《建筑結(jié)構(gòu)》第五章習(xí)題答案

1、第五章受彎構(gòu)件正截面承載力計(jì)算延筑結(jié)構(gòu)第五章習(xí)題：共用條件：一類環(huán)境使用，結(jié)構(gòu)安全等級(jí)為二級(jí)5-25一鋼筋混凝土矩形梁截面尺寸200mmX500mm,彎矩設(shè)計(jì)值M=120kNMo混凝土強(qiáng)度等級(jí)C25,試計(jì)算其縱向受力鋼筋截面面積：當(dāng)選用HPB235級(jí)鋼筋時(shí)；改用HRB400級(jí)鋼筋時(shí)；最后畫出相應(yīng)配筋截面圖。解：依題意查得參數(shù)：=1,fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,fy=210N/mm2,&=0.614;as=65mm。h0=500-65=435mm先按單筋矩形截面計(jì)算，%=M2=120X1062=0.266二1fcbh211.92004352=1-11

2、21s=1-1-20.266=0.32二b=0.614As=M/fyh0(1-0.5E)=1560.65mm2,選5?20,As=1571mm2>Pmin=0.45ftbh/fy=0.45X1.27乂200乂500*210=272mm2>0.02bh=0.002X200X500=200mm2,fy=360N/mm2,*=0.517;as=40mm,h0=500-40=460mm先按單筋矩形截面計(jì)算，«s=-M=120X1062=0.238二Tfcbh211.92004602-=1一.1二2三；-1-1-20.238=0.28：b=0.517As=M/fyh0(1-0.5E

3、)=120X106/360X460X(1-0.5X0.28)=842.61mm2,選3#20,As=941mm2,或4#18,As=1018mm2>Pmin=272mm25-26某大樓中間走廊單跨簡(jiǎn)支板,計(jì)算跨度2.18m,承受均布荷載設(shè)計(jì)值g+q=6kN/m2(包括自重)，混凝土強(qiáng)度等級(jí)C20,HPB235級(jí)鋼筋。試確定現(xiàn)澆板厚度h及所需受拉鋼筋截面面積，選配鋼筋，并畫配筋圖。取b=1000mm,as=25mm。解：依題意查得參數(shù)：的=1,fc=9.6N/mm2,ft=1.10N/mm2,c=20mm,fy=210N/mm2,5=0.614;板厚切80/35=62.3mm,取h=70m

4、m,h°=70-25=45mm1212M=(gq)20=62.182=3.5643kNm88M：1fcbh；3.561069.61000452=0.18=1-112心=1-1-20.18=0.204二b=0.614As:1fcbh0fy9.61000450.2042102=419.66mm,選?8/10150As=429mm2,或選？10180As=436mm2>Pmin=0.45X1000X70X1.1/210=136.37mm2>0.0015X1000X70=105mm2,5-27一鋼筋混凝土矩形截面梁200mmX500mm,混凝土強(qiáng)度等級(jí)C20,配有HRB335級(jí)鋼

5、筋(2W18,As=509mm2),試計(jì)算梁上承受彎矩設(shè)計(jì)值M=80kNm時(shí)是否安全。解：依題意查得參數(shù)：的=1,fc=9.6N/mm2,ft=1.10N/mm2,c=30mm,fy=300N/mm2,海=0.55;as=40mm,ho=460mm0.45ft/fy=0.0016<0.002Asmin=pminbh=0.002X200X500=200mm2VAs=509mm2fyAs二一y300509：1fcbh09.6200460=0.17<3=0.55Mu=fyAsh0(1-0.5)=300509460(1-0.50.17)=63.135kNm<M=80kNm承載力不足，

