PROJECTMARK

p2 p1A

Design of Scissor Stair -U type

Flight length L1 (m) = 2.8 mMidlanding L2 (m) = 2.7 m B t1>L1/30= 0.09

h (m) 1.5 m CWidth of the stair section, b b 1.4 m t2 > L2/20= 0.135

c 0.1 mflight thickness t2 0.14 m hmid landing thickness t1 0.1 m >1/30*L1

athread 0.3 m A' L2 L1/2Riser 0.15 mMax. thickness of finishes = 0.00 mAve thickness of slab incl finishes = 0.21 m

a 0.51 rad. 29.05 deg

Loadings flight landingKN/m2 kN/m KN/m2 kN/m

Self weight +ave steps = 5.18 5.92 8.29 2.50 3.63brickwall/railing = 0.00 0.00 0.00 0.00 0.00Finishes = 1.65 1.89 2.64 1.23 1.78

1.2 6.83 7.81 10.93 3.73 5.41Live Loads = 2.00 2.00 2.80 2.00 2.90

1.4 p2 p1Ulimate Loads = 12.17 17.04 7.28 10.55

`Analysis

I1 = 1/12(b+c/2)t1^3 = 0.000121 m4I2 = 1/12(b)t2^3 = 0.00032 m4

u1 = 0.5*I1*L2/(0.5*I1*L2+I2*L1cos a) 0.5I1*L2= 0.000163= 0.172 I2*L1cos a = 0.000784

u2 = 0.828

1. Factored Forces due to loading , p1 at landing p1R1 = 14.77 kN H1 AH1 = p1*l1^2/(12h)*(1+6*L2/L1-u1-0.5u2)

= 28.49 kNH1(dl) = 17.53 R1

landing Mc1 = (1+2u1)/24 *p1*L1^2 B H1= 4.63 kN.m B C

Mc1(dl) = 2.9 kN.m

Nc1 = -H1 = -28.49 kN hNc1 (dl) = -17.53 kNVc1 = 0 a

A' L2 L1/2MB1 = -u2*P1*L1^2/12

= -5.71 kN.mMB1 (dl) = -3.51 kN.m

Nb1=Nc1 = -28.49 kNNB1(dl) = -17.53 kNVB1 = -14.77028

flight MB1 = -5.71 kN.mMB1 (dl) = -3.51 kN.m

NB1 = -(p1*L1/2sin a + H1*Cos a )= -32.08 kN

NB1 (dl) = -19.73 kNVB1 = 0.9235MA1 = u2*p1*L2/24

= 2.85 kN.m

MA1 (dl) = 1.75 kN.m

NA1=NB1 = -32.08 kNNA1(dl) = -19.73 kNVA1 = 0.9235

p22.Factored Forces due to loading , p2 at flight

R2 = 46.0 H1H2 = p2*L2^2/12/h*(5-u1-0.5u2)

= 30.46 kNH2 (dl) = 23.45 R1

Landing Mc2 = -u1*p2*l2^2/12 B H1= -1.78 kN.m B C

Mc2(dl) = -1.37 kN.m

Nc2 = -H2 = -30.46 kN hNc2(dl) = -23.45 kNVc2 = 0 aMB2=Mc2 = -1.78 kN.m A' L2 L1/2MB2 (dl)= Mc2 = -1.37 kN.mNB2 =Nc2Vb2 = 0

Flight MB2 = -u2*p2L2^2/12= -8.57

MB2 (dl) = -6.60

NB2 = -H2sin a= -14.79

NB2 (dl) = -11.39VB2 = -14.79358MA2 = -(2+u2)/24*p2*L2^2

= -14.64MA2 (dl) = -11.27

NA2=NB2 = -(R2sin a + H2cos a)-48.97

NA2(dl) = -38.34VA2 = -25.426

LANDING FLIGHTC B B A

M N V M N V M N V M N V1 p1 4.63 -28.49 0.00 -5.71 -28.49 -14.77 -5.71 -32.08 0.92 2.85 -32.08 0.922 dl 2.85 -17.53 0.00 -3.51 -17.53 -9.09 -3.51 -19.73 0.57 1.75 -19.73 0.573 p2 -1.78 -30.46 0.00 -1.78 -30.46 0.00 -8.57 -14.79 -14.79 -14.64 -48.97 -25.434 dl -1.37 -23.45 0.00 -1.37 -23.45 0.00 -6.60 -11.39 -11.39 -11.27 -38.34 -19.91

