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抗震计算—桥墩抗震计算汇总

抗震计算选用最不利的空心板处的独柱墩进行抗震计算(一)设计资料1、上部构造:3孔25m连续桥面简支空心板,25m预制后张预应力空心板,计算跨径为24.26m,每跨横向设6块板。

桥面现浇10cm厚50号混凝土,7cm沥青混凝土。

2、桥面宽度(单幅):0.5(防撞护栏)+净7.0(行车道)+0.5m(护栏)=8.0m。

3、设计荷载:公路Ⅱ级。

4、支座:墩顶每块板板端设GYZ250x52mm板式橡胶支座2个。

5、地震动峰值加速度:0.10g。

6、下部构造:巨型独柱墩,1.3 x 1.5m;钻孔桩直径1.5m,均值长40m。

墩柱为30号混凝土,桩基础为30号混凝土,HRB335钢筋。

桥墩一般构造如下:(二)恒载计算1、上部恒载反力(单孔)空心板:4.7843×25×26=3109.8kN 桥面铺装(包括50号混凝土和沥青混凝土): 7×25×0.1×26+7×25×0.07×24=749kN 防撞护栏:0.351×25×25×2=438.8kN 合计:3109.8+749+438.8=4297.6kN 2、下部恒载计算 1) 盖梁加防震挡块重力P G =23.358×26=607.3kN 2) 墩身重力P d =3.23×13×26=1091.7kN 3) 单桩自重力P z =4π×1.52×40×25=1767.1kN (三)水平地震力计算 1、顺桥向水平地震力计算1)上部结构对板式橡胶支座顶面处产生的水平地震荷载 E ihs =sp h z i ni itpitpG K C C KK 11β∑=式中:C i =1.7,C z =0.3,K h =0.2根据地质资料分析,桥位所在地土层属Ⅲ类场地,所以有 β1=2.25×(145.0T )0.95对于板式橡胶支座的梁桥T 1=12ωπ其中:ω12=tpsp sp tp sp tp sp tp G G K K G G G K K K G G K K K G g2}4])({[)(2/1212211211-++-++K 1=∑=ni is K 1计算采用3孔×25m 为一联,故n =2 K is =∑∑=sn i rd tA G 1其中:n s =2×12=24,G d =1200kN/m 2 由橡胶支座计算知A r =4π×0.252=0.0491m 2 ∑t =0.032m ∴ K is =24×032.00491.01200⨯=44190kN/mK 1=44190kN/m K 2=∑=ni ip K 1K ip =3113il E I其中:墩柱采用30号混凝土,则 E c =3.00×104MPaE 1=0.8×3.00×104×103=2.4×107kN/m 2 按墩高H =13+2=15m 控制设计,支座垫石+支座厚度=0.1+0.052=0.152ml i =15+0.142=15.152m 柱惯矩: I 1=0.4531m 4K ip =37152.15104.24531.03⨯⨯⨯=9378.1kN/m K 2=9378.1kN/mG sp =3×4297.6÷2=6446.4kN G tp =G cp +ηG p其中: G cp =607.3kN G p =1091.7kNη=0.16(2f X +2221f X +21ff X X +21f X +1)顺桥向作用于支座顶面的单位水平力在支座顶面处的水平位移为: X d =X 0-φ0l 0+X Q 其中: l 0=l i =15.152mX Q =11303I E l =4531.0104.23152.1573⨯⨯⨯=0.000107 桩的计算宽度:b 1=0.9(d+1)=0.9×(1.5+1)=2.25m 桩在土中的变形系数:α=51EIm b m =20000kN/m 4 其中:桩采用30号混凝土,则 E c =3.0×104MPaEI =0.8×3.0×107×64π×1.54=5.964×106 ∴ α=5610964.525.220000⨯⨯=0.3763桩长h =40m ,∴ αh =0.3763×40=15.052m >2.5m 取αh =4.0,故K h =0 从而有 X 0=34433443203443344331B A B AC B C B EI l B A B AD B D B EI --⨯+--⨯αα φ0=)1(344334430344334432B A B AC A C A EI l B A B AD A D A EI --⨯+--⨯-αα 由公路桥涵地基与基础设计规范(JTJ 024-85)附表6.11查得 34433443B A B A D B D B --=2.44134433443B A B A C B C B --=34433443B A B A DA D A --=1.62534433443B A B A C A C A --=1.751故 X 0=EIl EI 203625.1441.2αα+ =626310964.53763.0152.15625.110964.53763.0441.2⨯⨯⨯+⨯⨯=0.00002328φ0=)751.1625.1(02EI l EIαα+- =)10964.53763.0152.15751.110964.53763.0625.1(662⨯⨯⨯+⨯⨯-=-0.000009116X d =0.00002328+0.000009116×15.152+0.000107 =0.0002684X f =dX X 0=0.00026840.00002328=0.0867X H/2=X 0-φ0l 0/2+X Q/2=X 0-φ0l 0/2+1130485I E