6、不安全5-28一鋼筋混凝土舉行截面梁bXh=250mmX600mm,配有4型25的HRB335級(jí)鋼筋，分別采用C20,C25,C30強(qiáng)度等級(jí)混凝土，試計(jì)算梁能承受的最大彎矩設(shè)計(jì)值，并對(duì)結(jié)果進(jìn)行分析。解：依題意查得參數(shù)：第=1,fy=300N/mm2,&=0.55;as=40mm,h0=560mm;0.45ft/fy=0.0016<0.002;Asmin=pminbh=0.002X250X600=300mm2<As=1964mm2C20:fc=9.6N/mm2,ft=1.10N/mm2,c=30mm,fyAs:ifcbhg30019649.6250560=0.438<*

7、=0.55Mu=fyAsh0(1-0.5)=3001964560(1-0.50.354)=257.69kNmC25:fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,.fyAs3001964-小=0.354Lfcbh。11.9250560Mu=fyAsh0(1-0.5)=3001964560(1-0.50.438)=271.61kNmC30:fc=14.3N/mm2,ft=1.43N/mm2,c=25mm,fyAs3001964=0.294：1fcbh014.3250560Mu=fyAsh0(1-0.5)=3001964560(1-0.50.294)=281.45kNm結(jié)論：在

8、截面尺寸和配筋一定時(shí)，隨混凝土強(qiáng)度等級(jí)的提高，構(gòu)件承接能力提高，截面延性增加。29.已知一鋼筋混凝土矩形截面梁200mmX500mm,承受彎矩設(shè)計(jì)值M=216kNm混凝土強(qiáng)度等級(jí)C25,在受壓區(qū)配有320的HPB235級(jí)鋼筋，試計(jì)算受拉鋼筋截面面積(采用HRB400鋼筋)。解：依題意查得參數(shù)：刀=1,fy，=210N/mm2,As，=942mm2fy=360N/mm2,i=0.517;as=65mm,as，=,35mm,h°=435mmC25:fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,M-Mu”1fcbh：(1-0.5)fyAs(h0-as)M-fyAs(h9

9、-as)：1fcbh。2216106-210942(435-35)111.92004352=0.3039as'''-fyAs(h0-2)20.5-1fcbh0=1.；_216/06-210294*3535):0373770.5111.92004352二1fcbh0fyAs=fyAs-As=.：1fcbh0fyAs111.92004350.382109423601642.32mm受拉鋼筋選6根直徑20mm(As=1884mm2)的HRB400鋼筋，?；蜻x3根直徑20mm+2根直徑22mm(1702mm2)的HRB400鋼筋A(yù)smin=pminbh=0.002X200X50

10、0=200mm2VAs=1884mm20.45ft/fy=0.0016<0.00230.已知一鋼筋混凝土矩形截面梁200mmX500mm,承受彎矩設(shè)計(jì)值M=216kNm混凝土強(qiáng)度等級(jí)C25,已配有HRB335級(jí)鋼筋6型20的，試復(fù)核此梁是否安全。若不安全，則重新設(shè)計(jì)，但不改變截面尺寸和混凝土強(qiáng)度等級(jí)。（a三=60mm）解：依題意查得參數(shù)：丫0=1,As=1884mm2,fy=300N/mm2,&=0.517;h0=440mmC25:fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,fyAs3001884c.0.54b=0.55Lfcbhb11.9200440Mu-

11、1fcbho(1-0.5)_2_=11.920044020.54(1-0.50.54)=181.67kNm：M=216kN,m重新設(shè)計(jì)取Z=1=0.517HRB400M=11fcbh2；(1-0.5b)fyAs(h0-as)=328.1mm2JM-：1fcbh2b(1-0.5b)216000000-111.920044020.517(1-0.50.517)As二:二fy(h0-as)300(440-40)選受壓鋼筋2根直徑16mm(As，=402mm2)的HRB400'-'二1fcbh0fyAs=fyAs-As-Lfcbh。fyAsfy111.92004400.517360As

