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悬臂式挡土墙设计讲解

悬臂式挡土墙工程实例——成都市三环路与铁路立交工程设计路段为K23+385.728—K23+486.726右幅快车道;已知,填方最大高度5米,地基承载力设计值[σ]=150kpa,墙身设计高度H=4m ;填土标准重度γ=18KN/m 3,填土表面均布荷载q=10KN/m 2, 填土内摩擦角Φ=35。

,底板与地基摩擦系数f=0.3,墙身采用C20混凝土,HRB335钢筋。

一、 截面选择选择悬臂式挡土墙。

尺寸按悬臂式挡土墙规定初步拟定,如图所示 根据规范要求H 1=110H=400mm, H 2=H-H 1=3600mm, H 0=810mm,b=250mm, B=0.8H=3200mm ;地面活荷载q 的作用,采用换算立柱高:01050.55189q H r ==== B 3的初步估算:22250(810)0.05=470mm B H =++⨯320 1.4348.78=22300.3(40.55) 1.0518r c K m Ex B B H m f μ•⨯=-=••⨯+⨯⨯•—0.47(H+)B 1 =B-B 3-B 2=3200-2230-470=500mmB20.27kpac22.22kpac图1 悬臂式支挡结构计算图(单位:mm)min=71.54kpa1=97.45kpa2=102.91kpamax=108.72kpa二、 荷载计算 1.土压力计算由于地面水平,墙背竖直且光滑,土压力计算选用朗金理论公式计算:2tan 450.2712K αφ⎛⎫=︒-= ⎪⎝⎭地面处水平压力:σA =γH 。

*Ka=18⨯59⨯0.271=2.71 kpa悬臂底B 点水平压力:σB =γ(H 。

+H 2) Ka =18⨯(59+3.6)⨯0.271=20.27 kpa 底板c 点水平压力:σc =γ(H 。

+ H 2 + H 1 )Ka=18⨯(59+3.6+0.4)⨯0.271=22.22 kpa土压力及合力作用点位置: Ea 1=σA H 2 =2.71⨯3.6=9.76 KN/m ;Za 1=22H + H 1 =2.2 m Ea 2=12(σB -σA )⨯H=12⨯(20.27-2.71)⨯3.6=31.61 KN/m ;Za 2= 13H 2 + H 1 =1.6 mEa 3= 12(σc -σA )⨯H= 12⨯(22.22-2.71)⨯4=39.02 KN/m ;Za 3= 13(H 1 + H 2)=1.333 m2.竖向荷载计算 (1)立臂自重力钢筋混凝土标准容重γk = 25kN/m3,其自重力G 1k =()0.2502.47+⨯(3.6+0.81)⨯25=39.69 KN/mX 1=0.5+[0.22⨯4.41⨯0.5⨯0.22⨯23+0.25⨯4.41⨯(0.22+0.125)] ÷(0.5⨯0.22⨯4.41+0.25⨯4.41) =0.7844 m (2)底板自重力G 2k=(0.5+0.47+2.23) ⨯0.4⨯25=32 KN/m X 2=3.22=1.6 m (3)地面均布活载及填土的自重力G 3k=(q+γH 2)B 1 =(10+18⨯3.6) ⨯2.23=166.81 KN/m X 3=0.5+0.47+2.232=2.085 m 三、抗倾覆稳定验算稳定力矩112233xk k k k M G x G x G x =++=39.69⨯0.7844+32⨯1.6+166.81⨯2.085 =430.13 KN*m/m 倾覆力矩Mq k =Ea1*Za1+Ea3*Za3=9.67⨯2.2+39.02⨯1.333=73.49 KN*m/m0430.135.8573.9.541xk qk M K M ==>=故稳定 四、抗滑稳定验算 竖向力之和G k =∑Gi k =39.69+32+166.81=238.50 KN/m 抗滑力Ff=Gk*f=238.500.3=71.55 KN/m 滑移力E= Ea1+ Ea3=9.76+39.02=48.78 KN/m71.5548.781.47 1.3k c G f K E ===> 故稳定 五、地基承载力验算地基承载力采用设计荷载,分项系数:地面活荷载r 1=1.30;土荷 载r 2=1.20;自重r 3=1.20。

