ω=(16*Q/π)/((Dx/Lx4)+(2H/(Lx2*Ly2))+(Dy/Ly4)) ω = 13.09 mm Long Term Deflection Ltdefl. = 3*ω Ltdefl. = 39.28 mm
span/deflection (Clause 23.2 IS 456) s/d = 56.00 mm Maximum deflection including long term effects is within permissible limits i.e. Ltdefl < s/d ratio
Maximum Moment & Shear Values Max Bending Moments Mx=Dx*(π/Lx)2*ω
My=Dy*(π/Ly)2*ω
Mx = 206 KN-m
My = 206 KN-m
Max Torsional Moments Mxy=(Cx*π2*ω1)/(Lx*Ly) Mxy = 7 KN-m Shear Force Qx=[(Dx*(π/Lx)3)+(Cy*(π3/(a*b2)))]*ω
Qy=[(Dy*(π/Ly)3)+(Cx*(π3/(b*a2)))]*ω
Qx = 48 KN
Qy = 48 KN
Staircase Design
Data Effective Span (l) Riser (R) Thread (T) Waist Slab thickness (t) Clear Cover Effective Depth of Waist Slab (d)
5.00 mm 150 mm 300 mm 150 mm 15 mm 135 mm
Grade of Concrete (fck) Grade of Steel (fy)
20 MPa 415 MPa
Loading Loads on going Self weight of waist slab Self weight of steps Live Load Floor Finish Load Total Load Factored Load
Loads on waist slab Self weight of landing slab Live Load Floor Finish Load Total Load Factored Load
0.80 from IS Code 0.90 manual Calculation Effective Length to be considered from Manual Calculation Effective Length (le) lex Ley 7425 7425 Slenderness Ratio le/D 8 Short Column le/b 37 Slender Column Moment due to Slen Muax 0 Muay 372 Min Ecc
ex ey Moment due to ecc
G
46.5 23.2 Mux Muy
125.55 62.55
Asc
2.18 3924
Puz
2841
Reduction of Moments Percentage assumed
x-x y-y
k1 0.219 0.184
Kx Ky
0.06 0.06
Additional Moments due to ecc
Modified Initial Moments
K2 0.096 -0.022
Max May
Mux Muy
Pb 367 291
0 21
3.6 70.6
Summary of Moments A Moment due to eccentricity + Modified additional moments Mux 126 Muy 83 B
Thickness of footing base slab Length of base slab or
tb = 0.08 * (h + hs)
iii)
L = 1.5 * √(Ca/3) * (h + hs) L = 0.6h to 0.65h
Proposed -
Adopted 0.20 meters
0.24 meters 1.61 meters 2.09 meters
0.30 meters
iv) Extra Height of Retaining Wall due to Surcharge
hs = Ws/γs
0.22 meters
v)
Hs = h+hs
3.22 meters
vi) Extra Height of RW due to inclined back fill
hi = (L-ts)* tanӨ
0.00 meters
vii) Total Height of RW due to inclined back fill
Hi = h+hi
3.00 meters
Total Height of Retaining Wall due to Surcharge
viii) Design Height of RW considered H = Max of H1 & H2
4
2.00 meters
3.22 meters
Stability against Overturning i)
Active pressure due Surcharge Load
Pa1 = Ca*Ws*h
4 KN
ii)
Active pressure due Backfill Load
Pa2 = Ca*γs*h2 / 2
27 KN
iii)
Total Load on stem
Pa = Pa1 + Pa2
31 KN
iv)
Overturning Moment
v)
Mo= (Pa1 * h/2) +(( Pa2*CosӨ)* h/3)
Load
33 KNm
Lever arm from end of stem
Moment
W1 Backfill Load W2 Surcharge Load
= (L-ts)*(h-tb)*γs
87 KN
(L-ts) / 2
0.90 meters
79 KNm
= Ca*Ws*h
4 KN
(L-ts) / 2
0.90 meters
4 KNm
W3 Inclined Backfill Load W4 Stem self weight
