Prepared by : Date : PRC # : TIN # : 2S-3 Issued On: Issued At:
STRUCTURAL ENGINEERING DESIGN and CONSTRUCTION SUPERVISION
NSCP 2010 Specification Section and Equations No.
Sheet Content : Two-Way Slab Design Date : Nov. 30, 2011
Arnel H. Sinconigue, C.E Oct. 13, 2011 116853 406-365-953-000 3/24/2011 Quezon City
Project Title : Three Storey Resedential Building Location : Brgy. Banale, Pagadian City, Zamboanga Del Sur Client : Address :
Engr. Arnel H. Sinconiegue Dagat-Dagatan, Caloocan City, Metro Manila
Design Refference : NSCP Volume 1, Fourth Edition 2010 : Design of Reinforce Concrete, 2ND Edition by Jack C. McCormac : Fundamentals of Reinforced Concrete (Using USD Method, NSCP 2001) by Besavilla A. Design Criteria Materials : 28.00 28.00 413.00 24870.00
Modulus of Elasticity forslab, Ebs =
24870.00 Mpa 3 24.00 KN/m
Unit Weight of Concrete, Ȣc = Compressive block deep, β1 = Capacity Reduction factor, Ф =
Mpa Mpa Mpa Mpa
0.85 0.90
Dead Load : 1. Floor Finish Ceramic Tile = Water Proofing =
0.80 Kpa 0.10 Kpa
2. Ceilling Suspended Steel Channel = Electrical Wirings =
0.20 Kpa 0.30 Kpa
3.ConcreteHollow Blocks CHB 4" = CHB 6" =
2.10 Kpa 2.73 Kpa
4. Partition Load Parttion =
1.00 Kpa
Live Load : Residential =
2.00 Kpa
B. Design Data Long Span, L = Short Span, S = Beam width, b = Beam Deep, d =
3.00 3.00 250.00 400.00
m m mm mm
C. Design of Thickness
C
B
250 x 400
250 X 400 A
250 x 400
410.3.7.3 409.4.2.1
Compressive strenght for slab,fc' = Compressive strenght for beam, fc' = Yeild strenght, fy = Modulus of Elasticity for beam, Ebb =
3.00
D
250 x 400 3.00
SIDE A = DISCONTINOUS EDGE SIDE C = DISCONTINOUS EDGE
C-1.
Type of Slab when S/L =
C-2.
1.00
Two-Way Slab
Calculation for slab thickness Assumed Thickness for Design Purposes, h =
100.00 mm
Check if αm is greater than 2 Beam A
y x h
A1
d a A2
a
b
h
e
Dimension : h= a= b= d= e=
100.00 300.00 250.00 400.00 1625.00
mm mm mm mm mm
Centroid :
A2 =
2 30000.00 mm 2 mm 100000.00
AT =
2 130000.00 mm
A1 =
By Varignon's Theorem AT(y) = A1(h/2) + A2(d/2) y=
165.38 mm
Calculation of the Moment of Inertia Ib = ((a*h^3/12 + A1*(y-h/2)^2)) + ((b*d^3/12 + A2*(d/2 -y)^2)) 4 1877564102.56 mm
Ib = Is =
4 135416666.67 mm
e*h^3/12
Beam B
h
A1
A2
d
a A3
a
b
a
h e
Dimension :
h= a= b= d= e=
100.00 300.00 250.00 400.00 3000.00
mm mm mm mm mm
Centroid : 2 30000.00 mm 2 30000.00 mm
A1 = A2 = A3=
2 100000.00 mm
AT =
2 160000.00 mm
By Varignon's Theorem AT(y)= A1(h/2) + A2(h/2) + A3(d/2) y=
143.75 mm
Calculation of Moment of Inertia Ib = ((a*h3/12) + A1(y-h/2)2) + ((a*h3/12) + A2(y-h/2)2) + ((b*d3/12) + A3(d/2 - y)2) 4 2227083333.33 mm
Ib =
4 250000000.00 mm
Is = e*h^3/12 Beam C
y x h
A1
d a A2 a
b
h
e Dimension : h= a= b= d= e=
100.00 300.00 250.00 400.00 1625.00
mm mm mm mm mm
Centroid :
A2 =
2 30000.00 mm 2 100000.00 mm
AT =
2 130000.00 mm
A1 =
By Varignon's Therem AT(y) = A1(h/2) + A2(d/2) y=
165.38 mm
Calculation of Moment of Inertia Ib = ((a*h^3/12) + A1*(y-h/2)^2)) + ((a*h^3/12) + A2*(d/2 - y)^2)) Ib = Is = e*h^3/12
4 1877564102.56 mm 4 135416666.67 mm
Beam D
h
A1
A2
d a A3
a
b
a
h e Dimension : h= a= b= d= e=
100.00 300.00 250.00 400.00 3000.00
mm mm mm mm mm
Centroid :
A2 =
2 30000.00 mm 2 30000.00 mm
A3 =
2 100000.00 mm
AT =
2 160000.00 mm
A1 =
By Varignon's Theorem AT(y) = A1(h/2) + A2(h/2) + A3(d/2) y=
143.75 mm
Calculation of Moment of Inertia Ib = ((a*h3/12) + A1(y-h/2)2) + ((a*h3/12) + A2(y-h/2)2) + ((b*d3/12) + A3(d/2 - y)2) Ib = Is = e*h^3/12
409.1
409.1
Eqn. (409-13)
4 250000000.00 mm
Calculation of ratio of flexural stiffness of beam section to flexural stiffness of a width of a slab bounded laterally by center line of adjacent panel (if any) on each side of beam.
