新規(guī)薄壁橋臺計算

1、- 1 -K5+320K5+320小小橋橋樁樁基基薄薄壁壁橋橋臺臺計計算算( (一一) ) 設(shè)設(shè)計計資資料料1、總體情況結(jié)構(gòu)重要性系數(shù)0 =1.0橋梁計算跨徑l =16m環(huán)境類別類2、地震資料橋梁抗震設(shè)防類別:C類地震動峰值加速度A =0.10g阻尼比 =0.053、汽車荷載汽車荷載等級:公路級汽車荷載提高或折減系數(shù)1行駛方向:雙向行駛設(shè)計車道數(shù)2車道折減系數(shù)1橋臺傳遞的制動力比例0.54、上部構(gòu)造一孔上部結(jié)構(gòu)重力7400kN上部結(jié)構(gòu)混凝土強度等級C40上部結(jié)構(gòu)跨中處延米結(jié)構(gòu)重力G =15kN/m上部結(jié)構(gòu)跨中截面慣矩Ic =0.04m45、橋臺尺寸橋梁斜度0 橋臺正寬度13m橋臺斜寬度13.0

2、00m背墻高度1.25m背墻頂寬度0.4m置搭板背墻高0.31m置搭板背墻寬0.25m臺帽高度1.3m臺帽寬度1.45m臺帽支撐寬度0.8m臺帽前緣帽檐0.35m臺身高度4.08m臺身厚度0.8m承臺高度1.6m- 2 -承臺順橋向?qū)挾?.2m臺身前緣與承臺前緣垂直距離0.7m橋臺樁基個數(shù)n樁 =4橋臺樁徑d =1.5m橋臺樁長10m樁基類型嵌巖樁6、橋頭搭板搭板長度8m搭板寬度13m搭板厚度0.3m7、支座數(shù)據(jù)支座中心與背墻前緣線正距離0.32m支座種類：板式橡膠支座(與混凝土接觸)支座摩擦系數(shù) =0.3支座+墊石高度0.2m8、地基及填土橋梁工程場地類別類場地地基土的比例系數(shù)m =3000

3、0kN/m4臺后土的重力密度 =19kN/m3臺后土的內(nèi)摩擦角 =359、建筑材料橋臺混凝土的重力密度25kN/m3臺身混凝土強度等級C30臺身主筋種類HRB335臺身主筋直徑25mm臺身主筋中心至混凝土表面的距離0.06m樁基混凝土強度等級C25樁基主筋種類HRB335樁基主筋直徑25mm樁基主筋中心至混凝土表面的距離0.075m10、其他計算數(shù)據(jù)是否考慮支撐梁作用考慮構(gòu)件計算長度系數(shù)(臺身)2.0構(gòu)件計算長度系數(shù)(樁基)0.511、技術(shù)標(biāo)準(zhǔn)與設(shè)計規(guī)范1)中華人民共和國行業(yè)標(biāo)準(zhǔn)公路橋涵設(shè)計通用規(guī)范(JTG D602004)2)中華人民共和國行業(yè)標(biāo)準(zhǔn)公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(J

4、TG D622004)- 3 -3)中華人民共和國行業(yè)標(biāo)準(zhǔn)公路橋涵地基與基礎(chǔ)設(shè)計規(guī)范(JTG D632007)4)中華人民共和國行業(yè)推薦性標(biāo)準(zhǔn)公路橋梁抗震設(shè)計細(xì)則(JTG/T B02-012008)( (二二) ) 豎豎向向恒恒載載計計算算1、恒載重力計算1)上部構(gòu)造恒載反力豎向力P1 =3700kN對臺身中心偏心距e1 =0.27m對承臺中心偏心距e1 =0.27m2)橋臺背墻重豎向力P2 = 162.5 +76.4 =238.9kN對臺身中心偏心距e2 =-0.25m ，-0.575m對承臺中心偏心距e2 =-0.25m ，-0.575m3)橋臺臺帽重豎向力P3 =612.6kN對臺身中心