12、2=1503.9328=1831.9mm選受拉鋼筋5根直徑22mm(As，=1900mm2)的HRB400或6根直徑20mm(As，=1884mm2)的HRB40031.已知一雙筋矩形截面梁200mmX450mm,混凝土強(qiáng)度等級(jí)C20,HRB335級(jí)鋼筋，承受彎矩設(shè)計(jì)值M=216kNm,配有2型12受壓鋼筋，配有3O25+2魚22受拉鋼筋，試求該截面所能承受的最大彎矩設(shè)計(jì)值。解：依題意查得參數(shù)：算=1,fy'=300N/mm2,As，=226mm2,fy=300N/mm2,As=2233mm2,&=0.55;as=70mm,as，=40mm,h°=380mmC20:f

13、c=9.6N/mm2,ft=1.10N/mm2,二1fcbh0fy'As=fyAs-fyAs-fyAs300(2233-226)=0.825=0.55二1fcbh019.6200380q之=取取=b=0.55Mu=:£岫：b(1-0.5b)fyAs(h0-as)=19.620038020.55(1-0.50.55)300226(380-40)=133.604kNm該梁能承受的最大彎矩為133.6kNm32.某連續(xù)梁中間支座處截面尺寸bxh=250mmX650mm,承受支座負(fù)彎矩設(shè)計(jì)值M=239.2kNm,混凝土強(qiáng)度等級(jí)C25,HRB335級(jí)鋼筋，現(xiàn)由跨中正彎矩計(jì)算鋼筋中彎起2

14、強(qiáng)18伸入支座承受負(fù)彎矩，試計(jì)算支座負(fù)彎矩所需鋼筋截面面積；如果不考慮彎起鋼筋的作用，支座需要鋼筋截面面積是多少？解：依題意查得參數(shù)：丫0=1,As1=500mm2,fy=300N/mm2,&=0.55;h0=440mm(a三=60mm)C25:fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,239.2106：ifcbho-11.92505902=0.23=1_1二21；=1一.1一20.23=0.265：二b=0.55應(yīng)按單筋矩形截面設(shè)計(jì)不考慮彎起鋼筋的作用時(shí)，As=f二九92505900.27;1579.725mm2fy3002)伸入支座承受負(fù)彎矩由跨中正彎矩鋼筋

15、中彎起218(As1=509mm時(shí),As2=As-As1=1579.73-509=1070.73mm233 .某T形截面梁b=250mm,br=500mm,h=600mm,hr=100mm,混凝土強(qiáng)度等級(jí)C30,HRB400級(jí)鋼筋，承受彎矩設(shè)計(jì)值M=256.kNm，試求受拉鋼筋截面面積，并繪配筋圖。解：依題意查得參數(shù)：第=1,fy=360N/mm2,&=0.517;as=40mm,h0=560mmC30:fc=14.3N/mm2,ft=1.43N/mm2,c=25mm,%fcbfhf(兒-0.5hf)=1父14.3父500M100M(530-0.5父100=34320kN,m>M

16、=256kNm為I類T形截面=0.114M_2561062fcbfh：14.3500560:=1一.1二2三；-1-1-20.114-0.12：b=0.517As二1fcbh。fy14.35005600.123602-1352.02mm選4根直徑22mm的(As=1520mm2)或3根直徑25mm的(As=1473mm2)34 .某T形截面梁b=200mm,b=1200mm,h=600mm,h廠=80mm,混凝土強(qiáng)度等級(jí)C20,配有4出20HRB335級(jí)鋼筋，承受彎矩設(shè)計(jì)值M=131.kNm,試復(fù)核截面是否安全？解：依題意查得參數(shù)：=1,fy=300N/mm2,&=0.55;As=12