= ((L-ts)*hi)/2*γs
0 KN
(L-ts) / 3
0.60 meters
0 KNm
= ts*(h-tb)*γconc
14 KN
(L- (ts/2))/2
0.95 meters
13 KNm
W5 Base self weight W6 Downward component
= L*tb*γconc
15 KN
L/2
1.00 meters
15 KNm
= Pa*sinӨ
0 KN
0 KNm
W6 Other Load ∑W
xw=∑Mw/∑W
vi) Distance of Resultant Vertical Force from end of heel
viii) Factor of Safety against OVERTURNING (FS)OT = 0.9 * (Mr/Mo)
3.54 > 1.4
Safe against Overturning
Stability against Sliding i) Sliding Force ii) Resisting Force iii)
Pa*CosӨ F = µ*∑W
Factor of Safety against SLIDING (FS)SL=0.9*(F/(Pa*CosӨ))
1.74 > 1.4
iv) Shear key Design
Distance from stem Heigth of exacavation
x y z h1
0.00 meters 0.00 meters 0.00 meters
Heigth of exacavation
h2 = h1 + y + (z * tanØ)
0.00 meters
e)
Passive Pressure
Pp = Cp*γs*(h12-h22) / 2
0 KN
v)
Revised Factor of Safety against SLIDING (FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))
Shear Key Size
b) c) d)
0.00 meters
1.74 > 1.4
Safe against Sliding
6
Soil Pressures at footing base ∑W = R i) Resultant Vertical Reaction ii) Distance of R from heel Lr = (Mw+Mo)/R iii) Eccentricity e = Lr- L/2 Eccentricity lies within middle third of the base hence OK iv) Pressure Distridution on soil
qmax = R/L * (1+(6*e/L))
qmin = R/L * (1-(6*e/L)) Max Pressure qmax
Pressure at junction of stem and q =q -((q -q )/L)*t ) sh max max min s heel
31 KN 60 KN
Safe against Sliding
Shear Key not required
a)
0.92 meters
Mr =∑W * (L - xw)
vii) Stabilizing Moment
5
0 KNm 110 KNm
∑Mw
120 KN
120 KN 1.19 meters 0.19 meters
95 KN/sqm 25 KN/sqm
88 KN/sqm
130 KNm
DESIGN OF L Shaped Cantilever RETAINING WALL 1
Preliminary Data i) Height of Retaining Wall ii) Soil Density iii) SBC iv) Angle of repose
Soil Pressures at footing base Mn = Mw - Mo 105 KN i) Net Moment at toe 0.77 meters ii) Point of application of Resultant R x = Mn/W 0.33 meters iii) Eccentricity e = (L/2) - x e
Moment 126 KNm
= ((L-ts)*hi)/2*γs
∑W
6
0.30 meters 2.20 meters
tb = 0.08 * (h + hs)
vi) Overturning Moment
5
Adopted 0.20 meters
ii) Thickness of footing base slab iii) Length of base slab
viii) Design Height of RW considered H = Max of H 1 & H2
4
Proposed min 200mm
qsh=qmax-((qmax-qmin)/L)*ts)
107 KN/sqm
L/6= 0.37
0 KNm
7
Constants for Working Stress Method Design Constants i) Grade of concrete ii) Grade of steel iii) iv) v) vi) vii) viii)
8
20 MPa 415 MPa
Compr stress in concrete Tensile stress in steel Modular ratio Neutral axis depth factor Lever arm Factor
c t m = 280/3c k=mc/(mc+t) j = 1 - k/3 R= cjk / 2
7.0 230 13.33 0.289 0.904 0.913
table 21 page 81 IS 456
Design A) Stem i) Beanding Moment at base of stem M = MODL + MOIL ii) Thickness required iii) Thickness provided
40 KN/m
dreq=√(Ms/(R*b)
