.00
0.0000 radian
0.2182 radian
Normal ConditionKa : coefficient of active earth pressure 0.393Kah : horizontal coefficient of active earth pressure 0.367Kav : vertical coefficient of active earth pressure 0.140
Converted Distribution Loads
max (1.0 we= 1.000
wev= 0.303
wee= 0.000 Iv= 0.747
Ie= 1.000
where, wev:
wep:Pt: Truck load at rear wheel Pt= 5.0 t Class III (BM50)Iv: Conversion coefficientIe: Conversion coefficientIi: impact coefficient Ii= 0.3a: Ground contact length of tire a= 0.10 m Class IIIb: Ground contact width of tire b= 0.25 m Class III
Unit weight of soil 1.80
Pedestrian load
wq= 0.0
Detailed Dimensionsfor compute Iv for compute Ie
H= 4.00 m 4.00 mho= 0.00 m 0.00 mx1= 0.00 m 0.00 mx2= 0.00 m 0.00 mx3= 0.50 m 0.50 mx= 0.50 m 0.00 m
t/m2
w: t/m3
d: t/m3
s: t/m3
c: t/m3
ck: kgf/m2
ca kgf/m2
sa: kgf/m2
a: kgf/m2
sy: kgf/m2
Cover of reinforcement barSide wallInvert (bottom slab)
: : : friction angle between earth and wall (=2/3 , normal condition) :
: tan1 kh
E: friction angle between earth and wall (=/2, seismic condition)
= Ka cos(+)= Ka sin(+)
we = wev+wee+wq tf/m2 or wev+wee+wq) t/m2
wev = Pt*(1+Ii)*Iv/H2 t/m2
wee = d*ho*Ie t/m2
Iv={[2/(b+2*(H+ho)]}*{(xHho)+(a+x+H+ho)*ln[(a+x+H+ho)/(a+2*x)]}
Ie=1+(x/H)2(2/)*[1+(x/H)2]*arcTan(x/H)(2/)*(x/H)
Converted distribution load of vehicle (t/m2)
Converted distribution load of trapezium embankment (t/m2)
d: d= t/m3
t/m2
H
Ptx
wevho
x1 x2 x3
H
BT
t1
Bt2 t2
t3
HT
Hf
Hf
t1
5 - 11
2. Stability Analysis Against Uplift
Fs=(Vd+Pv)/U > Fa Fs= 1.452 > 1.2 ok
where, Vd: Total dead weight Vd= 19.824 t/m
Pv: 50% of total vertical earth pressure Pv= 1.797 t/mU: Total uplift U= 14.887 t/mFa: Safety factor against uplift Fa= 1.2
3. Intersectional Force
3.1 Case 1: Without Inside Water Ground water level is assumed at H/2 above invert.
1) at 1/2 height of side wall: MmActing Load Acting Point Bending Moment
Sm (t/m) (m) Mm (t.m/m)P1= Kah*we*(H/2) P1= 0.733 H/4= 1.000 0.733
P2= 1.320 H/6= 0.667 0.880Sm= 2.053 Mm= 1.613
2) at bottom of side wall: MsActing Load Acting Point Bending Moment
Ss (t/m) (m) Ms (t.m/m)P1= Kah*we*(H/2) P1= 0.733 (3/4)*H= 3.000 2.199
P2= 1.320 (2/3)*H= 2.667 3.519P3= Kah*we*(H/2) P3= 0.733 H/4= 1.000 0.733
P4= 2.639 H/4= 1.000 2.639
P5= 0.733 H/6= 0.667 0.489
P6= 4.000 H/6= 0.667 2.667Ss= 10.158 Ms= 12.246
3) at edge of invert: MeMoment Mbe Mbe=Ms Mbe= 12.246 t.m/mReaction wb
(uniform load) wb= 1.135Shearing force Sbe=wb*BT/2 Sbe= 4.368 t/m
4) at middle of invert: Mb
Moment Mbm Mbm= 3.838 t.m/m (acting point: Bt/2)Shearing force Sbm= 0.000 t/m (acting point: Bt/2)
