暗板桥计算表格

梁模板碗扣钢管高支撑架计算书依据规范:《建筑施工碗扣式钢管脚手架安全技术规范》JGJ166-2008《建筑施工模板安全技术规范》JGJ 162-2008《建筑结构荷载规范》GB50009-2012《钢结构设计规范》GB50017-2003《混凝土结构设计规范》GB50010-2010《建筑地基基础设计规范》GB50007-2011《建筑施工木脚手架安全技术规范》JGJ 164-2008计算参数:钢管强度为205.0 N/mm2，钢管强度折减系数取1.00。

模板支架搭设高度为3.1m，梁截面 B×D=800mm×490mm，立杆的纵距(跨度方向) l=1.20m，立杆的步距 h=1.20m，梁底增加3道承重立杆。

面板厚度18mm，剪切强度1.4N/mm2，抗弯强度15.0N/mm2，弹性模量6000.0N/mm2。

木方100×100mm，剪切强度1.3N/mm2，抗弯强度13.0N/mm2，弹性模量9000.0N/mm2。

梁底支撑顶托梁长度 1.00m。

梁顶托采用100×100mm木方。

梁底按照均匀布置承重杆3根计算。

模板自重0.20kN/m2，混凝土钢筋自重25.50kN/m3。

倾倒混凝土荷载标准值2.00kN/m2，施工均布荷载标准值2.50kN/m2。

梁两侧的楼板厚度0.30m，梁两侧的楼板计算长度0.20m。

扣件计算折减系数取1.00。

310图1 梁模板支撑架立面简图计算中考虑梁两侧部分楼板混凝土荷载以集中力方式向下传递。

集中力大小为 F = 1.20×25.500×0.300×0.200×1.200=2.203kN 。

采用的钢管类型为φ48×3.0。

钢管惯性矩计算采用 I=π(D 4-d 4)/64，抵抗距计算采用 W=π(D 4-d 4)/32D 。

一、模板面板计算面板为受弯结构,需要验算其抗弯强度和刚度。

分块面积分块面积分块面积形心到上缘距离分块面积对上缘静矩分块面积自身惯矩di=ys-yi分块面积对截面形心惯矩I=Ii+Ix cm 2cm cm3cm4cm cm4cm4翼板36007.52700067500561136016911427669三角承托15016.667250020847331459331668腹板261087.52283754572938-2414815476054485下三角360153.3551888000-9028917672899767马蹄1080170183********-1061220946312245463∑780049666346846462827440632959052翼板27007.5202505062563.501088772410938349三角承托15016.667250020854.33442842443050腹板261087.52283754572938-16.507104105283347下三角360153.3551888000-82.3024382722446272马蹄1080170183********-99.001058467610620676∑69004899134667771250639232973169463.67cm 71.00cm36.33cm 66.36cm0.57分块面积分块面积分块面积形心到上缘距离分块面积对上缘静矩分块面积自身惯矩di=ys-yi分块面积对截面形心惯矩I=Ii+Ix cm 2cm cm3cm 4cm cm 4cm 4翼板36007.5270006750064.851513962115207121三角承托15016.667250020855.68465080465288腹板207072.51500752281313-0.15472281360下三角360123.3443888000-50.95934545942545马蹄2700155418500520833-82.651844401018964843∑888064246328778553498330337861157翼板27007.5202505062572.161406035914110984三角承托15016.667250020863.00595280595488腹板207072.515007522813137.161062172387530下三角360123.3443888000-43.64685499693499分块截面几何特性分块名称大毛截面小毛截面大毛截面形心到上缘距离ys1=小毛截面形心到上缘距离ys2=检验截面效率指标(希望>0.5)上核心距=下核心距=截面效率指标=说明以上初步拟定主梁跨中截面尺寸是合理的变化点截面跨中截面小毛截面分块名称大毛截面马蹄2700155418500520833-75.341532417415845007∑798063571328609803077152933632508ys1=72.35cm ys2=79.66cm分块面积分块面积分块面积形心到上缘距离分块面积对上缘静矩分块面积自身惯矩di=ys-yi分块面积对截面形心惯矩I=Ii+Ix cm 2cm cm3cm 4cm cm 4cm 