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第四章练习题参考答案【4-1】已知某轴心受拉杆的截面尺寸300400bhmmmm,配有820钢筋,混凝土和钢筋的材料指标为:22.0/tfNmm,42.110cE2/Nmm,2270/yfNmm,522.110/sENmm。试问此构件开裂时和破坏时的轴向拉力分别为多少?【解】配820钢筋,查混凝土结构设计规范(GB50010-2010)附录A,表A.0.1得22513sAmm。25132.09%3.0%300400sAbh,2300400120000Abhmm,542.110102.110sEcEE(1)由式(4-5),开裂荷载为0(1)(1)tcrcEttENEAfA2.0120000(1100.0209)290160N209.16kN(2)由式(4-7),构件的抗拉极限承载力为2702513678510678.51tuysNfANkN【4-2】已知某钢筋混凝土轴心受拉构件,截面尺寸为200300bhmmmm,构件的长度2000lmm,混凝土抗拉强度22.95/tfNmm,弹性模量422.5510/cENmm,纵向钢筋的截面积2615sAmm,屈服强度2270/yfNmm,弹性模量522.110/sENmm,求(1)若构件伸长0.2mm,外荷载是多少?混凝土和钢筋各承担多少外力?(2)若构件伸长0.5mm,外荷载是多少?混凝土和钢筋各承担多少外力?(3)构件开裂荷载是多少?即将开裂时构件的变形是多少?(4)构件的极限承载力是多少?【解】6151.025%3.0%200300sAbh,则220030060000Abhmm542.1108.2352.5510sEcEE,4042.951.157102.5510ttcfE(1)○1由0.2lmm可知,构件的应变为4400.21.0101.157102000tll构件未开裂,处于弹性工作状态,cs,构件所受的拉力为44(1)2.551060000(18.2351.025%)1.010tcENEA3165.9110N165.91kN○2此时混凝土承担的外力4432.55101.01060000153.010153.0tscNEANkN○3钢筋承担的外力165.91153.012.91tsttcNNNkN(2)○1由0.5lmm可知,构件的应变为4400.52.5101.157102000tll,且352701.286102.110yysfE构件开裂,钢筋未屈服,s,构件所受的拉力为542.1102.51061532287.532.29tssNEANkN○2此时,混凝土开裂,在开裂处混凝土应力0c○3钢筋的应力5422.1102.51052.5/ssENmm(3)○1开裂荷载为0(1)tcrcEtNEA442.551060000(18.2351.025%)1.15710191.96kN○2即将开裂时构件的变形401.1571020000.23tllmm(4)构件的极限承载力为270615166050166.05tuysNfANkN【4-3】某钢筋混凝土轴心受拉构件的截面尺寸为300300bhmmmm,配有822的纵向受力钢筋,已知22.3/tfNmm,422.410/cENmm,2345/yfNmm,521.9610/sENmm。(1)若允许构件开裂,求构件所能承受的最大轴向拉力。(2)若不允许构件开裂,求构件所能承受的最大轴向拉力。(3)对上述结果进行比较分析。【解】由规范822钢筋,23041sAmm,230030090000bhmm30413.379%3%90000sAbh,290000304186959sAbhAmm541.96108.1672.410sEcEE5042.39.583102.410ttcfE,353451.760101.9610yysfE,0ty(1)若允许开裂,则构件能承受的最大轴向拉力即极限荷载为345304110491451049.145tuysNfANkN(2)若不允许构件开裂,则构件能承受的最大轴向拉力即开裂荷载为(1)2.386959(18.1673.379%)255200255.20tcrtENfANkN(3)从以上的计算结果可知,若不允许开裂,构件能承受的最大轴向拉力将大大降低,不利于于材料的强度发挥,因此对普通的钢筋混凝土构件宜允许构件带裂缝工作。【4-4】有一钢筋混凝土下弦杆,承受轴向拉力150tNkN,若2270/yfNmm,且下弦允许出现裂缝,试求此下弦杆的配筋。【解】下弦允许出现裂缝,则此时构件能承受的最大轴向拉力即极限荷载为:ttuysNNfA,则2150000556270tsyNAmmf【4-5】某钢筋混凝土受压短柱400400bhmmmm,柱长2m,配有纵筋425,219/cfNmm,422.5510/cENmm,2357/yfNmm,521.9610/sENmm,试问:(1)此柱子的极限承载力为多少?(2)在1200cNkN作用下,柱的压缩变形量为多少?此时钢筋和混凝土各承受多少压力?(3)使用若干年后,混凝土在压力1200cNkN作用下的徐变变形为0.001cr,求此时柱中钢筋和混凝土各承受多少压力?