Stair case
DATA sheetBase on B.C.Punmia book RCCdesign exmpale 8.5DESIGN OF
STAIR CASE WITH CENTRAL STRINGER BEAMGenral lay out of stair
caseNote:- Red color data are theoretical calculation data where
black data are as per design data.Project name :-pknSpace available
for staire case5.20x4.40m1.402.401.40Vetical distance of
floor3.60m3600mmtreads=9width of stair
case1.40mtr1400mm1.502.251.455.20Risers0.16mtr160mmTreads0.25mtr250mmDC1.451.40Live
load4000N/m2ConreteM
-20m13.33wt.25000N/mm3scbc7N/mm2Treads=61.501.604.40Steelfy415sst230N/mm24.40Nominal
cover25mmEffective cover30mmtreads=6West slab
thickness80mmassumewidth of stringer
beam200mmReinforcementAB1.451.40Main Bars20mm FBars
Required4Nos.Anchor bars10mm FBars Required2Nos.1.501.45Waist slab
bars10mm FSapcing c/c250mm2.95Strirrups10mm FSapcing c/c90mm5.20No
of riser required =3600/160=22Space required (mm)Space required
(m)1.502.251.45No of tread required=22-1=21230No of treads
accomeded in long direction=2400/250=9x25022502.252 -10mm anchore
barsBottom of waistNo of tread accomeded in short
direction1600/250=6x25015001.5010mm f @1.50250mm c/cNo of treads
Required in other long direction=21-15=6x25015001.50stirrups 2
ldg.10mm F @25090mm c/c16010mm f @stirrups 2 ldg.250mm c/c10mm F
@Landing180mm c/c80mid span8 mm F @1.50300 mm c/cstirrups 2 ldg.L -
section10mm F @90mm c/c10mm f @250mm c/c145080mm2 -10mm f10mm f
@90mm c/cAnchor bars10mm F @180mm c/c4-20mm fstirrups 2 ldg.main
[email protected] section at mid span
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Design151152045334418402041204018401634163426DESIGN OF STAIR
CASE WITH CENTRAL STRINGER BEAMwidth of stair
case1.40mtr1400mmRisers0.16mtr160mmTreads0.25mtr250mmlive
load4000N/m2ConreteM-20Steelfy-415N/mm2Nominal cover25mmEffective
cover30mm1Design Constants:-For HYSD BarsCocrete M=20sst
==230N/mm2wt. of concrete=25000N/mm2scbc
==7N/mm3m=13.33k=m*c=13.33x7=0.289m*c+sst13.33x7+230j=1-k/3=1-0.289/3=0.904R=1/2xc
x j x k=0.5x7x0.904x0.289=0.9132Loading on waist slab:-Assume waist
slab thickness=80mmThe weight of waist slab on the slope should be
multi plied by the factorR2 +T2where R=160mm andT=250mmT=
1602+2502=1.19to get the equivalent weight of horizontal plane
.250Considered 1 m width of slab.Load per metre horizontal run will
be as follows.Self weight=0.08x1x1x25000x1.19=2380NWeight of
steps=0.5x0.161x1x25000=2000NLaoding of finishing=L.S.=100NLive
load==4000NTotal=8480NThe loading on landing will be lasser :
however , for simplicity , we will take the same loading
throught.3Design of waist slab:-the waist slab is supported on
central stringer beam . Hence the worst condition may bewhen we
considred concentrated live load of4000N to act to one side
only.Dead weight=2380+2000+100=4480NAssume width of stringer
beam=200mmProjection of slab beyond the rib of
beam=1.40-0.2=0.60mtr2B.M. due to dead
loadwL2=4480x(0.60)2=806N-m22B.M. due to U.D. live
loadwL2=4000x(0.60)2=720N-m22B.M. due to concentreted live
load=4000x0.60=2400N-mMax. B.M. M=806+2400=3206N-mEffective depth
required=BM=3206000=60mmBut available=80mmRxb0.913x1000However ,
keep minimum total depth=80mm . Efective depth=80-25=55mmAst =BM x
1000=3206000=280mm2sst x j x D230x0.904x55using10mm F
barsA=3.14xdia2=3.14x10x10=79mm24 x1004x100spacing of Bars
=A*1000/Ast=79x1000/280=280mmHowever , keep spacing=250mm , one bar
per stepDistribution reinforcement=1.2x80=96mm2using8mm F
barsA=3.14xdia2=3.14x8x8=50mm24 x1004x100spacing of Bars
=A*1000/Ast=50x1000/96=523mmMaimum permissible spacing=45x8=360mm
say300mmHowever , keep spacing=300mm, Maximum4Design of stringer
beam :-The stringer beam will act as T- beam. Flight CD is
longest,Hence we will design the stringer beam CDEffective
span=1.50-0.2+2.25+1.45=4.38m22The loading on stringer beam will be
as follows,asssuming the web to be200mm wide and200mm deep(a)
Weight of rib /m run=0.20x0.20x25000x1.19=1190N(b) Load from waist
slab=8480x1x1.50=12720NTotal=13910N say14000N/mAssuming partial
fixidity at ends,M=wL2=14000x4.382 x1000=2679687526.796875x10
6N-mm1010Taking lever arm=0.9 x d, balance depth is given by
Eq.M=0.45 bf. scbc. Df2kcd - Dwhere bf = flange width of isolated
T-Beam given byEq.kcbf=l0+bw,where lo = L=4.38m ;b = actual width
=1.50ml0+4and
bw=0.20mbbf=4.38+0.20=0.833m=833mm4.38+41.50Hence,=0.45x833x7x802x0.289d-80=267968750.289\2099162x0.289d-80=267968750.289\2d-80=127.660.289d=127.66+277.1921551817=202.00mm2Also,
d=Vewhere tc max =1.8 N/mm2 for m-20 concretebw . Tc maxVe=V+
1.6TWhere V=wL=14000x4.38=30625Nbw22T = torsional moment, which
will be induced due to live load acting only to one side of
step.T=4000x0.602 x4.38x1000=1575000N-mm22or
T=(4000x0.60)x4.4x1000=5250000N-mm2\ T=5250000which ever is
moreVe=30625+1.6x5250000=72625N200Hence, d=72625=227mmHowever, keep
total depth=230mm200x1.6using20mm main bars,10mm F ring and
cover25mmNet available d=230-10-10-25=185mmAst =BM x
1000=26796875=697mm2sst x j x D230x0.904x185using20mm F
barsA=3.14xdia2=3.14x20x20=314mm24 x1004x100spacing of Bars
=Ast/A=697/314=3Nos. Say4Actual Ast provided=4x314=1256mm2Note:-
the above reinforcement is for bending requirements only. there
will be additional longitudinal reinforcement for torsion, as
computed later.Location of N.A. Assuming the N.A. falls within the
flange, we haveb=-b +
(b2-4*a*c)0.5=833xn2=13.33x1256x(185-n)2*a2\833xn2=6194718-33484.96nN=40.1980312125-
(1615.8817133599-29747)0.5\n2=7437-40.20n2*1\n2+40.1980312125n--7437=0N=68.4mm\n=40.1980312125+
(1616+29747)0.52*1\n=68.4mmHence the resultant falls inside the
flanges y=22.8160606643mm\L.A. a=d -
y=185-22.8160606643=162.2mmStress in steel=M=26796875=132N/mm2