αA
= Eb*Ib/Es*Is
13.87
αB
= Eb*Ib/Es*Is
8.91
αC
= Eb*Ib/Es*Is
13.87
αD
= Eb*Ib/Es*Is
8.91
Average value for α for all beams on edges of a panel.
αm = (αA + αB + αC + αD)/4 409.6.3.3
4 2227083333.33 mm
11.39
Greater than 2, use Eqn.(409-13)
Since the average value is greater than 2, the thickness shall not be less than
hmin = ((ln(0.8+fy/1400))/(36 + 9β) ln = L-b β = L/s
therefore used thickness.h =
66.92 2750.00 1.00
90.00 mm
Non-Compliant
D. Design of Reinforcement by (COEFFICIENT METHOD)
Remarks
D-1.Calculation of Loadings Consideirng 1m strip, b =
1.00 m
Dead Loads :
426.409.2.1 426.409.2.1
Partition = Floor Finish = Ceiling = C.H.B wall = Selfweigth =
1.00 0.90 0.50 0.00 2.16
Kpa Kpa Kpa Kpa Kpa
DL = Live Load : LL =
4.56 Kpa
DLU = 1.4DL LLU = 1.7 LL
6.38 Kpa 3.40 Kpa
2.00 Kpa
Ultimate Load (considering 1m strip) W U = DLU + LLU
9.78 KN/m
D-2. Type of Slab m = Ls/Lb
1.00
Two-Way Slab
Coefficient for Negative Moment in Slab Ca neg. =
0.05000
Short Direction
Cb neg. =
0.05000
Long Direction
0.02700 0.02700
Short Direction Long Direction
Ca. LL =
0.03200
Short Direction
Cb.LL =
0.03200
Long Direction
D-3. Case Number : Case 4
Coefficients for Dead-Load Pos. Moments in Slab Ca. DL = Cb. DL = Coefficient for Live-Load Pos. Moment in Slab
D - 4. Negative Moment at Continous Edges Ms = Ca. neg*Wu*Ls^2
4.40 KN.m
Mb = Cb. Neg*Wu*Lb^2
4.40 KN.m
D - 5. Positive Moment along Short Direction Ms. DL = Ca.DL* DLu * Ls^2
1.55 KN.m
Ms. LL = Ca.LL * LLu * Ls^2
0.98 KN.m
MTs =
2.53 KN.m
D - 6. Positive Moment along Long Direction Mb. DL = Cb. DL*Dlu*Lb^2
1.55 KN.m
Mb. LL = Cb. LL*LL.u*Lb^2
0.98 KN.m
MTb =
2.53 KN.m
D - 7. Design of reinf. Spacing along short direction (mid-span)
Mu = Ф*fc'*b*ds^2*ω*(1-0.59ω) where : Mu = cc = ø= ds = h - cc - ø/2 b= 4.40*1000*1000 = 0.90*28*1000*74^2*ω(1-0.59ω) ω2 - 1.69ω + 0.0723 = 0 By Quadratic Equation :
4.40 20.00 12.00 64.00 1000.00
KN.m mm mm mm mm
a= b= c=
1.00 -1.69 0.0723
ω = (- b ± SQRT(b2 - 4ac))/2a
0.0439
Calculation of actual steel ratio, ρact ρact = ω*fc'/fy
0.00298
Non-Compliant
0.00339
Use for design
Calculation of min. steel ratio, ρmin ρmin = 1.4/fy Calculation of max. steel ratio, ρmax ρb = 0.85*β1*fc'*600/fy(fy+600)
0.02901
ρmax = 0.75*ρb
0.02176
Therefore used, ρact =
0.00339
Compliant
Calculation of steel area, As 2 216.95 mm
As = ρact*b*d Calculation for reinf. Spacing Use steel dia. D = 2
S = 1000*π*D /(4*As)
12.00 mm 521.00 mm
Spacing limits for Slab Reinforcement
407.7.5 407.7.5
s>h s < 3*h s < 450
90.00 mm 270.00 mm 450.00 mm
Design Spacing, S =
270.00 mm
D - 8. Design of reinf. Spacing along short direction (continous-edges)
Mu = Ф*fc'*b*ds^2*ω*(1-0.59ω) where : Mu = cc = ø= ds = h - cc - ø/2 b=
2.53 20.00 12.00 64.00 1000.00
KN.m mm mm mm mm