3.2 Case 2: With Inside Water Inside water level and ground water level is assumed at top of side wall.
1) at 1/2 height of side wall: MmActing Load Acting Point Bending Moment
Sm (t/m) (m) Mm (t.m/m)
-2.000 H/6= 0.667 -1.333
0.733 H/6= 0.667 0.489
2.000 H/6= 0.667 1.333Sm= 0.733 Mm= 0.489
2) at bottom of side wall: MsActing Load Acting Point Bending Moment
Ss (t/m) (m) Ms (t.m/m)
-8.000 H/3= 1.333 -10.667
2.933 H/3= 1.333 3.910
8.000 H/3= 1.333 10.667Ss= 2.933 Ms= 3.910
3) at edge of invert: MeMoment Mbe Mbe=Ms Mbe= 3.910 t.m/mReaction wb
(uniform load) wb= 1.135 t/m2Shearing force Sbe=wb*BT/2 Sbe= 4.368 t/m
4) at middle of invert: Mb
Moment Mb Mb= -4.498 t.m/m (acting point: Bt/2)Shearing force Sbm= 0.000 t/m (acting point: Bt/2)
3.3 Summary of Intersectional Force
Description at bottom of side wall at H/2 of side wall at edge of invert at middle of invertBending Moment (t.m/m) outside outside lower lower upper
Case 1 12.246 1.613 12.246 3.838 Case 2 3.910 0.489 3.910 4.498
for Design 12.246 1.613 12.246 3.838 4.498
Shearing force (t/m) outside outside lower lower upperCase 1 10.158 2.053 4.368 0.000 Case 2 2.933 0.733 4.368 0.000
for Design 10.158 2.053 4.368 0.000 0.000
Stability analysis against uplift is made taking into consideration that flume inside is empty and ground water level is at H/3 above invert.
={(t1+t2)*H+t3*BT+Hf2}*c
=(3/8)*Kav*d*H2+(1/8)*Kav*(sw)*H2
=w*BT*(t3+H/3)
P2=(1/2)*Kah*d*(H/2)2
P2=(1/2)*Kah*d*(H/2)2
P4=Kah*d*(H/2)2
P5=(1/2)*Kah*(sw)*(H/2)2
P6= w*(H/2)2
wb={[(t1+t2)*H+Hf2]*c}/BT t/m2
Mbm= Mbewb*(BT)2/8
Pwi' = w*H2/8
Pe' =Kah*(sw)*H2/8
Pwo' = w*H2/8
Pwi = w*H2/2
Pe = Kah*(sw)*H2/2
Pwo = w*H2/2
wb={[(t1+t2)*H+Hf2]*c}/BT
Mbm= Mbewb*(BT)2/8
5 - 12
4. Calculation of Required Reinforcement Bar
4.1 Check of Cracking Moment and Ultimate Bending Moment
Side wall Invert (bottom slab)Description Unit at bottom at H/2 at edge at middle
outside outside lower lower upper
1) Cracking moment, Mc
Mc= (kgf.cm) 938599 527962 938599 938599 938599(tf.m) 9.386 5.280 9.386 9.386 9.386
where, Zc: section modulus
60000 33750 60000 60000 60000design tensile strength of concrete
15.64 15.64 15.64 15.64 15.64design strength of concrete
175 175 175 175 175N: axial force (kgf) 0 0 0 0 0
Ac: area of concrete
Ac=b*h 6000 4500 6000 6000 6000b: unit length 100 100 100 100 100h: thickness of member 60 45 60 60 60
2) Check of cracking moment and design bending moment
Design bending moment, Mf (tf.m) 12.246 1.613 12.246 3.838 4.498
Check Mf & Mc
1.7*Mf (tf.m) 20.819 2.742 20.819 6.524 7.647Mc (tf.m) 9.386 5.280 9.386 9.386 9.386
1.7*Mf > Mc ? Yes No Yes No No
3) Ultimate bending moment, Mu
Mu=(kgf.cm) 2406516 324160 2406516 770023 901073
(tf.m) 24.065 3.242 24.065 7.700 9.011where, As: area of tensile bar
14.623 2.686 14.623 4.583 5.371yielding point of tensile bar
3200 3200 3200 3200 3200allowable stress of reinforcement bar
1850 1850 1850 1850 1850design compressive strength of concrete
175 175 175 175 175
allowable stress of con 60 60 60 60 60j: (=8/9 ) 0.854 0.854 0.854 0.854 0.854
or k:d: effective height
53 38 53 53 53d1: cover of reinforcement bar
7 7 7 7 7h: thickness of member 60 45 60 60 60b: unit length 100 100 100 100 100n: Young's modulus ratio 24 24 24 24 24
Check Mu & Mc
Mu (tf.m) 24.065 24.065Mc (tf.m) 9.386 9.386
Mu > Mc ? Yes Yes
Zc*('ck + N/Ac)
Zc=b*h2/6 (cm3)'ck:
'ck = 0.5*ck2/3 (kgf/cm2)ck:
(kgf/cm2)
(cm2)(cm)(cm)
1.7*Mf > Mc ? If "Yes", check ultimate bending moment. If "No", no need to check ultimate bending moment.