1+3 2.85 -58.95 0.00 -7.49 -58.95 -14.77 -14.27 -46.87 -13.87 -11.78 -81.05 -24.501+4 3.26 -51.94 0.00 -7.08 -51.94 -14.77 -12.30 -43.47 -10.47 -8.42 -70.42 -18.982+3 1.07 -47.99 0.00 -5.29 -47.99 -9.09 -12.08 -34.53 -14.23 -12.88 -68.71 -24.86

DESIGN1. Landing Mmax at B -7.49 kN.m -7488877 N.mm

N -58.95 kN -58950.06 Nrebar dia 0.016 m 16 mmCheck M/N 0.127 m > e 127.0377 mme = t1/2-dia/2-cov 0.017 m

Mt +eN -8.491 kN.m -8491028 N.m

fcu 20 N/mm2fy 210cover 0.025 m 25 mmt1 0.1 m 100 mmd 0.075 75 mm

width 1.45 1450 mmk = 0.052 m per m widthz = 0.94 * ds

= 71 mmAs = 652 mm2/mAs prov = 832 mm2/m OK

For b+c/2 As = 1206 mm2 6 T 16@ 240

2. Flight Mmax at A -12.88 kN.m -1.3E+07 N.mmN -81.05 kN -81048.92 N

Ecc= 0.02 m 20 mmCheck M/N 0.159 m > e 158.9352 mme = t1/2-ecc -0.02 m

Mt +eN -11.261 kN.m -1.1E+07 N.m

fcu 20 N/mm2fy 210cover 0.025 m 25 mmt1 0.14 m 140 mmd 0.115 115 mmwidth 1.4 1400 mmk = 0.030 per m widthz = 0.95 * ds

= 109 mmAs = 564 mm2/mAs prov = 718 mm2/m OK

For b As = 1005 mm2 5 T 16@ 300

PROJECTMARK

p2 p1A

Design of Scissor Stair - Z type

Flight length L1 (m) = 0.9 mMidlanding L2 (m) = 2.52 m B t1>L1/30= 0.03

h (m) 1.75 m CWidth of the stair section, b b 1.5 m t2 > L2/20= 0.126

c 0.2 mflight thickness t2 0.15 m hmid landing thickness t1 0.15 m >1/30*L1

athread 0.28 m A' L2 L1/2Riser 0.16 mMax. thickness of finishes = 0.12 mAve thickness of slab incl finishes = 0.34 m

a 0.61 rad. 34.78 deg

Loadings flight landingKN/m2 kN/m KN/m2 kN/m

Self weight +ave steps = 8.49 10.33 15.50 3.75 6.00brickwall/railing = 7.80 7.80 11.70 7.80 12.48Finishes = 0.00 0.00 0.00

1.4 16.29 18.13 27.20 11.55 18.48Live Loads = 5.00 5.00 7.50 5.00 8.00

1.6 p2 p1Ulimate Loads = 33.38 50.08 24.17 38.67

`Analysis

Ix1 = 1/12(b+c/2)t1^3 = 0.00045 m4Ix2 = 1/12(b)t2^3 = 0.000421875 m4It2 = Xbt2^3 = 0.001581188 m4