4翼板36007.5270006750063.451449317914560679三角承托15016.667250020854.28441994442202腹板891097.586872520214563-26.55628075426495317∑12660898225202822712121592741498198翼板27007.5202505062568.311259730612647931三角承托15016.667250020859.14524608524816腹板891097.586872520214563-21.69419342524407988∑11760891475202653961731533937580736ys1=70.95cm k x =46.20cmys2=75.81cmg=17.25g1=20.18g2=10.96跨中四分点变化点支点α0.500.250.050.00弯距2110.911583.18387.950.00剪力0.00145.58263.05291.16弯距1152.17864.13211.750.00剪力0.0079.46143.58158.92弯距3263.082447.31599.690.00剪力0.00225.04406.62450.08支点Mmax Qmax Mmax Qmax Mmax Qmax Qmax KN.m KN KN.m KN KN.m KN KN 一期恒载2110.910.001583.18145.58387.95263.05291.16二期恒载1152.170.00864.1379.46211.75143.58158.92总恒载=1+23263.080.002447.31225.04599.69406.62450.08汽-201935.88104.331603.57195.59404.70225.05292.50挂-1002350.40162.091913.60266.09490.02276.53277.56恒+汽5198.96104.334050.88420.631004.39631.67742.58恒+挂5613.48162.094360.91491.131089.71683.15727.64Σ荷载类型变化点截面跨中截面四分点截面恒载内力一期内力组合计算支点截面二期小毛截面分块名称大毛截面Sji=1.2*恒+1.4*汽6625.93146.065181.77543.871286.21803.02949.60Sjm=1.2*恒+1.1*挂6501.14178.305041.73562.751258.65792.13845.41汽/6*100%0.37 1.000.400.460.400.360.39提高系数 1.03 1.00 1.03 1.03 1.03 1.00 1.03挂/7*100%0.42 1.000.440.540.450.400.38提高系数 1.00 1.03 1.00 1.02 1.00 1.00 1.00提高后Sji 6824.71146.065337.22560.191324.80803.02978.08提高后Sjm 6501.14183.655041.73574.001258.65792.13845.41钢束其弯高度y1y2L1x3ΦR N1(N2)2112.198.8110099.2571182.35N35112.1938.8110099.2575207.12N4103.325.8877.4210096.59152272.05N512025.8894.1210096.59152762.15N6120.8830.9089.9810095.11181838.41x4(cm)R （cm)sin cos a0(cm)ai(cm)ay(cm)N1(N2)/1182.3599.00N3/5207.1299.00N4/2272.0516.716.70N565.232762.150.023620.999723030.77N682.651838.410.044960.998994243.86N1(N2)71.031182.350.060070.99819911.14N3565.215207.120.108550.99409939.77N4515.342272.050.226820.9739416.775.92N5650.232762.150.235410.9719030107.63y 角度a x5x5*tan(a)a0ai N1(N2)21.007.0032.32 3.979.0026.03N351.0015.0028.637.679.0052.33N4103.3015.0029.307.8516.70112.15N5120.0015.0021.265.7030.00144.30N6RΦ曲线长S 直线长X1直线长L1有效长度预留长度N1(N2)1182.357.00144.451238.97100.002966.85140.00N35207.127.00636.17744.79100.002961.91140.00N42272.0515.00594.82794.66100.002978.96140.00N52762.1515.00723.13659.77100.002965.80140.00N61838.4118.00577.55642.35100.002639.82140.00分块名称分块面积分块面积重心到上缘距离分块面积对上缘静矩全截面重心到上缘距离分块面积自身惯矩di管道面积=46.566n=6n y =毛截面6900.0071.0048991329731694-4.2619.72钢束布置计算各计算截面钢束位置及钢束群位置1/4点支点72.17钢束长度计算49.12变化点截面面积和惯矩计算扣除管道面积-279.40160.72-449050-93.97Σ6667.1744500829731694毛截面7800.0063.67496663329590522.78钢束换算面积230.40160.7237030-94.26Σ8030.4053369332959052毛截面6900.0071.0048991329731694-4.24扣除管道面积-279.40160.28-44781-93.51Σ6667.1744513229731694毛截面7800.0063.67496663329590522.77钢束换算面积230.40160.2836928-93.83Σ8030.4053359132959052毛截面7980.0079.6663571333632508-1.54扣除管道面积-232.83130.88-30474-52.76Σ7747.1760523933632508毛截面8880.0072.35642463378611571.24钢束换算面积192.00130.8825130-57.30Σ9072.0066759337861157毛截面11760.0075.8189147537580736-0.65扣除管道面积-232.83107.83-25106-32.67Σ11527.1786636937580736毛截面12660.0070.95898225414981980.55钢束换算面积192.00107.8320704-36.33Σ12852.0091892941498198b1=180r s =66.75b2=240rs=Ai(cm2)yi(cm)Si(cm3)Ai(cm2)yi(cm)翼板270059159965翼板360059三角承托150507512三角承托15050肋板90494432肋板9049171909下三角3608731171下三角36087马蹄1080103111514马蹄1080104肋板3608329971肋板36084管道-27994-26256管道23094146401翼板270059159965翼板360058三角承托150507512三角承托15049肋板9322624108肋板93225191584-1翼板270059159965翼板360058三角承托150507512三角承托15049肋板9262624098肋板92625191575rs=67rs=Ai(cm2)yi(cm)Si(cm3)Ai(cm2)yi(cm)净截面换算截面66.7666.4578.1273.591/4点1/4点跨中66.7566.46换算截面净截面换算截面跨中75.1671.50截面对重心轴静矩计算净截面净轴以上面积对净轴静矩换轴以上面积对净轴静矩静矩翼缘对换轴静矩马蹄部分对换轴静矩净轴以上面积对换轴静矩换轴以上面积对换轴静矩静矩变化点支点净截面换算截面翼缘对净轴静矩马蹄部分对净轴静矩翼板270059160015翼板360058三角承托150507515三角承托15049肋板90494434肋板9048171963下三角3608731165下三角36088马蹄1080103111494马蹄1080104肋板3608329965肋板36084管道-27994-26128管道23095146496翼板270059160015翼板360058三角承托150507515三角承托15049肋板9322624108肋板93225191637翼板270059160015翼板360058三角承托150507515三角承托15049肋板9262624098肋板92625191628rs=78rs=Ai(cm2)yi(cm)Si(cm3)Ai(cm2)yi(cm)翼板270071190685翼板360066三角承托150619219三角承托15057肋板90615456肋板9056205359下三角3604516275下三角36050马蹄270077207565马蹄270081肋板3604215075肋板36046管道-23353-12284管道23057226632翼板270071190685翼板270066三角承托150619219三角承托15057肋板11363235862肋板108327235765翼板270071190685翼板270066三角承托150619219三角承托15057肋板10553435677肋板102530235580rs=75rs=Ai(cm2)yi(cm)Si(cm3)Ai(cm2)yi(cm)翼板270068182679翼板360064三角承托150588774三角承托15055肋板2705815568肋板27054207021翼板270068182679翼板360064三角承托150588774三角承托15055肋板32493097715肋板324926净轴以上面积对净轴静矩变化点翼缘对净轴静矩马蹄部分对净轴静矩净轴以上面积对净轴静矩净轴以上面积对换轴静矩换轴以上面积对净轴静矩静矩翼缘对净轴静矩马蹄部分对净轴静矩翼缘对换轴静矩翼缘对净轴静矩净轴以上面积对净轴静矩换轴以上面积对换轴静矩静矩翼缘对换轴静矩支点净轴以上面积对换轴静矩翼缘对换轴静矩马蹄部分对换轴静矩净轴以上面积对换轴静矩换轴以上面积对换轴静矩静矩换轴以上面积对净轴静矩静矩马蹄部分对换轴静矩289168翼板270066178443翼板360062三角承托150578538三角承托15053肋板30512886193肋板305125273174跨中四分点变化点支点A j cm 266676667774711527I j cm 