As*sy{d(1/2)*(As*sy)/(0.85*ck*b)}
As=Mf/(sa*j*d) (cm2)sy:
(Spec >295 N/mm2) (kgf/cm2)sa:
(kgf/cm2)'ck:
(kgf/cm2)
ca: (kgf/cm2)= 1k/3= n/(n+sa/ca)
d=hd1 (cm)
(cm)(cm)(cm)
Mu > Mc ? If "Yes", design dimensions are ok. If "No", check design dimensions.
5 - 13
4.2 Bar Arrangement
Side wall Invert (bottom slab)Description Unit at bottom at H/2 at edge at middle
outside outside lower lower upper
1) Check of single or double bar arrangement
M1= (kgf.cm) 3150286 1619442 3150286 3150286 3150286(tf.m) 31.503 16.194 31.503 31.503 31.503
M2= (kgf.cm) 54953 54953 54953 54953 54953(tf.m) 0.550 0.550 0.550 0.550 0.550
where, M1: resistance moment (kgf.cm)M2: resistance moment at compressive side (kgf.cm)
Cs: 12.8436 12.8436 12.8436 12.8436 12.8436s: =(n*sca)/(n*sca+ssa) 0.4377 0.4377 0.4377 0.4377 0.4377
m: 30.8333 30.8333 30.8333 30.8333 30.8333d: effective height of tensile bar
53 38 53 53 53d': effective height of compressive bar
7 7 7 7 7h: thickness of member 60 45 60 60 60b: unit length 100 100 100 100 100
allowable stress of reinforcement bar
1850 1850 1850 1850 1850allowable stress of concrete
60 60 60 60 60n: Young's modulus ratio 24 24 24 24 24
Check M1 & Mf
M1 (tf.m) 31.503 16.194 31.503 31.503 31.503Mf (tf.m) 12.246 1.613 12.246 3.838 4.498
M1 > Mf ? Yes Yes Yes Yes Yes
2) Tensile bar
Max. bar area
As max = 0.02*b*d 106.0 76.0 106.0 106.0 106.0Min. bar area As min =
As min = b*4.5% 4.5 4.5 4.5 4.5 4.5
Required bar area As req 14.623 2.686 14.623 4.583 5.371 16 16 16 16 16
spacing @ 125 250 125 250 250Required bar nos. b/spacing (nos.) 8 4 8 4 4
Area of tensile bar As 16.085 8.042 16.085 8.042 8.042ok ok ok ok ok
3) Compressive bar, in case M1 < Mf
(tf.m) 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000
where, d: effective height of tensile bar53 38 53 53 53
d': effective height of compressive bar7 7 7 7 7
allowable stress of reinforcement bar
1850 1850 1850 1850 1850M1: resistance moment at tensile side
(tf.m) 31.503 16.194 31.503 31.503 31.503Mf: design bending moment
(tf.m) 12.246 1.613 12.246 3.838 4.498
Required bar area As' req 0.000 0.000 0.000 0.000 0.000 13 13 16 16 16
spacing @ 250 250 250 250 250
Area of comp. bar As' 5.309 5.309 8.042 8.042 8.042
(d/Cs)2*sa*b
(d'/Cs)2*sa*b
=[2m/{s*(1s/3)}]0.5
=sa/ca
(cm)
(cm)(cm)(cm)
sa:
(kgf/cm2)ca:
(kgf/cm2)
M1 > Mf ? If "Yes", design tensile bar only. If "No", design tensile and compressive bars.
