《建筑結(jié)構(gòu)》第五版偏壓構(gòu)件習(xí)題

6-13已知某對(duì)稱配筋的矩形截面偏心受壓短柱，截面尺寸bXh=400mmX600mm,承受軸向壓力設(shè)計(jì)值N=1500kN，彎矩設(shè)計(jì)值M=360kN?m,該柱采用的混凝土強(qiáng)度等級(jí)為C25,縱向受力鋼筋為HRB400級(jí)，試求縱向受力鋼筋面積As=Asz=?選擇配筋直徑，根數(shù)，畫配筋斷面圖（箍筋按構(gòu)造規(guī)定選?。?。解：f=11.9N/mm2,f=360N/mm2,g=0.517cyb取a=a'=40mm,h=600一40=560mm,ss0—,20mm30=20mm—,20mm30=20mm，e=e+e=260mm，i0ae===240mm，e=0N1500x103amaxhnl,e=e+——a=260+300一40=520mmi2N=afbhg=11.9x400x560x0.517=1378115.2=1378.11kN<N=1500kNb1c0b為小偏心受壓柱TOC\o"1-5"\h\zgN-afbhg+gg=1~c0b+gNe一0.43afbh2b1c亠+afbh(卩-g)(h-a')1c01b01500x103-1.0x11.9x400x560x0.517+0.5171500000x520-0.43x1.0x11.9x400x5602+1.0x11.9x400x560(0.8-0.517)(560-40)0.551121884.40.551780000000-641876480+2665600147.16AsNe-afbh2g(1-0.5g)Asr0—f'(h-a')y0s=987mm21500000x520-1x11.9x400x5602x0.55x(1-=987mm2360x(560-40)4根直徑18mm(As=As‘=1018mm2)或3根直徑22mm(As=As‘=1140mm2)0.002bh=0.002X400X600=480mm2<l0l8mm2<ll40mm20.006bh=0.006X400X600=1440mm2〈2X1018mm2〈2X1140mm20.05bh=0.05X400X600=12000mm2>2X1140mm2>2X1018mm26-14已知某矩形截面偏心受壓柱截面尺寸bXh=350mmX550mm,計(jì)算長(zhǎng)度l°=4.80m,承受軸向壓力設(shè)計(jì)值N=1200kN,彎矩設(shè)計(jì)，M1=220kN?m,M2=250kN?m,采用C30混凝土和HRB400級(jí)縱向鋼筋,HPB235級(jí)箍筋，，試求按對(duì)稱配筋鋼筋截面面積As=Asz=?繪配筋圖(取a=a'=40mm)ss解：fc=14.3N/mm2,fy二fy'=360N/mm2,gb=0.517,ho=55O-4O=51Omm,Cm=0.7+0.3(M1/M2)=0.7+0.3*220/250=0.964m12G=0.5fcA/N=0.5X14.3X350X550/1200000=1.14取^=1e=[550/30,20mm]=20mm,l/h=4.80/0.55=8.72amax0

nnsh01300(M2+nnsh01300(M2+e)Nal()2匚hc1300x(510250x1061200x103+20)x8.722x1x1=1.13M=CnM2=0.964X1.13X250=265.22kN?mmns2e0=M/N=265.22X106/1200X103=221.29mm.e=e0+e=221.29+20=241.29mm.i0ae=ei+h/2-as'=241.29+550/2-40=476.29mmisNb=fbh0E=14.3X350X510X0.517=1319.668kN>N=1200kN大偏心c0bN

aN

afbh1c0120000014.3x350x510二0.47>2as'/h0=80/510=0,16AsNe-afbh2g(1-0.5g)Asr0—f(h-a)y0s1200x103x476.29-1x14.3x350x5102x0.47x(1-0.5x0.47)360x(510-40)=611.62mm2>0.002bh=0.002x350x550=385mm26-15矩形截面偏心受壓柱尺寸bXh=500mmX700mm,計(jì)算長(zhǎng)度l0=4.80m,承受軸向壓力設(shè)計(jì)值N=2800kN，彎矩設(shè)計(jì)值M1=70kN?m,M2=75kN?m,采用C25混凝土,HRB500級(jí)縱筋和HPB235級(jí)箍筋，試求按對(duì)稱配筋鋼筋截面面積As=Asz=?繪配筋圖解：fc=11.9N/mm2,fy=435N/mm2,fy'=410N/mm2,gb=0.482,h0=700-45=655mm,Cm=0.7+0.3(M1/M2)=0.7+0.3*70/75=0.98,l0/h=4.80/0.7=6.86<15g=0.5fcA/N=0.5X11.9X500X655/1200000=1.14取^=1e=[700/30,20mm]=23.3mm,匚=0.5fcA/N=0.5X11.9X500X700/2800000=0.74amaxchl655n=1+^0()2匚=1+x6.862x0.74=1.35nsMhc75x1061300(亠+e)1300x(+23.3)Na2800x103M=CnM2=0.98X1.35X75=99.225kN?mmns2e0=M/N=99.225X106/2800X103=35.44mm.e=e0+e=35.44+23.3=58.74mm.,e=e+h/2-a'=58.74+700/2-45=363.74mmi0aisNbT占h§￡=11.9X500X655X0.482=1878.47kN〈N=2800kN小偏心e=58.74mm.<0.3h=0.3X655=196mm按小偏心計(jì)算i0