427389284274122913300329637337114y js cm 67677875y jx cm 113113102105梁上边缘W js cm 3410350410580422448496776梁下边缘W jx cm 3241840242083323955356130翼缘部分面积S a-j cm 3171909171963205359253200净轴以上面积S j-j cm 3191584191637235765324446换轴以上面积S o-j cm3191575191628235580307763马蹄部分面积S h-j cm 31464011464962266320e j cm98.5193.5152.7632.67A o cm 280308030907212852I o cm 435066653350475203850508941755461y os cm 66.4666.4573.5971.50y ox cm 113.54113.55106.41108.50梁上边缘W os cm3527643527455523250583986梁下边缘W ox cm 3308846308643361850384846翼缘部分面积S a-o cm 3224128220924252332253200净轴以上面积S j-o cm 323064239638217100324446换轴以上面积S o-o cm 3239659239635217836307763马蹄部分面积S h-o cm31948911964842668420e o cm 98.8093.8357.3036.33a ycm14.7419.7249.1272.17θ=Φ-α角度弧度N1(N2)70.127.570.03080.030342.29N3150.267.540.05730.055777.66N4150.267.540.05730.055777.67N513.650.247.460.05270.051471.64N615.420.27 5.810.05700.055477.23N1(N2)70.1214.820.03800.037352.06N3150.2614.790.06450.062587.17N4150.2614.790.06450.062587.18N5150.2614.710.06450.062487.08N6180.3113.060.07280.070297.88钢束群重心到净轴距离换算截面换算面积换算惯距截面形心至上缘距离截面形心至下缘距离截面抗弯模量对形心轴静矩混凝土净截面净面积净惯矩截面形心至上缘距离截面形心至下缘距离截面抗弯模量单位截面换轴以上面积对净轴静矩静矩面积对净轴静矩截面管道摩擦损失σs1截面位置钢束x (m)μ*θ+k*x 1-e -(μθ+kx)σk [1-e-(μθ+kx)](Mpa)面积对换轴静矩换轴以上面积对换轴静矩静矩截面特性汇总1/4点钢束群重心到换轴距离钢束群重心到下缘距离对形心轴静矩名称符号跨中N1(N2)11.560.20 1.720.04000.039354.76N38.770.15 1.690.03080.030342.26N4 1.890.03 1.690.00800.007911.06N5 1.380.02 1.610.00620.00628.63N1(N2)000.320.00030.00030.45N3000.290.00030.00030.40N4000.290.00030.00030.41N5000.210.00020.00020.30钢束N1(N2)N3N4N5N6l(mm)31068.4931019.1431189.5831057.9927798.16σs2(Mpa)73.3973.5073.1073.4182.02σy0σy0*Δay cos αN y0A j =6667I j =27412291N21279.3210746.30110746.3010746.30103.751114928.70N11246.8310473.40110473.4021219.70103.751086615.52N51195.5410042.560.99972110810039.7631259.4681.98823059.59N31153.959693.1419693.1440952.60103.751005663.14N41131.349503.2619503.2650455.8796.05912788.38Aj=6667Ij=27389284.01N21269.5510664.22110664.2210664.22103.761106519.33N11237.2910393.20110393.2021057.42103.761078398.71N51179.699909.3619909.3630966.7882.76820098.48N31144.369612.6619612.6640579.44103.76997409.44N41131.269502.6019502.6050082.0496.05912724.49Aj=7747Ij=33003295.98N21266.8610641.590.99819400710622.3710622.3790.86965148.32N11244.4110453.080.99819400710434.2021056.5790.86948051.50N51299.6410916.960.97