2.0 Poprzecznica.
2.1. Zestawienie obciążeń.
2.1.1. Obciążenia stałe.
Na szerokości jezdni:
gmax=9.31 kN/m2
gmin=6.53 kN/m2
Na szerokości chodnika:
Δgchmax=4.80 kN/m2
Δgchmin=2.89 kN/m2
2.1.2. Obciążenie użytkowe.
Po=181.5 kN
qo=3.00 kN/m2
qto=3.25 kN/m2
2.2 Wyznaczenie współczynników γ dla n=1,3,5.
Dla obciążenia równomiernego od Δgch
γ1gmax=4⋅Δgchmax/1⋅π=4⋅4.80/1⋅π=6.11 kN/m2
γ1gmin=4⋅Δgchmin/1⋅π=4⋅2.89/1⋅π=3.67 kN/m2
γ3gmax=4⋅Δgchmax/3⋅π=4⋅4.80/3⋅π=2.03 kN/m2
γ3gmin=4⋅Δgchmin/3⋅π=4⋅2.89/3⋅π=1.23kN/m2
γ5gmax=4⋅Δgchmax/5⋅π=4⋅4.80/5⋅π=1.22 kN/m2
γ5gmin=4⋅Δgchmin/5⋅π=4⋅2.89/5⋅π=0.73 kN/m2
Dla obciążenia równomiernego taboru samochodowego
γ1q=4⋅Δqo/1⋅π=4⋅6/1⋅π=7.63 kN/m2
γ3q=4⋅Δqo/3⋅π=4⋅6/3⋅π=2.54 kN/m2
γ5q=4⋅Δqo/5⋅π=4⋅6/5⋅π=1.52 kN/m2
Dla obciążenia ciągnikiem K
γ1p=(8⋅Po/2)/L⋅cos(1⋅π⋅a/L)⋅cos(2⋅1⋅π⋅a/L) ⋅sin(1⋅π⋅xo/L)=
=4⋅181.5/32.2⋅cos(π⋅0.5/32.2)⋅cos(2⋅0.5⋅π/32.8) ⋅sin(π⋅16.1/32.2)==
=22.54⋅cos0.048⋅cos0.097=22.4 kN/m
γ3p=(8⋅Po/2)/L⋅cos(3⋅π⋅a/L)⋅cos(2⋅3⋅π⋅a/L) ⋅sin(3⋅π⋅xo/L)=
=4⋅181.5/32.2⋅cos(3⋅π⋅0.5/32.2)⋅cos(6⋅0.5⋅π/32.2)⋅sin(3π⋅16.1/32.2)==
=22.54⋅cos0.144⋅cos0.289=-21.30 kN/m
γ5p=(8⋅Po/2)/L⋅cos(5⋅π⋅a/L)⋅cos(2⋅5⋅π⋅a/L) ⋅sin(5⋅π⋅xo/L)=
=4⋅181.5/32.5⋅cos(5⋅π⋅0.5/32.5)⋅cos(10⋅0.5⋅π/32.2)⋅sin(5π⋅16.1/32.2)==
=22.54⋅cos0.241⋅cos0.484=19.37 kN/m
Dla obciążenia od tłumu.