5、偏心距e3 =0.025m對承臺中心偏心距e3 =0.025m4)橋臺臺身重豎向力P4 = 1060.8kN對承臺中心偏心距e4 =0m5)橋臺承臺重豎向力P5 = 1144.0kN6)承臺上土重豎向力P6 = 705.4 +221.3 =926.7kN對承臺中心偏心距e6 =-0.75m ，-0.9m7)橋頭搭板反力按跨徑為搭板長度的0.7倍的簡支梁計算豎向力P7 =273.0kN對臺身中心偏心距e7 =-0.575m對承臺中心偏心距e7 =-0.575m2、恒載對各截面所產(chǎn)生的垂直力及彎矩1)對臺身底截面豎向力P恒 = P1+P2+P3+P4+P7 = 5885.3kN彎矩M恒 = P1e

6、1+P2e2+P3e3+P7e7 =772.8kNm2)對承臺底截面豎向力P恒 = P1+P2+P3+P4+P5+P6+P7 = 7956.0kN彎矩M恒 = P1e1+P2e2+P3e3P4e4+P6e6+P7e7 =44.5kNm- 4 -( (三三) ) 水水平平土土壓壓力力計計算算1、臺后填土自重引起的土壓力土的內(nèi)摩擦角 =35 橋臺與豎直面的夾角 =0 填土表面與水平面的夾角 =0 臺背與填土間的摩擦角 =/2 = 17.5 主動土壓力系數(shù) = 0.2461主動土壓力標(biāo)準(zhǔn)值E = BH2/2土的重力密度 =19kN/m3橋臺的計算寬度B = 13.000m對臺身底截面計算土層高度H1

7、 =6.63m主動土壓力E1 = 1336.1kN自計算土層底面算起土壓力的著力點C1 = H1/3 =2.210m彎矩ME = E1C1 = 2952.8kNm對承臺底截面計算土層高度H2 = H1 =6.63m主動土壓力E2 = E1 = 1336.1kN自計算截面算起土壓力的著力點C2 = C1+ 1.6 =3.810m彎矩ME = E2C2 = 5090.6kNm2、汽車荷載引起的土壓力橋臺與豎直面的夾角 =0 土的內(nèi)摩擦角 =35 臺背與填土間的摩擦角 =/2 = 17.5 = += 52.5 破壞棱體破裂面與豎直線間夾角tan = 0.5835填土高度H =6.63m破壞棱體長度l

8、0 = H(tan+tan) =3.868m破棱體上作用軸數(shù)2 軸車道系數(shù)2車輪的總重力G =560.0kN橋臺橫向全寬B = 13.000m土的重力密度 =19.0kN/m3車輛荷載等代均布土層厚度h = G/(Bl0) =0.586m主動土壓力系數(shù) = 0.2461()()()()()222coscossinsin1coscoscos-+-+-()()tantantancottan-+- 5 -主動土壓力標(biāo)準(zhǔn)值E = BHh對臺身底截面計算土層高度H1 =6.63m汽車引起的主動土壓力E1 =236.2kN自計算土層底面算起土壓力的著力點C1 = H1/2 =3.315m彎矩Me = E1

9、C1 =783.1kNm對承臺底截面計算土層高度H2 = H1 =6.63m汽車引起的主動土壓力E2 = E1 =236.2kN自計算截面算起土壓力的著力點C2 = C1+ 1.6 =4.915m彎矩Me = E2C2 = 1161.0kNm( (四四) ) 汽汽車車荷荷載載計計算算1、汽車荷載反力計算車道荷載的均布荷載標(biāo)準(zhǔn)值qK =7.9kN/m車道荷載的集中荷載標(biāo)準(zhǔn)值PK =168.0kN車道系數(shù)2橋梁計算跨徑l =16m汽車荷載反力P汽 = (qKl/2+1.2PK)*車道系數(shù) =529.2kN對臺身中心偏心距e1 =0.27m對承臺中心偏心距e1 =0.27m汽車荷載對臺身底截面產(chǎn)生的