189685810610.1631666.73-5.63-59735.21N31230.3810335.190.9940914110274.1241940.8583.37856553.64N41268.7510657.470.97393711710379.7152320.5626.08270702.82A=8030.4Io=35047519.92N611235.7510380.280.99898900210369.7869.69722721.48N2914.407680.9317680.93104.55803069.23N1914.937685.3917685.39104.55803534.73N5888.337461.960.9997211087459.8882.78617553.08N3882.687414.5217414.52104.55775214.85N4881.477404.3817404.3896.54714783.45N6890.037476.230.9989890027468.6769.69520528.85Σ45113.774234684.19A=8030.4Io=35066652.86变化点1/4点支点锚具变形，钢束回缩引起的损失σs2（Mpa)截面σs4计算表钢束号锚固时预加纵向轴力N y0ΣNy0(0.1KN)e yi M y0=Ny0*eyi1/4点跨中变化点成桥后张拉N6N611235.7510380.27515110380.2751571.54742614.5091N2929.797810.24333317810.243333104.54816490.0799N1891.347487.28532117487.285321104.54782727.7499N5892.207494.47881917494.47881983.54626095.7096N3896.707532.25247817532.252478104.54787428.6581N4892.307495.27927917495.27927996.87726074.6536N6890.987484.22985217484.22985271.54535428.7432Σ45303.769084274245.594σs5=0.045*139562.775截面Ny(Mpa)My(Mpa)Mg(Mpa)My-Mg I (m 4) A (m 2)e (m)Ny/A 跨中5008.204915.152110.912804.240.273892840.670.997.511/4点5045.594943.061583.18253359.870.2741229050.670.947.57变化点5232.062980.72387.94562592.780.330032960.770.53 6.75βα(τ)=0.312u=818.74h=λ*2*Ah/u=28.58查表Φf2= 1.61Φf =2*1.61= 3.22Φ(∞,т)=Φ(t,т)= 2.77ε=0.23*10^3配筋率跨中1/4点变化点A (cm 2)8030.408030.409072.00Ay (cm2)50.4050.4050.40μ0.010.010.01跨中1/4点变化点r 24366.744364.364244.39e A98.8093.8357.30e A 29761.628804.463282.83ρ3.24 3.02 1.771+10*μ*ρ 1.20 1.19 1.10Φ(∞,т) 2.773 2.773 2.773ε=0.000230.000230.00023σh17.6019.0310.90n*σh*Φ(∞,т)271.86293.98168.36Ey*ε42.5542.5542.55n*σh*Φ(∞,314.41336.53210.91261.34282.94192.00跨中混凝土收缩须变损失σs6σh的计算分母分子σs6 (Mpa)σs1σs2σs4N11395.0052.0673.3932.261237.29N21395.0052.0673.390.001269.55N31395.0087.1773.5089.961144.36N41395.0087.1873.10112.971121.75N51395.0087.0873.4154.831179.69N61395.0097.8882.021215.10N11395.0054.7673.3922.441244.41N21395.0054.7673.390.001266.86N31395.0042.2673.5048.861230.38N41395.0011.0673.1042.091268.75N51395.008.6373.4113.321299.64截面M (KN.m)N (KN)σs5+σs6N y N y1M'M y1变化点2980.7252320.560.005232.060.002980.72（一）混凝土法向应力的验算梁截面下缘最大压应力бha ≤0.75R ab’＝0.75×0.9×35＝23.625MPa 梁截面上缘最大拉应力бhl ≤0.75R lb’＝0.70×0.9×3.0＝1.89MPa 截面应力部位M g1 （kN·m）N y0(kN)M y0(kN·m)A j （m 2）I 1（m 4)e 1s e 1x (m)上缘0.67下缘 1.13上缘0.67下缘 1.13上缘0.78下缘1.02采用两定点吊装。

