第5章練習題參考答案

第5章練習題參照答案第5章練習題參照答案【5-1】已知鋼筋混凝土梁的截面尺寸為b250mm，600mm，混凝土保護層厚度c25mm，混凝土和鋼筋資料的性能指標為fc23N/mm2，ft2.6N/mm2，Ec2.51104N/mm2；fy357N/mm2，Es1.97105N/mm2，受拉區(qū)配有325（As1472mm2）的縱向受拉鋼筋。試計算（1）當截面所受的彎矩M50kNm時的s、c和；t（2）截面的開裂彎矩Mcr及相應的s、c和cr。t【解】（1）求當截面所受的彎矩M50kNm時的s、t和cEEs1.971057.849，EAs7.84914720.077，Ec2.51104bh250600A2EAs0.1540bh12EAsh10.1540600xcrbh321mm1EAs210.0772bhh0hcd60025562.5mm2252Mcrftb(hxcr)hxcr2xcr2EftAsh0xcr2332.6250(600321)600321232127.8492.6147250032123393506071Nmm93.506kNmM50kNmMcr93.506kNm，截面處于彈性階段，此時采納線性的物理關系tbtbt，scc，tsEcEcEs由幾何變形方程：tbctsxnhxnh0xn將幾何變形方程代入物理方程得：ttxnEc，ccEcsh0xnEs1）

bbhxnEcttEcsh0xnEs由受力均衡：X0，1ctxnbsAs1tb(hxn)b22代入（1）式，得：xn2Ec2sAs(hxn)2Ech0sbh0sbxnEsxnEsxn2Ecb2As(h0xn)Es(hxn)2Ecb2(AsEsbhEc)xn2Ash0Esbh2EcxnAsh0Es0.5bh2EcAsh0E0.5bh21472562.57.8490.52506002AsEsbhEcAsEbh14727.849319mm250600由力矩均衡：M0，MsAsh0xn1tb(hxn)b2h323xn(hxn)2EcbhsAsh0h0xnEss33解得：sxM(hx)250106(600319)218.27N/mm2bh1472562.5319250600Ash0nn33h0xn337.849562.5319EtxnEc31918.275828.133.05N/mm2ch0xnEss319)7.8491911.2315(562.5s(h0s(562.518.2718.271073.811071/mmh0xnxn)Es319)1.971054.79695（2）截面的開裂彎矩Mcr及相應的s、c和crt由前面計算可知，McrkNm93.506s2Eft27.8492.640.81N/mm2由截面靜力均衡條件得tftb(hxcr)sAs2.6250(600321)40.811472241422.322c0.5bxcr0.5250321401256.02N/mmcrft2.6321)7.431071/mm0.5Ec(hxcr)0.52.51104(600【5-2】條件同練習題5-1，試計算1）截面的極限彎矩Mu及相應的u；2）按等效矩形應力爭形的簡化方法求截面的極限彎矩Mu3）與例5-2的計算結(jié)果進行比較?！窘狻浚?）求截面的極限彎矩Mu及相應的uAs14720.981%min0.45ft0.452.60.328%bh250600fy357nb1.01.00.646fy3571150.0033Es0.00331.9710對強度等級不大于C50的混凝土，ccu0.0033，00.002，代入靜力均衡方程，得tfc20.00414Es(1n)0，As1472nbh02501.05%562.523n20.004141.971051.05%(1n)020.37233n0.372330n0.372330.37233240.372330.9036n220.452nb1nt1.9710510.4520.0033788.17N/mm2fy357N/mm2sEsc0.452n混凝土壓碎前，鋼筋已折服（處于Ⅲa狀態(tài)），以fy代人得fy1.2531.05%357n1.2530.204nbfc23MufyAsh0(10.412n)3571472562.5(10.4120.204)106270.75kNmt0.003328.761061/mmucnh00.204562.5（2）簡化方法fy3570.16300.80.81.05%23bfy0.5161fc1.0113570.0033Es50.00331.9710MuAsfyh0(10.5)1472357562.5(10.50.163)106271.50kNm3）聯(lián)合例5-2當As760mm2時，Mu當As1472mm2時，Mu