基础底面偏心距e 0,先计算总竖向力 到墙趾的距离:0V HkM M e G -=M H =1.3Ea1*Za1+1.Ea3*Za3=1.3⨯9.76⨯2.2+1.2⨯39.02 ⨯1.333e 0=90.33 KN/mG k =1.2 ⨯(39.69+32+18 ⨯3.6 ⨯2.23 ⨯2.085) =288.42 KN/mMv=1.2 ⨯(39.69⨯0.7844+32⨯1.6+18⨯3.6⨯2.23⨯2.085)+1.3⨯ (10⨯2.23⨯2.085) =520.79 KN*m/m 偏心距e =()520.7990.33288.42-=1.49 m=2B -e=3.22-1.49=0.11 m<6B=0.53 m 地基压力σmax =6e (1+)Gk B B =288.423.2⨯(1+6⨯0.113.2)=108.72 kpa σmin =6e (1)Gk B B -=288.423.2⨯(1-6⨯0.113.2)=71.54 kpa σmax =108.72 < [σ]=150 kpa 故地基承载力满足要求. 六、结构设计立臂与底板均采用C20混凝土和HRB335级钢筋,查表得f cd = 9.2 Mpa ,f td = 1.06 Mpa ,f tk=1.54 Mpa,E c=2.55⨯104Mpa, f sd = 280 Mpa ,f 1sd=280 Mpa ,E s = 2×105Mpa(1) 立臂设计底截面设计弯矩M=1.3⨯9.76⨯3.62+1.2⨯31.61⨯3.63=68.36 KN*m/m 标准弯矩 Mk=9.76⨯3.62+31.61⨯3.63=55.50 KN*m/m 有效高度h 0=250-30=220 mm 由f cd*b *X= f sd*As 得 X=2809.0(200)1As⨯⨯=0.03As其中混凝土保护层厚度C=30 mm M= f sd* As*(250-30-2X ) 代入化简得:0.0152 A 2s-220 As+244143=0 即As=13257 mm 2(舍),As=1217 mm 2 取φ16@165钢筋,As=1219 mm 2 裂缝验算s ts tsA A ρ== 12190.0098,=0.010.51000250s ts ts ts A A ρρ===⨯⨯取 6055.50102380.870.872201219k sk s M Mpa h A σ⨯===⨯⨯0.650.65 1.541.10 1.100.680.01238tkts skf ψρσ⨯=-=-=⨯最大裂缝宽度2.10,30,16cr cq a c mm d mm ===max max51.90.08238162.10.68 1.9300.080.310.202100.01cq sk cr s t s d w a c E w mm mmσψρ⎛⎫=+ ⎪⎝⎭⎛⎫=⨯⨯⨯⨯+=> ⎪⨯⎝⎭不满足,改用φ16@125钢筋,As=1609 mm 216090.0130.5100250ts ρ==⨯⨯655.50101800.872201609sk Mpa σ⨯==⨯⨯0.65 1.541.100.670.013180ψ⨯=-=⨯max 5180162.10.67 1.9300.080.190.202100.013w mm mm ⎛⎫=⨯⨯⨯⨯+=< ⎪⨯⎝⎭故裂缝宽度满足要求 墙踵板根部D 点设计弯矩:2.23 2.23 2.232.230.425 1.218 2.233.6 1.210 2.23 1.302222.231 2.2371.54 2.23(97.4571.54) 2.2356.15223D M kN m=⨯⨯⨯⨯+⨯⨯⨯⨯+⨯⨯⨯-⨯⨯--⨯⨯⨯=⋅墙趾板根部B 点设计弯矩:0.50.5120.50.425 1.2102.910.5(108.72102.91)0.50.2222312.10B M kN m=-⨯⨯⨯⨯+⨯⨯+-⨯⨯⨯⨯=⋅ 标准弯矩计算,由前面计算可知,标准荷载作用时:430.1373.491.495238.50sk qkkM M e m G --===0 3.2 1.4950.10522B e e m =-=-= 此时地基压力:0max 6230.5060.105(1)(1)89.203.2 3.2k G e kpa B B σ⨯=+=+= min06230.5060.105(1)(1)59.863.2 3.2k G e kpa B B σ⨯=-=-=2.23 2.23 2.232.230.42518 2.233.610 2.232221 2.23(97.4571.54) 2.2311.5023D M kN m=⨯⨯⨯+⨯⨯⨯+⨯⨯--⨯⨯⨯=⋅墙踵板强度设计:混凝土保护层厚度C=30 mm ,有效高度h 0=400-30=370 mm,b=1000 mm 同理受压区高度X=0.03As D M = f sd* As*(370-2X ) 代入化简得:0.015 A 2s-370As+200536=0 解得As=24100 mm 2(舍),As=567 mm 2 取φ12@140钢筋,As=808 mm 2 裂缝验算:8080.004,=0.01.0.51000400s ts ts ts A A ρρ===⨯⨯取 6055.5010213pa 0.870.87370808k sk s M M h A σ⨯===⨯⨯0.650.65 1.541.10 1.100.630.01213tkts skf ρσ⨯ψ=-=-=⨯最大裂缝宽度max 5213122.100.63 1.9300.080.220.22100.01w mm mm ⎛⎫=⨯⨯⨯⨯+⨯=> ⎪⨯⎝⎭取φ12@130钢筋,As=870 mm 28700.004,=0.01.0.51000400s ts ts ts A A ρρ===⨯⨯取 6055.5010198pa 0.870.87370870k sk s M M h A σ⨯===⨯⨯0.650.65 1.541.10 1.100.590.01198tkts skf ρσ⨯ψ=-=-=⨯max 5198122.100.59 1.9300.080.1870.22100.01w mm mm ⎛⎫=⨯⨯⨯⨯+⨯=> ⎪⨯⎝⎭满足要求根据构造要求,底板墙趾的配筋与墙踵一致。

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