γ1t=4⋅3.25/π=4.13 kN/m2
γ3t=4⋅3.25/3π=1.37 kN/m2
γ5t=4⋅3.25/5π=0.82 kN/m2
2.3 Obwiednia momentów .
b=6.46m
myn=b⋅sin(n⋅π⋅xo/L)⋅Σγn⋅μn
dla przekroju y=0 n=1
my1max=6.46⋅sin(π⋅16.1/32.2)⋅[(-0.784)3.67+7.36⋅0.802+22.40(0.249+0.156+0.064)]=
=6.46⋅sin0.5π⋅[(-2.87)+5.90+10.438]=67.00 kN
my1min=6.46⋅sin(π⋅16.1/32.2)⋅[(-0.784)6.11-7.36⋅ 0.0056+(-0.304-0.304)⋅4.13]=
=6.46⋅sin0.5π⋅[(-4.79)-2.51-0.0412]=-47.42 kN
dla przekroju y=0 n=3
my3max=6.46⋅sin(3π⋅16.1/32.2)⋅[(-0.772)1.23+2.54⋅0.784-21.3(0.247+0.154+0.062)]=
=6.46⋅sin1.5π.⋅[(-0.949)+1.99-9.86.]=36.97 kN
my3min=6.46⋅sin(3π⋅16.1/32.2)⋅[(-0.772)2.03-2.54⋅0.0058+(-0.299-0.299)⋅1.37]=
=6.46⋅sin1.5π⋅[(-1.56)-0.819-0.014]=15.46 kN
dla przekroju y=0 n=5
my5max=6.46⋅sin(5π⋅16.1/32.2)⋅[(-0.758)0.73+1.52⋅0.773+19.37(0.242+0.15+0.06)]=
=6.46⋅sin2.5π⋅[(-0.553)+1.17+8.75)]= 40.51kN
my5min=6.46⋅sin(5π⋅16.1/32.2)⋅[(-0.758)1.22+(-0.289-0.289)⋅0.82-1.52⋅0.0058]=
=6.46⋅sin2.5π⋅[(-0.924)-0.473-0.00881]=-9.08 kN
dla y=0.5b n=1
my1max=6.46⋅sin(π⋅16.1/32.2)⋅[(-0.292-0.176)3.67+0.0239⋅6.11+7.63⋅0.44
+22.40(0.143+0.113+0.083+0.053)]=
=6.46⋅sin0.5π⋅[(-1.71)+0.146+3.23+8.78]=47.48 kN
my1min=6.46⋅sin(π⋅16.1/32.2)⋅[(-0.292-0.176)6.63-0.239⋅3.67+(-0.239-0.132)⋅4.13
-0.0067⋅7.63]=
=6.46⋅sin0.5π⋅[(-3.10)-0.877-1.53-0.051]=-35.9 kN
dla y=0.5b n=3
my3max=6.46⋅sin(3π⋅16.1/32.2)⋅[(-0.288-0.17)1.23+0.026⋅2.03
+2.54⋅0.40-21.30(0.142+0.112+0.081+0.051)]=
=6.46⋅sin1.5π⋅[(-0.51)+0.052+1.016-8.22]=29.50 kN
my3min=6.46⋅sin(3π⋅16.1/32.2)⋅[(-0.288-0.17)2.03+0.026⋅1.23-2.54⋅0.0065+
(-0.236-0.127)1.37]=
=6.46⋅sin1.5π⋅[(-0.929)+0.032-0.016-0.62]=9.91 kN
dla przekroju y=0.5b n=5
my5max=6.46⋅sin(5π⋅16.1/32.2)⋅[(-0.284-0.163)0.73+0.025⋅1.22+1.52⋅0.42+
19.37(0.14+0.109+0.049+0.079)]
=6.46⋅sin2.5π⋅[(-0.326)+0.03+0.0638+7.30]= 29.37kN
my5min=6.46⋅sin(5π⋅16.1/32.2)⋅[(-0.284-0.163)1.22+0.025⋅0.73-1.52⋅0.064+(-0.233-0.122)0.82+]=
=6.46⋅sin2.5π⋅[(-0.545)+0.018-0.097-0.291]=-5.91 kN
Dla przekroju y=0
mymax= my1max+ my3max+ my5max=144.48 kN
Mymax= mymax⋅xo=2326.12 kNm
mymin= my1min+ my3min+ my5min=-41.04kN
Mymin= mymin⋅xo=-660.74 kNm
Dla przekroju y=0.5b
mymax= my1max+ my3max+ my5max=106.35 kN
Mymax= mymax⋅xo=1712.235 kNm
mymin= my1min+ my3min+ my5min=-31.9 kN
Mymin= mymin⋅xo=-513.59 kNm
2.4 Wymiarowanie .
Beton B40 Rb=23.1Mpa Eb=36.4Gpa
Stal AII 18G2 Ra=295Mpa Ea=210Mpa
n=Ea/Eb=5.77
Maksymalny moment ujemny.
M=513.59kNm
h1=1.45m
b=0.40m
t=0.21m
t/h=0.20
wz=n*M/Ra*b*h12=0.010
m1=0.159
mz=0.954
mx=0.138
x=mx*h1=0.22>t
σb=m1*Ra/n=8.129Mpa<Rb=23.1MPa
As=M/(Ra*mz*h1)=17.73cm2
6 φ 20 Aa=18.85cm2
μ=18.85/0.40*1.45=0.003 <μmin=0.004
Aa=0.004*0.4*1.45=24.8cm2
10 φ 20 Aa=31.42cm2
Moment przenoszony przez zbrojenie
M=Ra*mz*h1*Aa=1370.59kNm
σa=n*σb*(h1-x/x)=25.79Mpa<295MPa
Maksymalny moment ujemny.
M=2326.12 kNm
wz=0.047
m1=0.378
mz=0.908
mx=0.275
x=mx*h1=0.426>t
σb=m1*Ra/n=19.32Mpa<Rb=23.1MPa
As=M/(Ra*mz*h1)=56.02cm2
14 φ 24 Aa=63.33cm2
μ=56.54/0.40*1.45=0.009 >μmin=0.004
Moment przenoszony przez zbrojenie
M=Ra*mz*h1*Aa=2629.35kNm
σa=n*σb*(h1-x/x)=117.83Mpa<295MPa