10、彎矩M汽 =142.9kNm汽車荷載對承臺底截面產(chǎn)生的彎矩M汽 =142.9kNm2、汽車沖擊力計算上部結(jié)構(gòu)跨中處的單位長度質(zhì)量mc =G/g = 1529.1kg/m上部結(jié)構(gòu)混凝土的彈性模量Ec = 3.25E+10 N/m2上部結(jié)構(gòu)跨中截面慣矩Ic =0.04m4橋梁計算跨徑l =16m結(jié)構(gòu)基頻f =5.66Hz沖擊系數(shù)當(dāng)f1.5Hz，=0.05當(dāng)1.5Hzf14Hz，=0.1767lnf-0.0157當(dāng)f14Hz，=0.45 =0.291汽車沖擊力P沖 = P汽 =153.7kN汽車沖擊力對臺身底截面產(chǎn)生的彎矩cccmIEl22- 6 -M沖 =41.5kNm汽車沖擊力對承臺底截面產(chǎn)生的

11、彎矩M沖 =41.5kNm( (五五) ) 汽汽車車荷荷載載制制動動力力、支支座座摩摩阻阻力力計計算算1、汽車荷載制動力計算車道荷載的均布荷載標(biāo)準(zhǔn)值qK =7.9kN/m車道荷載的集中荷載標(biāo)準(zhǔn)值PK =168.0kN一個設(shè)計車道總重力的10%29.4kN 17.5 考慮偏心距增大系數(shù)偏心矩增大系數(shù) =式中：軸向力對截面重心軸的偏心距e0 = Md/Nd =0.883m截面有效高度h0 = h-a =0.74m荷載偏心率對截面曲率的影響系數(shù)1 = 0.2+2.7e0/h0 =3.4231.0212000)(/140011xxhlhe+hAI121=承載能力極限狀態(tài)基本組合- 11 -1 =1.0

12、00構(gòu)件長細(xì)比對截面曲率的影響系數(shù)2 = 1.15-0.01l0/h =1.0111.02 =1.000 =1.116e0 =0.986m軸向力至受拉邊縱向鋼筋合力點的距離e =e0+h/2-a =1.326m軸向力至受壓邊縱向鋼筋合力點的距離臺身混凝土軸心抗壓強度設(shè)計值fcd =13.8MPa縱向鋼筋的抗拉、抗壓強度設(shè)計值fsd = fsd =280MPa截面受壓區(qū)矩形應(yīng)力圖高度與實際受壓區(qū)高度的比值 =0.80矩形截面對稱配筋，As = As假定為大偏心受壓，s=fsd，則0Nd fcdbx 截面受壓區(qū)高度x =0.043m相對受壓區(qū)高度 = x/h0 =0.058b =0.56 為大偏心

13、受壓構(gòu)件0Nde fcdbx(h0-x/2)+fsdAs(h0-as)As = As = 0.0247m2矩形截面對稱配筋的鋼筋混凝土小偏心受壓構(gòu)件，其鋼筋截面面積可按下式計算As = As =式中相對受壓區(qū)高度 = 0.5589As = As = -0.1539m2 最小受拉或受壓區(qū)縱向鋼筋面積As = As = 0.0247m2橋臺臺身縱向主筋直徑為 25 mm 持久狀況承載能力極限狀態(tài)計算臺身一側(cè)所需最小縱向鋼筋根數(shù)為5151根2、構(gòu)造規(guī)定根據(jù)公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(JTG D622004)第9.1.12條，偏心受壓構(gòu)件全部縱向鋼筋的配筋百分率不應(yīng)小于0.5橋臺臺身縱向

14、主筋直徑為 25 mm 構(gòu)造規(guī)定臺身一側(cè)最小縱向鋼筋根數(shù)為53根3、正常使用極限狀態(tài)臺身裂縫寬度驗算1)作用臺身底面處短期效應(yīng)組合作用臺身底面處正常使用極限狀態(tài)短期效應(yīng)組合以組合控制設(shè)計軸向力Ns = 6255.7kN最大彎矩Ms = 5110.9kNm()()bcdsbcddcdbdbhfahbhfeNbhfN+-002000043. 0()()5 . 010200ssdcddahfbhfeN- 12 -臺身正常使用極限狀態(tài)作用效應(yīng)以臺身底截面(-截面)組合控制設(shè)計。2)作用作用臺身底面處長期效應(yīng)組合作用于臺身底面處長期效應(yīng)組合軸向力為Nl = 6097.0kN3)裂縫寬度驗算按公路鋼筋混凝