可知146.40kNm，u55.721061/mm270.75kNm，u28.761061/mm當As1520mm2時，Mu279.57kNm，u27.861061/mm跟著配筋量的增添，截面的抗彎承載力會提升，但截面的變形能力會降低。5-3】條件同練習題5-1，求當截面的縱向受拉鋼筋分別為212和1028時截面的抗彎承載力?！窘狻浚?）當截面的縱向受拉鋼筋為212（As226mm2）時As2260.15%<min0.45ft0.452.60.328%0.2%bh250600fy357E7.849，A2EAs27.8492260.02365bh250600MuMcr0.292(12.5A)ftbh20.292(12.50.02365)2.6250600210672.37kNm（2）當截面的縱向受拉鋼筋為1028（As6158mm2）時b0.80.80.516fy135710.0033Es0.00331.97105bb1fc0.5161.0233.324102fy357縱筋許多，需要分三層部署，從下往上鋼筋的數(shù)目分別為4、4、2。4600252846002528282826002542828h0222516.2mm10As61584.772102b3.324102，超筋梁bh0250516.2sfy0.8，代入靜力均衡方程，1fcbh0sAs，得b0.80.80.80.57831fcbh0(0.8b)11.023250516.21(0.80.516)fyAs3576158xh00.5783516.2299mmMu1fcbh02121.023250516.220.578310.57831062629.85kNm【5-4】已知某簡支鋼筋混凝土平板的計算跨度為l02.8m，板厚h90mm，配置10@200的鋼筋，混凝土和鋼筋資料的性能指標為fc11.9N/mm2，ft1.6N/mm2；fy280N/mm2，Es2.0105N/mm2。試求該板每m2承受的荷載是多少？【解】板的保護層厚度c15mm，取c15mm；h0hcd90151070mmd220.20.257，取min0.257%min45ft451.6fy280b0.80.80.5617fy280110.00332.01050.0033Esbb1fc0.56171.011.92.387102fy280取單寬即b1000mm，因配置10@200，因此在單寬范圍內(nèi)為410，As314mm2。As3140.4486%，minb，為適筋矩形截面。bh0100070由靜力均衡得，xfyAs2803147.388mm1fcb1.011.91000由力矩平衡得，MufyAsh0x280314707.3881065.904kNm22M1qbl02Mu5.904kNm8q85.9046.024kN/m21.02.82【5-5】鋼筋混凝土簡支梁的截面尺寸為b220m，h500m，計算跨度為l06m，承受均布q24kN/m（包括梁的自重），配有受拉縱筋和鋼筋資料的性能指標為fc

2222213N/mm，

20，混凝土2ft1.2N/mm；fy365N/mm2，Es1.97105N/mm2。問此梁的正截面能否安全？【解】（1）計算最小配筋率、界線配筋率min0.45ft0.451.21.479103fy3650.80.8bfy0.512113650.0033Es0.00331.97105bb1fc0.5121.0131.824102fy365（2）當縱筋為222220時As7606281388mm2As13881.262102min1.479103bh220500h05002522464mm2As13881.360102b1.824102bh0220464為適筋截面（3）截面承載力計算fyAs3651388x177mm1fcb1.013220截面的極限承載力：MufyAsh0x3651388464177190.24106Nmm190.24kNm22梁中遇到的最大彎矩為：Mmax1ql212462108kNmMu190.24kNm88此梁正截面安全。5-6】某簡支梁的截面尺寸為b200mm，h500mm，混凝土和鋼筋資料的性能指標為fc13N/mm2，ft1.2N/mm2；fy的彎矩分別為求相應的配筋論之。【解】

310N/mm2，Es1.97105N/mm2。當其所受M40,60,80,100,120,140,160,180,200,220kNm時，As為多少？畫圖表示MAs關系并討1）計算最小配筋率、界線配筋率、適筋構件的最大抗彎承載力min0.45ft0.451.21.7421030.2%fy310min0.2%b0.80.80.542fy310110.0033Es0.00331.971051fc0.5421.0132.273102bbfy310s,maxb10.5b0.54210.50.5420.395因為不知道直徑，取h050035465mmMu,maxs,max1fcbh020.3951.0132004652222.06106Nmm222.06kNm（2）當M40kNmMu,max222.06kNm時1fcbxfyAs由Mu1fcbxx得Mh02x34mm,As288mm2；As2.88103min2.0103bh故取As288mm2（3）當M60kNmMu,max222.06kNm時同理得x53mm,As441mm2（4）當M80kNmMu,max222.06kNm時同理得x72mm,As601mm2（5）當M100kNmMu,max222.06kNm時同理得x92mm,As770mm2（6）當M120kNmMu,max222.06kNm時同理得x113mm,As948mm2（7）當M140kNmMu,max222.06kNm時同理得x136mm,As1137mm2（8）當M160kNmMu,max222.06kNm時同理得x160mm,As1340mm2（8）當M180kNmMu,max222.06kNm時同理得x205mm,As1721mm2（注：配328，As1847mm2排能夠放下）（9）當M200kNmMu,max222.06kNm時，此時與Mu,max