17、56mm2as=40mm,h°=560mmC20:fc=9.6N/mm2,ft=1.1N/mm2,c=30mm,fcbfhf=19.6120080=921.60kN*mfyAs=3001256=3768kN為I類T形截面.fyAsfcbfh030012569.61200560=0.06<&=0.55Mu=fyAsh0(1-0.5)=3001256560(1-0.50.06)=204.68kNm35 .某T形截面梁b=200mm,bf，=400mm,h=600mm,hr=100mm,as=60mm,混凝土強(qiáng)度等級(jí)C25,配有HRB335級(jí)鋼筋620,試計(jì)算該梁能承受的最大

18、彎矩設(shè)計(jì)值。解：依題意查得參數(shù)：=1,fy=300N/mm2,i=0.55;As=1884mm2C20:fc=11.9N/mm2,ft=1.27N/mm2,c=25mm,as=60mm,h°=540mmFF:1fcbfhf=111.9400100=476.0kN*m：fyAs=3001884=5652kN為II類T形截面fyAs-：1fc(bf-b)hf：ifcbho=0.2546<&=0.5300188411.9(400200)10011.92005405Mu=fyAsh0(1-0.5)=3001884540(1-0.50.25)=267.06kNm36 .已知某承受

19、均布荷載的矩形截面梁bxh=250mmX600mm,采用C20混凝土，箍筋為HPB235級(jí)鋼筋，若已知剪力設(shè)計(jì)值V=150kN，試求采用6雙肢箍的箍筋間距So解：fc=9.6N/mm2,ft=1.10N/mm2,fyv=210N/mm2,Asv1=28.3mm2,n=2,取as=65mm,h0=600-65=535mmh0/b=535/250<4,0.25fcbh0=0.25X9.6X250X535=321kN>V=150kN截面尺寸滿足要求需配0.7ftbh0=0.7X1.1X250X535=102987.5N=103kN<V=150kN置箍筋fyvAsVh0s二V-0.7

20、ftbh0210228.3535150000-102987.5=135.26mm,取s=130mm0.94ftbh0=0.94X1.1X250X535=138297.5N=138.3kN<V=150kN按37 .圖5-54所示一鋼筋混凝土簡(jiǎn)支梁,集中荷載設(shè)計(jì)值F=120kN,均布荷載設(shè)計(jì)值（含梁自重）q=100kN/m。選用C20混凝土，HPB235級(jí)鋼筋。試選擇梁的箍筋（注：圖中為凈跨ln=4000mm）2LT>F=120kNq=lQkH/m霖E2EE"I,151。,100。1y1500匕r|250|解：fc=9.6N/mm2,ft=1.10N/mm2,fyv=210N

21、/mm2,支座邊緣剪力Vmax=120+10*4/2=140kN,h0=550-40=510mm。選Asv1=28.3mm2,n=2,1)驗(yàn)截面尺寸h0/b=510/250<4,0.25fcbh0=0.25X9.6X250X510=306kN>Vmax=140kN2) 0.7ftbh0=0.7X1.1X250X510=98.175kN<V=140kN需配置箍筋3) 0.94ftbh0=0.94X1.1X250X510=131.835N<V=140kN按Psvmin不可fyvASVh0s二V-0.7ftbh。210228.3510140000-98175=144.93mm

22、,取s=140mm5-38某T形截面簡(jiǎn)支梁bxh=200mmx500mm（as=35mm）,bt，=400mm,ht，=100mm;采用C25混凝土，箍筋為HPB235級(jí)鋼筋；由集中荷載產(chǎn)生的支座邊剪力設(shè)計(jì)值V=120kN（含自重），入=3.試選擇該梁箍筋。解：fc=11.9N/mm2,ft=1.27N/mm2,fyv=210N/mm2,選中8雙肢箍Asv1=56.3mm2,n=2,ho=500-35=465mm,hw=h0-ht，=465-100=365mm1)驗(yàn)截面尺寸hw/b=365/250<4,0.25fcbh0=0.25X11.9X200X465=276.675kN>Vmax=120kN2) 1.75ftbh0/(1+入)=0.4375X1.27X200X465=51.673kN<V=12