15、土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(JTG D622004)第6.4.3、6.4.4條計算軸向力Ns的偏心距e0 = Ms/Ns =0.817m截面高度h =0.80m截面有效高度h0 =0.74m構(gòu)件的計算長度l0 =11.160m使用階段的偏心距增大系數(shù)s = 1.0441l0/h =13.95014取s =1.0000截面重心至縱向受拉鋼筋合力點的距離ys =0.34m軸向壓力作用點至縱向受拉鋼筋合力點的距離es = se0+ys =0.340m受壓翼緣截面面積與腹板有效截面面積的比值f =0縱向受拉鋼筋合力點至截面受壓區(qū)合力點的距離z = 0.87-0.12(1-f)(h0/es)2h0=0

16、.2230.87h0 =0.644m取z =0.223m縱向鋼筋直徑d =25mm一側(cè)縱向鋼筋設(shè)計采用根數(shù)53根受拉區(qū)縱向鋼筋截面面積As =0.0260m2 鋼筋應(yīng)力ss = Ns(es-z)/(Asz) =125.91MPa縱向受拉鋼筋配筋率 = As/bh0 = 0.00270.022.5 m根據(jù)公路橋涵地基與基礎(chǔ)設(shè)計規(guī)范附錄P第P.0.4條，按表P.0.4計算作用效應(yīng)及位移。影響系數(shù)kh =0樁頂水平位移x0 =樁頂轉(zhuǎn)角0 =取h4.0，由公路橋涵地基與基礎(chǔ)設(shè)計規(guī)范表P.0.8查得= 2.4007= 1.5998= 1.5998= 1.7322樁頂水平位移x0 = 0.0040m樁頂轉(zhuǎn)

17、角0 = -0.0018rad樁身彎矩Mz =A3、B3、C3、D3由公路橋涵地基與基礎(chǔ)設(shè)計規(guī)范表P.0.8查得，計算見下表h=zA3B3C3D3zMz(m)(m)(kNm)00.000000.000001.000000.0000002404.92404.90.1-0.00017-0.000011.000000.100000.2422404.3FALSE0.2-0.00133-0.000130.999990.200000.4832400.3FALSE0.3-0.00450-0.000670.999940.300000.7252390.3FALSE0.4-0.01067-0.002130.999

18、740.399980.9672372.1FALSE0.5-0.02083-0.005210.999220.499911.2082344.6FALSE0.6-0.03600-0.010800.998060.599741.4502306.8FALSE0.7-0.05716-0.020010.995800.699351.6922258.3FALSE)(33032030302DEIHCEIMBAxEIaaafa+51EImb2112211220211221123011BABACBCBEIMBABADBDBEIH-+-aa)11(2112211202112211220BABACACAE IMBABADA

19、DAE IH-+-aa21122112BABADBDB-21122112BABACBCB-21122112BABACACA-21122112BABADADA- 15 -0.8-0.08532-0.034120.991810.798541.9342199.1FALSE0.9-0.12144-0.054660.985240.897052.1752129.9FALSE1-0.16652-0.083290.975010.994452.4172051.1FALSE1.1-0.22152-0.121920.959751.090162.6591963.8FALSE1.2-0.28737-0.172600.9

20、37831.183422.9001868.8FALSE1.3-0.36496-0.237600.907271.273203.1421767.6FALSE1.4-0.45515-0.319330.865731.358213.3841661.2FALSE1.5-0.55870-0.420390.815041.436803.6251561.8FALSE1.6-0.67629-0.543480.738591.506953.8671438.3FALSE1.7-0.80848-0.691440.646371.566214.1091324.3FALSE1.8-0.95564-0.867150.529971.