(cm2)
(cm2)
(cm2)apply (mm)
(mm)
(cm2)
M' = MfM1=sa*As'*(dd')
As' = M'/{sa*(dd')} (cm2)
(cm)
(cm)sa:
(kgf/cm2)
(cm2)apply (mm)
(mm)
(cm2)
d1
h d
d2
d1
hd
5 - 14
4.3 Check of Stress
Side wall Invert (bottom slab)Description Unit at bottom at H/2 at edge at middle
outside outside lower lower upper
1) Tensile bar only
Design bending moment, Mf (tf.m) 12.246 1.613 12.246 3.838 4.498Design shearing force, S (tf) 10.158 2.053 4.368 0.000 0.000
Bending compressive stress of concrete
30.87 9.03 30.87 12.57 14.74ok ok ok ok ok
Bending tensile stress of reinforcement bar
Mf/(As*j*d) 1605.48 580.37 1605.48 977.23 1145.40ok ok ok ok ok
Mean shearing stress of concrete
S/(b*j*d) 2.142 0.594 0.921 0.000 0.000ok ok ok ok ok
where, p: =As/(b*d) 0.0030 0.0021 0.0030 0.0015 0.0015
k: 0.3157 0.2720 0.3157 0.2359 0.2359j: 0.8948 0.9093 0.8948 0.9214 0.9214
As: area of tensile bar 16.085 8.042 16.085 8.042 8.042b: unit length 100 100 100 100 100d: effective height 53 38 53 53 53n: Young's modulus ratio 24 24 24 24 24
2) Tensile & compressive bars
Design bending moment, Mf (tf.m) 12.246 1.613 12.246 3.838 4.498Design shearing force, S (tf) 10.158 2.053 4.368 0.000 0.000
Bending compressive stress of concrete
29.30 8.70 28.58 11.75 13.77ok ok ok ok ok
Bending tensile stress of reinforcement bar
1603.48 582.98 1602.80 980.01 1148.65ok ok ok ok ok
Bending compressive stress of reinforcement bar
398.62 62.85 383.60 115.26 135.09ok ok ok ok ok
Mean shearing stress of concrete
S/(b*j*d) 2.139 0.597 0.920 0.000 0.000ok ok ok ok ok
where, p: =As/(b*d) 0.0030 0.0021 0.0030 0.0015 0.0015p': =As'/(b*d) 0.0010 0.0014 0.0015 0.0015 0.0015
k:0.3049 0.2636 0.2997 0.2234 0.2234
Lc: =(1/2)*k*(1-k/3)+(n*p'/k)*(k-d'/d)*(1-d'/d)0.1488 0.1285 0.1526 0.1163 0.1163
j:0.8959 0.9053 0.8963 0.9188 0.9188
As: area of tensile bar 16.085 8.042 16.085 8.042 8.042
As': area of comp. bar 5.309 5.309 8.042 8.042 8.042b: unit length 100 100 100 100 100d: effective height (As) 53 38 53 53 53d': effective height (As') 7 7 7 7 7n: Young's modulus ratio 24 24 24 24 24
c = 2*Mf/(k*j*b*d2) (kgf/cm2)
s = (kgf/cm2)
m = (kgf/cm2)
={(n*p)2+2*n*p}0.5 n*p= 1 k/3
(cm2)(cm)(cm)
c = Mf/(b*d2*Lc) (kgf/cm2)
s = n*c*(1-k)/k (kgf/cm2)
s' = n*c*(k-d'/d)/k (kgf/cm2)
m = (kgf/cm2)
={n2(p+p')2+2*n*(p+p'*d'/d)}0.5n*(p+p')
=(1-d'/d)+k2*(d'/d-k/3)/{2*n*p*(1-k)}
(cm2)
(cm2)(cm)(cm)(cm)
hd
x=kd
b
As
d1
As'
d2
hd
x=kd
b
As
d1
5 - 15
5. Summary of Required Reinforcement Bar, Bar Arrangement and Stress
Side wall Invert (bottom slab)Description Abbr. Unit at bottom at H/2 at edge at middle
outside outside lower lower upper