0.01 meters 0.20 meters
ts Thickness of Stem is OK Ast = M/(t*j*tse)
iv) Ast required v) Ast provided vi) Percentage of Steel
1387 sqmm 1608 sqmm 0.99 %
16 mm dia @ 125 mm c/c pt = Ast/(b*d) Steel OK
B) Base Slab Force i) Force due to backfill+surcharge
α = 1 - (q0/2.7*γs*H) L = H*sqrt((Ca*cosβ)/((1-α)*(1+3α)) α = 1 - (q0/2.2*γs*H) L = 0.95*H*sqrt((Ca)/((1-α)*(1+3α)) L = 0.6h to 0.65h
-0.60 meters 0.00 meters
iv) Extra Height of Retaining Wall due to Surcharge
hs = Ws/γs
0.22 meters
v)
Hs = h+hs
3.22 meters
vi) Extra Height of RW due to inclined back fill
hi = (L-ts)* tanӨ
0.00 meters
vii) Total Height of RW due to inclined back fill
Hi = h+hi
3.00 meters
i)
Thickness of Stem
ts
ii)
Thickness of footing base slab
iii) Length of base slab
if sloped backfill if horizontal backfill
Total Height of Retaining Wall due to Surcharge
-0.96 meters 0.00 meters 2.09 meters
viii) Design Height of RW considered H = Max of H1 & H2
4
3.22 meters
Stability against Overturning i)
Active pressure due Surcharge Load
PHS = Ca*Ws*h
4 KN
ii)
Active pressure due Backfill Load
PH = Ca*γs*h2 / 2
31 KN 35 KN
iii) Total Load on stem (Force)
Pa = PHS + PH
iv) Overturning Moment due to Imposed load
MOIL = PHS*h/2
7 KN
v)
MODL = PH*h/3
33 KN
Mo = (1.2*MDIL) + (1.4*MOIL)
50 KN
Overturning Moment due to Backfill load
vi) Overturning Moment
v) Load W1 Front fill Load W3 Stem self weight W4 Base self weight W5 Other Load
= (L-ts)*(hp-tb)*γs
2 KN
Lever arm at start of heel ((L-ts) / 2) 1.13 meters
Moment 2 KNm
= ts*(h-tb)*γconc
14 KN
(ts/2) + (L-ts)
2.35 meters
33 KNm
= L*tb*γconc
28 KN
L/2
1.23 meters
34 KNm
PT Beam Load
0 KN 43 KN
∑W viii)
5
2.45 meters
Mw not less than (1.2*MODL) +(1.4*MOIL) -clause 20.1 page 33 of IS 456 2000
∑Mw Safe against Overturning
Stability against Sliding i) ii)
Sliding Force Resisting Force
iii)
(FS)SL= (0.9*F)/(Pa) -clause 20.2 page 33 of IS 456 2000
5a
Pa = PHS + PH F = µ*∑W 0.55 < 1.4
Unsafe against Sliding
Shear key Design x y z h1
0.30 meters 0.30 meters 0.30 meters
Heigth of earth mobilization
h2 = h1 + y + (z * tanØ)
1.07 meters
e)
Passive Pressure
Pp = Cp*γs*(h12-h22) / 2
21 KN
v)
Revised Factor of Safety against SLIDING
a)
Shear Key Size
b) c)
Distance from stem Heigth of exacavation
d)
0.60 meters
35 KN 22 KN
69 KNm
v)
(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))
1.09 > 1.4 Unsafe against Sliding. Shear Key Required
6
Soil Pressures at footing base Mn = Mw - (MOIL+MODL) 28 KN i) Net Moment at toe 0.65 meters ii) Point of application of Resultant R x = Mn/W 0.58 meters iii) Eccentricity e = (L/2) - x e>L6 Eccentricity lies outside the middle third of the base. Revise the base dimensions iv) Pressure Distridution on soil