21、611624.3501210.2FALSE1.9-1.11796-1.073570.385031.639694.5921097.0FALSE2-1.29535-1.313610.206761.646284.834985.8FALSE2.2-1.69334-1.90567-0.270871.575385.317772.3FALSE2.4-2.14117-2.66329-0.948851.352015.801574.9FALSE2.6-2.62126-3.59987-1.877340.916796.284396.4FALSE2.8-3.10341-4.71748-3.107910.197296.7

22、67237.7FALSE3-3.54058-5.99979-4.68788-0.891267.25197.8FALSE3.5-3.91921-9.54367-10.34040-5.854028.459-189.8FALSE4-1.61428-11.73066 -17.91860 -15.075509.668-436.4FALSE由上表得知最大彎矩處z =0.000m最大彎矩Md = 2404.9kNm該處軸力Nd = 2554.1kN4)樁基配筋計算軸向力偏心距e0 = Md/Nd =0.942m構(gòu)件計算長度系數(shù)0.5構(gòu)件的計算長度l0= 0.5 4/ =4.834m慣性半徑i= d/4 =0

23、.375m長細(xì)比l0/i = 12.89017.5 不考慮偏心距增大系數(shù)偏心矩增大系數(shù) =式中：圓截面半徑r =0.75m縱向鋼筋所在圓周的半徑rs =0.675m截面有效高度h0 = r+rs =1.425m截面高度h = 2r =1.5m荷載偏心率對截面曲率的影響系數(shù)1 = 0.2+2.7e0/h0 =1.9841.0212000)(/140011xxhlhe+AI- 16 -1 =1.000構(gòu)件長細(xì)比對截面曲率的影響系數(shù)2 = 1.15-0.01l0/h =1.1181.02 =1.000 =1.000e0 =0.942m由公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(JTG D62-200

24、4)附錄C有配筋率 =樁的混凝土軸心抗壓強度設(shè)計值fcd =11.5MPa普通鋼筋的抗壓強度設(shè)計值fsd =280MPag = rs/r =0.900假定 =0.27A =0.4992B =0.3717C = -1.1254D =1.6584 = 0.0036Ar2fcd+Cr2fsd = 2590.2kN Nd = 2554.1kNBr3fcd+Dgr3fsd = 2438.9kN Nde0 = 2404.9kN 最小縱向鋼筋面積As = r2 = 0.0064m2橋臺樁基縱向主筋直徑為 25 mm 持久狀況承載能力極限狀態(tài)計算樁基所需最小縱向鋼筋根數(shù)為1313根3、構(gòu)造規(guī)定根據(jù)公路鋼筋混凝

25、土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(JTG D622004)第9.1.12條，偏心受壓構(gòu)件全部縱向鋼筋的配筋百分率不應(yīng)小于0.5橋臺臺身縱向主筋直徑為 25 mm 構(gòu)造規(guī)定樁基最小縱向鋼筋根數(shù)為19根4、正常使用極限狀態(tài)樁基裂縫寬度驗算1)作用短期效應(yīng)組合作用于承臺底面處正常使用極限狀態(tài)短期效應(yīng)組合以組合控制設(shè)計豎向力P短 = 8326.5kN水平力H短 = 1662.3kN最大彎矩M短 = 7042.4kNm單樁頂作用短期效應(yīng)橋臺樁基個數(shù)n樁 =4單樁頂豎向力P0短 = P短/n樁 = 2081.6kN單樁頂水平力H0短 = H短/n樁 =415.6kN單樁頂彎矩M0短 = M短/n樁 = 176

26、0.6kNmDgrCeAeBrffsdcd-00- 17 -考慮支撐梁作用，則樁頂水平力H0短 =0.0kN樁基最大彎矩計算樁頂水平位移x0 = 0.0030m樁頂轉(zhuǎn)角0 = -0.0013rad樁身彎矩Mz計算見下表h=zA3B3C3D3zMz(m)(m)(kNm)00.000000.000001.000000.0000001760.61760.60.1-0.00017-0.000011.000000.100000.2421760.2FALSE0.2-0.00133-0.000130.999990.200000.4831757.2FALSE0.3-0.00450-0.000670.99994

27、0.300000.7251749.9FALSE0.4-0.01067-0.002130.999740.399980.9671736.6FALSE0.5-0.02083-0.005210.999220.499911.2081716.5FALSE0.6-0.03600-0.010800.998060.599741.4501688.7FALSE0.7-0.05716-0.020010.995800.699351.6921653.2FALSE0.8-0.08532-0.034120.991810.798541.9341609.9FALSE0.9-0.12144-0.054660.985240.8970