rec.beam rec.beam rec.beam rec.beam rec.beam
Design strength of concrete 175 175 175 175 175Unit width of member b cm 100 100 100 100 100Thickness of member h cm 60 45 60 60 60Cover of Re-bar (tensile) d1 cm 7 7 7 7 7Cover of Re-bar (compressive) d2 cm 7 7 7 7 7Effective height of member d cm 53 38 53 53 53
d' cm 7 7 7 7 7
Allowable comp. stress (conc.) 60 60 60 60 60
Allowable tensile stress (R-bar) 1850 1850 1850 1850 1850
Allowable comp. stress (R-bar) 1850 1850 1850 1850 1850
Allowable shearing stress (conc.) 5.5 5.5 5.5 5.5 5.5
Yielding point of Re-bar 3200 3200 3200 3200 3200Young's modulus ratio n 24 24 24 24 24
Tensile bar required As req. 14.62 2.69 14.62 4.58 5.37
designed As 16.08 8.04 16.08 8.04 8.04(outside) (outside) (lower) (lower) (upper)
D16@125 D16@250 D16@125 D16@250 D16@250
Compressive bar required As' req. 0.00 0.00 0.00 0.00 0.00
designed As' 5.31 5.31 8.04 8.04 8.04(inside) (inside) (upper) (upper) (lower)
D13@250 D13@250 D16@250 D16@250 D16@250
Distribution bar required 2.68 1.34 2.68 1.34 1.34
(tensile side) designed As1 5.31 5.31 5.31 5.31 5.31bar size D mm 13 13 13 13 13spacing mm 250 250 250 250 250
ok ok ok ok ok
Distribution bar required 0.88 0.88 1.34 1.34 1.34
(compressive side) designed As2 5.31 5.31 5.31 5.31 5.31bar size D mm 13 13 13 13 13spacing mm 250 250 250 250 250
ok ok ok ok okFillet bar bar size D mm 13
spacing mm 250
Design bending moment Mf tf.m 12.246 1.613 12.246 3.838 4.498Design shearing force S tf 10.158 2.053 4.368 0.000 0.000Design axis force N tf 0.000 0.000 0.000 0.000 0.000
Cracking moment Mc tf.m 9.386 5.280 9.386 9.386 9.3861.7*Mf tf.m 20.819 2.742 20.819 6.524 7.647
1.7*Mf<Mc ? If no, check Mu check Mu ok check Mu ok okUltimate bending moment Mu tf.m 24.065 24.065
Mu>Mc ? ok ok
Max. Re-bar As max 106.00 76.00 106.00 106.00 106.00
Min. Re-bar As min 4.50 4.50 4.50 4.50 4.50
Required area of tensile bar As req. 14.62 2.69 14.62 4.58 5.37
Designd area of tensile bar As 16.08 8.04 16.08 8.04 8.04
Check of stress
Bending compressive ctress 30.87 9.03 30.87 12.57 14.74of concrete ok ok ok ok ok
Bending tensile stress 1605.48 580.37 1605.48 977.23 1145.40of reinforcement bar ok ok ok ok ok
Bending compressive stress - - - - - of reinforcement bar
Mean shearing stress 2.142 0.594 0.921 0.000 0.000of concrete ok ok ok ok ok
Calculation conditions
Design dimensions
ck kgf/cm2
ca kgf/cm2
sa kgf/cm2
sa' kgf/cm2
a kgf/cm2
sy kgf/cm2
Reinforcement bar
cm2
cm2
cm2
cm2
As1>As/6 cm2
cm2
<30cm, @
As2>As'/6 cm2
cm2
<30cm, @
<30cm, @
Design load
Check of minimum reinforcement bar
cm2
cm2
cm2
cm2
c kgf/cm2
s kgf/cm2
s' kgf/cm2
m kgf/cm2