單值較靠近，考慮部署二排鋼筋，取h050060440mm同理得x241mm,As2018mm2（10）當M220kNmMu,max222.06kNm時，此時與Mu,max值較靠近，考慮部署二排鋼筋，取h050060440mm同理得x284mm,As2381mm2（11）繪制MAs關系圖（略）u,max議論：梁的正截面承載能力與鋼筋的面積之間不是簡單的線性關系，跟著配筋量的增添，承載能力增添的速度漸漸降落，并趨于M?！?-7】已知某簡支混凝土平板的計算跨度為l01.92m，板厚h80mm，承受均布荷載q4kN/m2（包括梁的自重），混凝土和鋼筋混資料的性能指標為fc13N/mm2，ft1.2N/mm2；fy270N/mm2，Es1.90105N/mm2。求板的配筋。【解】取單寬板帶為剖析對象，則b1000mm，h0802060mm跨中最大彎矩為：Mmax1ql02141.9221.84kNm88b0.80.80.559fy127010.0033Es0.00331.90105s,maxb10.5b0.55910.50.5590.403Mu,maxs,max1fcbh020.4031.013100060218.86106Nmm18.86kNmMmax1fcbxfyAs由Mu1fcbxh0x得x2.4mm,As116mm2M2min0.45ft0.451.22.01030.2%fy270故min0.2%As1161.451030.2%bh100080按結(jié)構配筋，受力鋼筋可選