28、52.1751559.3FALSE1-0.16652-0.083290.975010.994452.4171501.6FALSE1.1-0.22152-0.121920.959751.090162.6591437.6FALSE1.2-0.28737-0.172600.937831.183422.9001368.1FALSE1.3-0.36496-0.237600.907271.273203.1421294.0FALSE1.4-0.45515-0.319330.865731.358213.3841216.1FALSE1.5-0.55870-0.420390.815041.436803.62511

29、43.4FALSE1.6-0.67629-0.543480.738591.506953.8671053.0FALSE1.7-0.80848-0.691440.646371.566214.109969.5FALSE1.8-0.95564-0.867150.529971.611624.350886.0FALSE1.9-1.11796-1.073570.385031.639694.592803.1FALSE2-1.29535-1.313610.206761.646284.834721.7FALSE2.2-1.69334-1.90567-0.270871.575385.317565.4FALSE2.4

30、-2.14117-2.66329-0.948851.352015.801420.9FALSE2.6-2.62126-3.59987-1.877340.916796.284290.2FALSE2.8-3.10341-4.71748-3.107910.197296.767174.0FALSE3-3.54058-5.99979-4.68788-0.891267.25171.6FALSE3.5-3.91921-9.54367-10.34040-5.854028.459-138.9FALSE4-1.61428-11.73066 -17.91860 -15.075509.668-319.4FALSE由上表

31、得知最大彎矩處z =0.000m最大彎矩Ms = 1760.6kNm- 18 -該處軸向力Ns = 2081.6kN2)作用長期效應(yīng)組合作用于承臺底面處長期效應(yīng)組合豎向力為P長 = 8167.7kN單樁頂豎向力P0長 = P長/n樁 = 2041.9kN作用短期效應(yīng)組合最大彎矩處z =0.000m該處長期效應(yīng)組合軸向力Nl = 2041.9kN3)裂縫寬度驗算按公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范(JTG D622004)第6.4.5條計算按作用短期效應(yīng)組合計算的軸向力Ns = 2081621 N軸向力Ns的偏心距e0 = Ms/Ns =846mm截面高度h = 2r =1.5m截面有效高

32、度h0 = r+rs =1.425m構(gòu)件的計算長度l0 =4.834m使用階段的偏心距增大系數(shù)s = 1.0044l0/h =3.22314取s =1.0000構(gòu)件的截面半徑r =750mm混凝土強度等級fcu,k =25MPa縱向鋼筋直徑d =25mm設(shè)計采用鋼筋根數(shù)19根截面配筋率 = As/r2 = 0.0053截面受拉區(qū)最外緣鋼筋應(yīng)力ss =144.8MPa 24 MPa 應(yīng)驗算裂縫寬度鋼筋表面形狀系數(shù)C1 =1.0作用長期效應(yīng)影響系數(shù)C2 =1+0.5Nl/Ns =1.490鋼筋的彈性模量Es =200000MPa混凝土的保護層厚度C =60.8mm 最大裂縫寬度Wfk = C1C2

33、0.03+ss/Es(0.004d/+1.52C)=0.165mm 0.20 mm 滿足規(guī)范裂縫寬度要求( (十十) ) 計計算算結(jié)結(jié)果果匯匯總總2000/400011+hlhe320,265. 10 . 180. 242.59-refrNskcus- 19 -項目臺身厚度或樁徑(m)混凝土 強度等級主筋種類主筋直徑(mm)計算所需主筋根數(shù)構(gòu)造最小主筋根數(shù)構(gòu)造最大主筋根數(shù)(超過可采用束筋)設(shè)計采用 主筋根數(shù)鋼筋間距(cm)裂縫寬度(mm)臺身(一側(cè))0.8C30HRB3352551531645324.80.136樁基1.5C25HRB335251319391922.30.165樁長 (m)10#DIV/0!- 20 -P (kN)H (kN)8018.51870.6基本組合6841.41870.6基本組合7062.42201.3基本組合588