l=0.00002328+0.0000091×2152.15+4531.0104.248152.15573⨯⨯⨯⨯ =0.0001255 X f/2=dH X X 2/=0002684.00001255.0=0.4676 ∴ η=0.16×(0.08672+2×0.46762+0.0867×0.4676+0.4676+1) =0.3125G tp =607.3+0.3125×1091.7=948.5kN∴ω12=tpsp sp tp sp tp sp tp G G K K G G G K K K G G K K K G g2}4])({[)(2/1212211211-++-++=4.64465.9482}1.9378441904.64465.9484]4.6446)1.937844190(441905.948{[4.6446)1.937844190(441905.9488.92/12⨯⨯⨯⨯⨯⨯-⨯++⨯-⨯++⨯⨯=10.67ω1=3.267T 1=267.32π=1.92 β1=2.25×(92.145.0)0.95=0.567K itp =ipis ip is K K K K +=1.9378441901.937844190+⨯=7736.3kN/m则 E ihs =4.6446567.02.03.07.11⨯⨯⨯⨯⨯=372.82kN 2)墩身自重在板式支座顶面的水平地震荷载E hp =tp h z i G K C C 1β=5.948567.02.03.07.1⨯⨯⨯⨯=54.86kN 支座顶面的水平地震力总和为E ihs +E hp =372.82+54.86=427.68kN(四)墩柱截面内力及配筋计算(柱底截面) 1、荷载计算上部恒载反力:4297.6kN下部恒载重力:1091.7+607.3=1699kN 作用于墩柱底面的恒载垂直力为N 恒=4297.6+1699=5996.6kN水平地震力:H =427.68kN水平地震力对柱底截面产生的弯矩为 M =427.68×15.152=6480.2kN ∙m 2、荷载组合1)垂直力:N =5996.6kN 2)水平力:H =427.68kN 3)弯矩: M =6480.2kN ∙m 3、截面配筋计算偏心矩: e 0=M d /N d =6480.2/5996.6=1.081m 构件计算长度:l 0=2l =2×13=26mi =A I =23.34531.0=0.3745 l 0/i =26/0.3745=69.43>17.5 ∴应考虑偏心矩增大系数η η=1+212000)(/14001ξξhl h eh 0=1.24m ,h =1.3mξ1=0.2+2.70h e =0.2+2.7×24.1455.1=3.368>1.0∴取 ξ1=1.0ξ2=1.15-0.01h l0=1.15-0.01×3.126=0.95<1.0 ∴取 ξ2=0.95η=1+95.00.1)3.126(24.1/455.1140012⨯⨯⨯=1.231ηe 0=1.231×1.455=1.791m选用双侧50φ25HRB335钢筋,A s =0.0245m 2>0.5%A= 0.01615m 2 (五)桩身截面内力及配筋计算 1、内力计算作用于地面处桩顶的外力为 承台重=6.3×2.5×2×25=787.5N 0=(5996.6+787.5)÷2=3392.1kN ,H 0=427.68÷2=213.84kN , M 0=213.84×(15.152+2)=3667.8kN ∙m 1) 桩身弯矩利用单桩内力计算,最大弯矩在y =0.8m 处,M y =3779.2 kN ∙m 垂直力: N d =3392.1+4π×1.52×0.8×25=3427.4kN 2、截面配筋计算偏心矩: e 0=M d /N d =3779.2/3427.4=1.103m 构件计算长度:l 0=0.7×α4=0.7×3763.04=7.441m i =A I =4/5.164/5.124⨯⨯ππ=0.375 l 0/i =7.441/0.375=19.84>17.5∴应考虑偏心矩增大系数η η=1+212000)(/14001ξξhl h eh 0=r +r s =0.75+0.66=1.41m h =2r =2×0.75=1.5m ξ1=0.2+2.70h e =0.2+2.7×41.1793.0=1.72>1.0∴取 ξ1=1.0ξ2=1.15-0.01h l0=1.15-0.01×5.1441.7=1.1>1.0 ∴取 ξ2=1.0η=1+0.10.1)5.1441.7(41.1/793.0140012⨯⨯⨯=1.031ηe 0=1.031×1.103=1.137m由公路钢筋混凝土及预应力混凝土桥涵设计规范(JTG D62-2004)附录C 有 配筋率 ρ=DgrCe Ae Br f f sd cd --⋅00' f cd =13.8MPa ,f sd ’ =280MPag =r s /r =0.66/0.75=0.88 假定ξ=0.34,A =0.6915,B =0.4699,C =-0.7657,D =1.8071 ρ=75.088.08071.1137.17657.0137.16915.075.04699.02808.13⨯⨯-⨯-⨯-⨯⨯=0.00987 N d ≤Ar 2f cd +C ρr 2f sd ’Ar 2f cd +C ρr 2f sd ’=0.6915×0.752×13.8×103-0.7657×0.00987×0.752×280×103=4162kN>N d=3427.4Kn∴纵向钢筋面积A s=ρπr2=0.00987×π×0.752=0.0174m2 选用36φ25HRB335钢筋,A=0.0177m2> A s=0.0174m2。

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