3.1设计资料：设计荷载：公路一级桥面净宽：净-31+2×0.5防撞墙标准跨径：16米3.2材料选用：1.混凝土上部结构：16米预应力混凝土预制板采用40号混凝土、铰缝采用30号砼，桥面铺装采用30号沥青混凝土。

下部结构：盖梁，墩柱用C30，系梁及钻孔灌注桩用C252.钢材上部结构：预应力钢筋1×7钢绞线，直径15.2mm，非预应力钢筋采用HRB335，R235 下部结构：盖梁主筋用HRB335，其他均用R235钢筋3.其它支座：采用圆板式橡胶支座。

伸缩缝：采用D40伸缩缝。

3.3板的横断面图图1-1 桥梁横断面(尺寸单位:cm)503.4板的尺寸重心轴o图1-2 空心板截面构造及尺寸(尺寸单位:cm)表3板的尺寸（m ）3.5结构重力内力计算：（1）毛截面面积Ah=99×62-2×8×38-2×3.14×19²-8×（0.5×7×2.5+7×2.5+0.5×7×5）=3174.3cm²（2）全断面对1/2板高处的静矩：对称部分消去，既只取计算铰对1/2板处的静矩S1/2板高=2[2.5×7/2（7/3+24）+2.5×7×（24+7/2）+2.5×7（24+7/3）]=2181.7cm³铰面积：A铰=2（5×7/2+2.5×7+2.5×7/2）=87.5cm³则毛截面离中心线的距离为：dh=S1/2板高/Ah=2187.7/3174.3=0.7（向下）铰垂心对1/2板高的距离：d铰=2187.7/87.5=24.9cm（3）毛截面对垂心的惯性：面积：A´=1/8πR²=1/8×3.14×38²=567.1cm²重心：y=4R/3π=4×19/3π=8.06cm半圆对自身的惯矩：I´=I1-1-A´y²=14304cm4由此得到毛截面的惯矩：Ih={99×62³/12-2[38×8³/12+38×8×0.72]+99×62×0.72}-4×14304-2×567.1×[（8.06+4+0.7）²+（8.06+4-0.7）²]-87.5×（24.9+0.7）2=1.5201×1010mm4抗扭惯矩：IT=2.6645×1010mm4O IIO图1-3 挖空半圆构造(尺寸单位:cm)图1-4 IT的空心板截面简化图3.6永久荷载作用下1.空心板自重g1g1=A ×γ=3174.3×10-4×25=7.936KN/m 2.桥面系自重防撞墙采用C25混凝土γ=23 KN/m 3单侧按23×0.2=4.6 KN/m ，桥面铺装 用等厚10cm 的沥青混凝土，则全桥铺装每延米重力为：0.1×15×23=34.5 KN/m每块板分摊到的每延米桥面系自重为： g2=4.6×2+34.5/32=2.185KN/m 3.铰缝自重g3：g3=（87.5+1×62）×10-4×24=0.359KN/m由此得空心板每延米总重力g为：g=2.185+0.359+7.936=10.48 KN/m由此可计算出空心板永久作用（自重）效应：作用gi 计算跨径作用效应M 作用效应V跨中1/4跨支点1/4跨跨中g1 7.936 15.6 120.7 90.5 30.9 15.5 0 g2 2.544 15.6 38.7 29.0 9.9 4.9 0 g=g1+g2 10.48 15.6 159.4 119.5 40.8 20.4 0 3.7基本可变荷载（活载）作用下1.荷载横向分布系数：跨中和四分点的横向配系数按铰接板计算，对于具有10块板以上铰接板桥，参照《公路桥梁荷载横向分布计算》采用划分板组的方法，将四块板合为一块板组当做一块宽板计算。