Asminbh0.2%100080160mm26@150散布鋼筋，單位寬度上的配筋不宜小于單位寬度上受力鋼筋的15%，且配筋率不宜小于0.15%；散布鋼筋的直徑不宜小于6mm，間距不宜大于250mm。故散布鋼筋可選6@200?！?-8】已知某雙筋矩形截面梁b400mm,h1200mm，配置的受壓鋼筋428，1228的受拉鋼筋，混凝土和鋼筋資料的性能指標為fc14.3N/mm2，ft1.43N/mm2，Ec3.0104N/mm2；fy310N/mm2，Es1.97105N/mm2，試計算（1）截面的開裂彎矩Mcr及相應的cr（2）截面的極限彎矩Mu及相應的u（一般方法）（3）截面的極限彎矩Mu及相應的u（簡化方法）【解】壓區(qū)鋼筋面積As2463mm2，受拉鋼筋的面積As7390mm2EEs1.971056.567Ec3.01042EAs26.5677390Abh0.20240012002EAs26.5672463Abh0.0674001200（1）截面的開裂彎矩計算Mcr0.29212.5A0.25Aftbh20.29212.50.2020.250.0671.4340012002366.00106Nmmcr2tu4ft41.431.59107hEch3.01041200（2）受拉鋼筋雙排部署，h0hcd28141130mmd1200282ascd282842mm22nb110.677fy310110.0033Es0.00331.97105As73901.635102bh04001130As24635.449103bh04001130n1.253fyfy1.2531.6351023105.4491033100.292fcfc14.314.3nb，受拉鋼筋能折服xnnh00.2921130330mm2.5as105mm，受壓鋼筋能折服asMufyAsh010.412nfyAsh00.412nh03107390113010.4120.292310246311300.412420.29211302349.01106Nmm2349.01kNmucu0.00331.001051/mmnh00.2921130（3）As2fyAs2463mm2，As1AsAs2739024634927mm2fyMufyAsh0as3102463113042830.72106Nmm830.72kNmfyAmx1.014.31fcb400b0.80.80.542fy310111050.00331.970.0033Es2as24284mmx267mmbh00.5421130612mm，為適筋截面Mu1fyAs1h0x310492711302671522.02106Nmm1522.02kNm22MuMuMu1830.721522.022352.74kNmu1cu0.80.00339.891061/mmx267【5-9】簡支梁如圖5-48所示，混凝土和鋼筋材料的性能指標為fc16N/mm2，ft1.5N/mm2；fy365N/mm2，Es1.97105N/mm2。求所能承受的均布荷載（包含梁的自重）q?！窘狻渴芾摻钆浣預s942mm2，受壓鋼筋配As628mm2fyAs365628628mm2As2fy365As1AsAs2942628314mm2c25mm，h0hcd3502520315mm，ascd35mm222MufyAsh0as3656283153564.18106Nmm64.18kNmb0.80.80.512fy365110.0033Es0.00331.97105bh00.512315161mm，2as23570mmfyAs136531436mmx1.0162001fcb2as，受壓鋼筋不可以折服MufyAsh01as36594231513596.27106Nmm96.27kNmh0315MuM1ql02q8Mu896.2743.66kN/m8l024.22【5-10】圖5-49所示的兩跨連續(xù)梁，混凝土和鋼筋的資料性能指標為fc13N/mm2，ft1.2N/mm2；fy370N/mm2，Es1.97105N/mm2。求所能承受的荷載P值。【解】對稱配筋，AsAs1520mm2c25mm，h0hcd5002522464mm，ascd252236mm2222此時，As1AsAs20mm2，xfyAs10mm，x2as，受壓鋼1fcb筋不可以折服MufyAsh01as3701520464136240.71106Nmm240.71kNmh0464作出彎矩圖（略），跨中的最大彎矩為M0.156Pl，中支座的最大負彎矩為M0.188PlMuMu0.188PlP214kN0.188l【5-11】已知鋼筋混凝土簡支梁的截面尺寸為200mm,h500mm，混凝土和鋼筋資料的性能指標為fc16N/mm2，ft1.5N/mm2；fy320N/mm2，Es1.97105N/mm2。承受的彎矩M250kNm，求所需受拉受壓鋼筋As及As?！窘狻浚?）計算參數(shù)確立h050035465mm0.80.8bfy0.5363200.0033Es10.00331.971052）求As1和M1xbh0249mmAs11fcbx1.0162002492490mm2fy320M1Mu1As1fyh00.5x24903204650.5249271.31106Nmm271.31kNmMu1M250kNm，僅配受拉鋼筋即能知足受彎要求。（3）結(jié)構配筋（略）【5-12】某鋼筋混凝土梁的截面尺寸為250mm,h600mm，受壓區(qū)已配有322的縱筋，混凝土和鋼筋資料的性能指標為f1.2N/mm；fc13N/mm22tfy310N/mm2，Es1.97105N/mm2。承受的彎矩M330kNm，求所需受拉鋼筋As?！窘狻浚?）計算參數(shù)確實定受壓區(qū)配置h0h6060060540mmacd252236mms22（2）計算As2和MAs2Asfy/fyAs1140mm2MAs2fyh0as114031054036178.11106Nmm178.11kNmMu1MMu330178.11151.89kNm1fcbxfyAs1即1.013250x310As1Mu11fcbxh0xMu11.013x解得x95mm22250x540As1995mm2b0.80.80.542fy131010.0033Es0.00331.97105bh00.542540293mm2asxbh0AsAs1As299511402135mm2【5-13】某鋼筋混凝土梁的截面尺寸為250mm,h600mm，受壓區(qū)已配有214的縱筋，混凝土和鋼筋資料的性能指標為f1.2N/mm；fc13N/mm22tfy370N/mm2，Es1.97105N/mm2。承受的彎矩M390kNm，求所需受拉鋼筋As?！窘狻緼s308mm2，h0565mm，as25732mm，取As2As308mm2MufyAsh0as3703085653260740680Nmm60.74kNmMu1MMu39060.74329.26kNm1fcbxfyAs1Mu1xfyAs1x1fcbxh0h022解得，224mmAs11963mm20.80.8bfy0.510370110.0033Es0.00331.971052as23264mmx224mmbh00.510565288mmAsAs1As230819632271mm2【5-14】已知T形截面梁bf280mm，hf120mm，b180mm，450mm，計算跨度l05m，配置325的縱筋，混凝土和鋼筋資料的性能指標為fc13N/mm2，ft1.2N/mm2；fy370N/mm2，Es1.97105N/mm2。試求截面的抗彎承載力。【解】bf280mm，bf280mml0/35000/31667mmbf280mmb12hf180121201620mm切合要求。受拉區(qū)，As1473mm2，minft1.230.450.451.45910fy370As,minminbh1.459103180450118mm2，As,minAs1fcbfhf1.013280120436800N436.8kNfyAs3701473545010N545.01kN屬于第二類T形截面。h04502525412.5mm2Muf1fcbfbhfh0hf1.0132801801201206mm2412.554.9910N21fcbx1fcbfbhffyAs解得:x166mm0.80.80.510bfy370111050.0033Es0.00331.97x1660.402h0b412.5Mu11fcbxh0x1.013180166412.5166127990980Nmm127.99kNm22MuMu1Muf127.9954.99183kNm【5-15】已知T形截面梁bf2500mm，hf180mm，b400mm，h1200mm，計算跨度l012mm，配置1225的縱筋，混凝土和鋼筋資料的性能指標為fc14.3N/mm2，ft1.4N/mm2；fy370N/mm2，Es1.97105N/mm2。試求截面的抗彎承載力。【解】bf2500mm，bf2500mml0/312000/34000mmbf2500mmb12hf400121802560mm切合要求。min0.45ft451.40.170%0.2%fy370Asminminbh0.2%4001200960mm2As5890mm2Asmin，h012002525251137.5mm21fcbfhf1.014.325001806435000N6345kNfyAs2179300N2179.3kN第一類xfyAs370589061.0mm1fcbf1.014.32500MufyAsh0x37058901137.561.01062412.