ξ1 =Eix2/EIx1) = 0.9375ξ2 =Eix2/GIt2) = 0.635 where G = 0.42E

(b+c)/2 = 0.85

δ11 = 0.333*h^2*L2+ξ2*(b+C)/2^2sin^2a L23.015213742

δ22 = ξ2L2 Cos^2 a 0.821371.080013195 0.570396

δ33 = L2 + 0.5ξ1L1cos a2.866515454

δ44 = 0.25ξ2L1L2sin(a)^20.295316108

δ12 = δ21 = -(b+c)/2 ξ2 L2 sin a cos a-0.637507789

δ13 = δ31 = -0.5L2*h-2.205

δ14 = δ41 = 0.5*(b+c)/2*ξ2*L1*L2*sin^2a 0.199221184

δ23 = δ32 = δ34 = δ43 = 0

δ24 = δ42 = -0.5*ξ2*L1L2sin(a)cos(a)-0.337504123

∆1p1 = -1/48*p1*L1L^2*(3L1+8L2)tan(a)-73.09921626

∆2p1 = ∆4p1 = 0

∆3p1 = 1/48*ξ1p1L1^3cos(a)+1/8*p1L1L2(2L2+L1)65.57552632

∆1p2 = -1/8*p2L2^4*tan(a)-175.3039724

∆2p2 = ∆4p2 = 0∆3p2 = 1/6*p2L2^3

133.5649314

3.015214 -0.637508 -2.205 0.199221184 X1 -73.09922 + -175.304-0.637508 1.080013 0 -0.337504123 X2 = - 0 + 0

-2.205 0 2.866515 0 X3 65.57553 + 133.56490.199221 -0.337504 0 0.295316108 X4 0 + 0

1.060713 0.626115 0.815928 0 248.4032 X1 = 101.0001 kN0.626115 1.809893 0.481624 1.646070424 0 = X2 = 59.61809 kN.m0.815928 0.481624 0.976489 -1.51036E-16 -199.1405 X3 = 8.220663 kN

-2E-16 1.64607 -1.51E-16 5.267425356 0 X4 = -1.94E-14 kN.m

MA = X1*h-X3-p1*L1/8(L1+4L2)-1/2*p2L2^2)-38.2 kN.m

NA = -x1cos(a)-(p1L1/2+p2L2)sin(a)-164.9 kN in tension

Mc = -X3-8.2 kN.m

VA = x1sin(a)-(p1L1/2+p2L2)cos(a)175.6 kN

fcu = 35fy = 460cover = 30

1. Flighte0 = M/N

0.231982747 m = 231.9827 mm> t2/2-cover-dia/2 0.037 = 37 mm

rebar = 0.016 m = 16 mm

in tension MA+Ne = -38.24603074 + -6.100036-44.34606688

width 1.5 md 112 mmk 0.06733793z 0.92 d

102.8770616 mmAs = 1077 mm2/mAs prov = 1206 mm2/m OK

For b As = 1810 mm2 9 T 16@ 128

Shear stress v = 0.78025204 N/mm2100As/b/d = 1.077117481400/d = 3.571428571vc = 0.996302365 N/mm2 shear link is not required

2. Landing Mc = -8.220662596 kN.m

width 1.7 md 114 mmk 0.010631148z 0.95 d

108.3 mmAs = 190 mm2/mAs prov = 399 mm2/m OK

For b+c/2 As = 679 mm2 6 T 12

2b+c As = 1357 mm2 12 T 12@ 280

from reynoldsX = 1/3-3.36/16*t/b*(1-(t/b)^4/12)

from 6-6 b/t 1 1.5 1.75 2 2.5 3 4 6 8 10 ###X 0.141 0.196 0.214 0.229 0.249 0.263 0.281 0.299 0.307 0.313 0.333ξ 1.4072 1.0123 0.9272 0.8664 0.7968 0.7544 0.7061 0.6636 0.6463 0.6339 0.5958η 1 0.4444 0.3265 0.25 0.16 0.1111 0.0625 0.0278 0.0156 0.01 01 0 0 0 0 0 0 0 0 0 0 0.3332 0 0 0 0 0 0 0 0 0 0.313 0

b1 1.6 b1/t1 10.667 X 0.3136t1 0.15 ξ 0.6326 1/5.04x

b 1.5 b/t2 10 X 0.3123t2 0.15

u1 = 0.5*I1*L2/(0.5*I1*L2+I2*L1cos a) 0.5I1*L2= 0.0006= 0.645 I2*L1cos a = 0.0003