【解】查425,21964sAmm19641.1275%3%400400sAbh,2400400160000Abhmm(1)柱子的极限承载力:19160000357196437411483741.148cucysNfAfANkN(2)120032.08%30%3741.148ccuNN,宜考虑混凝土材料应力和应变之间的非线性。若应力-荷载关系处于第Ⅰ阶段,则1000(1250)ccssNfAEA351200101000(1250)191600001.96101964276000342.49440.120得43.82910353571.82101.9610yysfE,处于第Ⅰ阶段。○1柱的压缩变形量为43.8291020000.766llmm○2钢筋的应力:5421.96103.8291075.0484/ssENmm混凝土的应力:4421000(1250)10003.82910(12503.82910)196.5787/ccfNmm钢筋承受的轴压力541.96103.829101964147395147.395sssssNAEANkN混凝土承受的轴压力6.578716000010525921052.592ccNANkN(3)若0.001cr,取43.82910i,则4/0.001/3.829102.611648tcriC钢筋的应力:221(1)(12.611648)75.0484271.0484/stsCNmm钢筋承受的轴压力:22271.04841964532339532.339sssNANkN混凝土承受的轴压力:221200532.339667.661ccsNNNkN【4-6】某轴心受压短柱,长2m,350350bhmmmm,配有425的纵筋,215/cfNmm,2270/yfNmm,521.9610/sENmm,00.002,试问:(1)压力加大到多少时,钢筋将屈服?此时柱长缩短多少?(2)该柱所能承担的最大轴压力为多少?【解】查表425,21964sAmm19641.603%3%350350sAbh,2350350122500Abhmm(1)钢筋屈服,此时:352701.37755101.9610yysfE○1此时受压短柱承受的压力:1000(1250)ccysNfAfA3310001.3775510(12501.3775510)15122500270196416595185302802189798N2189.798kN○2此时柱长缩短:31.377551020002.755llmm(2)该柱所能承担的最大轴压力(00.002y)0.90.9()0.9(151225002701964)21310022131.002cucysNNfAfANkN【4-7】已知某多层房屋中柱的计算高度为4.2m,2310/yfNmm,210/cfNmm,轴向压力为700kN,柱子截面为250250bhmmmm,试确定纵筋数量。【解】225025062500bhmm,04.24200lmmm0420016.8250lb,查表4-1得:016lb,0.87;018lb,0.81内插得:016.8,0.846lb22310/400/yfNmmNmm由0.90.9()ccucsyNNAfAf,取262500Abhmm得2/(0.9)700000/(0.90.846)6250010950310csyNAfAmmf9501.52%3%62500sAbh,则262500Abhmm由附表4-1知,min0.6%,min查规范表A.0.1,实配418纵向钢筋(221017950sAmmmm,安全)【4-8】某轴心受压柱,柱计算高度4.7m,混凝土棱柱体抗压强度210/cfNmm,配置纵筋420,2360/yfNmm,试求:(1)当截面尺寸为300300mmmm时,该柱子能承受的轴力;(2)当截面尺寸为250250mmmm时,该柱子能承受的轴力。【解】柱计算高度04.74700lmmm,22360/400/yfNmmNmm配置纵筋420(查表,21256sAmm)(1)当截面尺寸为300300mmmm时0470015.7300lb,查表014lb,0.92;016lb,0.87内插得:015.7lb,0.87812561.396%3%90000sAbh,则230030090000Abhmm柱子的轴心抗压承载力:0.90.9()0.90.878(90000101256360)10684761068.476ccucsyNNAfAfNkN(2)当截面尺寸为250250mmmm时0470018.8250lb,查表018lb,0.81;020lb,0.75内插得:018.8lb,0.78612562.010%3%62500sAbh,则225025062500Abhmm柱子的轴心抗压承载力:0.90.9()0.90.786(62500101256360)761983761.983ccucsyNNAfAfNkN【4-9】轴心受压螺旋筋柱,直径450mm,柱的计算高度为03.5lm,混凝土轴心抗压强度设计值210/cfNmm,配置纵向钢筋822,2270/yfNmm,轴向压力为2500kN。若螺旋箍筋的
本文标题:混凝土结构基本原理第4章-练习题参考答案
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