2.53*1000*1000 = 0.90*28*1000*74^2*ω(1-0.59ω) ω2 - 1.69ω + 0.04155 = 0 By Quadratic Equation : a= b= c=
ω = (- b ± SQRT(b2 - 4ac))/2a
1.00 -1.69 0.0416
0.0250
Calculation of actual steel ratio, ρact ρact = ω*fc'/fy
0.00169
Non-Compliant
0.00339
Use for Design
Calculation of min. steel ratio, ρmin ρmin = 1.4/fy Calculation of max. steel ratio, ρmax ρb = 0.85*β1*fc'*600/fy(fy+600)
0.02901
ρmax = 0.75*ρb
0.02176
Therefore used, ρact =
0.00339
Compliant
Calculation of steel area, As 2 216.95 mm
As = ρact*b*d Calculation for reinf. Spacing Use steel dia. D = 2
S = 1000*π*D /(4*As)
12.00 mm 521.00 mm
Spacing limits for Slab Reinforcement
407.7.5 407.7.5
s>h s < 3*h s < 450
90.00 mm 270.00 mm 450.00 mm
Design Spacing, S =
270.00 mm
D - 9. Design of reinf. Spacing along long direction (mid-span)
Mu = Ф*fc'*b*ds^2*ω*(1-0.59ω) where : Mu = cc = ø= ds = h - cc - Ø - Ø/2 b=
4.40 20.00 12.00 52.00 1000.00
KN.m mm mm mm mm
4.40*1000*1000 = 0.90*28*1000*74^2*ω(1-0.59ω) ω2 - 1.69ω + 0.10951 = 0 By Quadratic Equation : a= b= c= ω = (- b ± SQRT(b2 - 4ac))/2a
1.00 -1.69 0.10951 0.06750
Calculation of actual steel ratio, ρact ρact = ω*fc'/fy
0.00458
Compliant
0.00339
Use actual steel ratio for Design
Calculation of min. steel ratio, ρmin ρmin = 1.4/fy Calculation of max. steel ratio, ρmax ρb = 0.85*β1*fc'*600/fy(fy+600)
0.02901
ρmax = 0.75*ρb
0.02176
Therefore used, ρact =
0.00458
Compliant
Calculation of steel area, As As = ρact*b*d
2 237.96 mm
Calculation for reinf. Spacing Use steel dia. D = S = 1000*π*D2/(4*As)
12.00 mm 475.00 mm
Spacing limits for Slab Reinforcement
407.7.5 407.7.5
s>h s < 3*h s < 450
90.00 mm 270.00 mm 450.00 mm
Design Spacing, S =
270.00 mm
D - 10. Design of reinf. Spacing along long direction (continous-edges) Mu = Ф*fc'*b*ds^2*ω*(1-0.59ω) where : Mu = cc = ø= ds = h - cc - Ø/2 b=
2.53 20.00 12.00 64.00 1000.00
KN.m mm mm mm mm
2.53*1000*1000 = 0.9*28*1000*74^2*ω*(1-0.59ω) ω2 - 1.69ω + 0.04155 = 0 By Quadratic Equation : a= b= c=
1.00 -1.69 0.04155
ω = (- b ± SQRT(b2 - 4ac))/2a
0.02496
Calculation of actual steel ratio, ρact ρact = ω*fc'/fy
0.00169
Non-Compliant
0.00339
Use for Design
Calculation of min. steel ratio, ρmin ρmin = 1.4/fy Calculation of max. steel ratio, ρmax ρb = 0.85*β1*fc'*600/fy(fy+600)
0.02901
ρmax = 0.75*ρb
0.02176
Therefore used, ρact =
0.00339
Compliant
Calculation of steel area, As 2 216.95 mm
As = ρact*b*d Calculation for reinf. Spacing Use steel dia. D = 2
S = 1000*π*D /(4*As)
12.00 mm 521.00 mm
Spacing limits for Slab Reinforcement
407.7.5 407.7.5
s>h s < 3*h s < 450
90.00 mm 270.00 mm 450.00 mm
Design Spacing, S =
270.00 mm
E . Design Summary For short direction the reinforcement spacing :
Ø12mm spaced @
270.00 mm
For long direction the reinforcement spacing :
Ø12mm spaced @
270.00 mm