u2 = 0.355

1. Factored Forces due to loading , p1 at landing p1R1 = 17.40 kN H1 AH1 = p1*l1^2/(12h)*(1+6*L2/L1-u1-0.5u2)

= 25.32 kNH1(dl) = 16.94 R1

landing Mc1 = (1+2u1)/24 *p1*L1^2 B H1= 2.99 kN.m B C

Mc1(dl) = 2.0 kN.m

Nc1 = - = -25.32 kN hNc1 (dl) = -16.94 kNVc1 = 0 a

A' L2 L1/2MB1 = -u2*P1*L1^2/12

= -0.93 kN.mMB1 (dl) = -0.62 kN.m

Nb1=Nc = -25.32 kNNB1(dl) = -16.94 kNVB1 = -17.4

flight MB1 = -0.93 kN.mMB1 (dl) = -0.62 kN.m

NB1 = -(p1*L1/2sin a + H1*Cos a )= -30.73 kN

NB1 (dl) = -20.56 kNVB1 = 0.1510MA1 = u2*p1*L2/24

= 0.46 kN.mMA1 (dl) = 0.31 kN.m

NA1=NB= -30.73 kNNA1(dl) = -20.56 kNVA1 = 0.1510

p22.Factored Forces due to loading , p2 at flight

R2 = 126.2 H1H2 = p2*L2^2/12/h*(5-u1-0.5u2)

= 63.26 kNH2 (dl) = 48.10 R1

Landing Mc2 = -u1*p2*l2^2/12 B H1= -17.10 kN.m B C

Mc2(dl) = -13.00 kN.m

Nc2 = - = -63.26 kN hNc2(dl) = -48.10 kNVc2 = 0 aMB2=Mc= -17.10 kN.m A' L2 L1/2MB2 (dl)= Mc2 = -13.00 kN.mNB2 =Nc2Vb2 = 0

Flight MB2 = -u2*p2L2^2/12= -9.40

MB2 (dl) = -7.15

NB2 = -H2sin a= -36.08

NB2 (dl) = -27.44VB2 = -36.08MA2 = -(2+u2)/24*p2*L2^2

= -31.20MA2 (dl) = -23.73

NA2=NB= -(R2sin a + H2cos a)###

NA2(dl) = -59.06

VA2 = -67.57

LANDING FLIGHTC B B A

M N V M N V M N V M N V1 p1 2.99 -25.32 0.00 -0.93 -25.32 -17.40 -0.93 -30.73 0.15 0.46 -30.73 0.152 dl 2.00 -16.94 0.00 -0.62 -16.94 -11.64 -0.62 -20.56 0.10 0.31 -20.56 0.103 p2 -17.10 -63.26 0.00 -17.10 -63.26 0.00 -9.40 -36.08 -36.08 -31.20 -123.94 -67.574 dl -13.00 -48.10 0.00 -13.00 -48.10 0.00 -7.15 -27.44 -27.44 -23.73 -59.06 -32.20

1+3 -14.11 -88.58 0.00 -18.02 -88.58 -17.40 -10.33 -66.81 -35.93 -30.74 -154.67 -67.421+4 -10.01 -73.43 0.00 -13.93 -73.43 -17.40 -8.08 -58.16 -27.29 -23.26 -89.78 -32.042+3 -15.10 -80.20 0.00 -17.72 -80.20 -11.64 -10.02 -56.64 -35.98 -30.89 -144.50 -67.47

DESIGN1. Landing Mmax at B -18.02 kN.m -2E+07 N.mm

N -88.58 kN -88585 NEcc= 0.02 m 20 mmCheck M/N 0.203 m > e 203.46 mme = t1/2-ecc 0.055 m

Mt +eN ### kN.m -2E+07 N.m

fcu 35 N/mm2fy 460cover 0.03 m 30 mmt1 0.15 m 150 mmd 0.12 120 mmwidth 1.6 1600 mmk = 0.028 m per m widthz = 0.95 * ds

= 114 mmAs = 502 mm2/mAs prov = 495 mm2/m CHECK

For b+c/ As = 792 mm2 7 T 12

2. Flight Mmax at A -30.89 kN.m -3E+07 N.mmN ### kN -2E+05 N

Ecc= 0.02 m 20 mmCheck M/N 0.200 m > e 199.74 mme = t1/2-ecc ### m

Mt +eN ### kN.m ### N.m

fcu 35 N/mm2fy 460cover 0.03 m 30 mmt1 0.15 m 150 mmd 0.12 120 mmwidth 1.5 1500 mmk = ### per m widthz = ### * ds

= 114 mmAs = ### mm2/mAs prov = 377 mm2/m ###

For b As = 565 mm2 5 T 12