N-afbhg1c——N-afbhg1c——0bic亠+afbh(卩-g)(h-a')ic01b0+gb2800x103-1.0x11.9x500x655x0.482+0.4822800000x363.74-0.43x1.0x11.9x500x655+gb+1.0x11.9x500x655921525.51018472000-1097660462.5195.57+3897250+0.482=0.264921525.51018472000-1097660462.5195.57+3897250+0.482=0.264+.0482=0.746「Ne-afbh2g(1-0.5g)As=_0—f(h-a)y02800000x363.74-1x11.9x500x6552x0.75x(1-0.5x0.75)410x(655-40)1018472000-1233393164.=-852mm2252150按構(gòu)造配筋6-16已知承受軸向壓力設(shè)計(jì)值N=800kN，偏心矩e0=403mm的矩形截面偏心受壓柱，其截面尺寸bXh=400mmX600mm,計(jì)算長(zhǎng)度l0=8.90m,采用C30混凝土，并配有HRB400級(jí)縱向鋼筋A(yù)s=As'=1964mm2(每邊各4血5),試校核該柱受壓承載力是否滿足要求(取a=a'ss=40mm)解：fc=14.3N/mm2,fy二fy'=360N/mm2,gb=0.517,ho=6OO-4O=56Omm,e=e0+e=403+20=423mm.e=ei+h/2-as'=423+600/2-40=683mmis先按大偏心計(jì)算N=fbh0C=14.3X400X560^=3203200^c0Ne=afbh2g(1-0.5g)+fA's(h-a')1c0y0s683x3203200g=1761903000(g-0.5g2)+3676608002*2187785600g_”“367660800*21761903000g-g248g_2g-g2+0.42g2+0.48g-0.42_0匕-0.48^.0.48*0.48+4*0.42-0.48土1.38…g___0.452解得C=0.45N=fbh0C=14.3X400X560X0.45=1441.44kN>N=800kNuc0

6-17某矩形截面偏心受壓短柱，截面尺寸bXh=300mmX400mm，采用C25混凝土，對(duì)稱配筋，并已知As=Asz=1520mm2(每邊各4蟲22,HRB335級(jí))，試求偏心矩使截面恰好為界限破壞時(shí)截面所能承受的軸向壓力設(shè)計(jì)值Nb和相應(yīng)的彎矩設(shè)計(jì)值Mb.(未變)解：n=1，fC=11.9N/mm2,fy=300N/mm2,gb=0.55,as=45，h0=4OO-45=365mmea=[400/3,20mm]max=20mmamaxNb=fcbh0?=11.9X300X365X0.55=1142275NN?e=ufbh2^(1-0.5g)+f'As(h-a')b1c0bby0s1142275?e二11.9x300x3652x0.55(1-0.5x0.55)+300x1520x(365-45)e=293.26mme=e+h/2-a=e+e+h/2-ais0ase0=e-(ea+h/2-as)=293.26-20-200+45=118.26mmMb=eoNb=118.26X1142275N=135.°9kN?m6-18某矩形截面偏心受壓柱截面尺寸bXh=350mmX500mm,計(jì)算長(zhǎng)度l°=3.90m,采用C25混凝土,HRB335級(jí)縱筋，且已知采用對(duì)稱配筋時(shí)As=Asz=509mm2(每邊各2蟲18)試求當(dāng)軸向壓力設(shè)計(jì)值N=1200kN,,e0=140mm時(shí)，該配筋是否能滿足受壓承載力的要求？解：fc=11.9N/mm2,fy=fy'=300N/mm2,gb=0.55,h(=500-40=460mm,e=[500/30,20mm]=20mm,amaxe=e0+e=140+20=160mm.i0ae=ei+h/2-as'=160+500/2-40=370mmis先按大偏心計(jì)算N二f”％2=11.9X350X460^=1915900^Ne二afbh2g(1-0.5g)+fA's(h-a')1c0y0s370x191590比二1915900x460(g-0.5g2)+300x509x(460-40)370x1915900x264134000x2g二2(g—0.5g2)+1915900x4601915900x460g2-0.4g-0.146=00.4±g2-0.4g-0.146=00.4±0.4x0.4+4x0.146g==0.63>g=0.55b2故為小偏心受壓，須重求EN二gafbh+fAs'(1-0.8-g)二1915900g+488641c0y0.8-gbNe二afbh2g(1-0.5g)+fA's(h-a')二1915900x460(g-0.5g2)+641340001c0y0s370x1915900x2g_2(g_仆*?)(64134000-48864x370)x21915900x4601915900x460g-(g-.1915900x4601.6g=2g-g2+0.1g2-0.4g—0.1二0詐0.4O4*°.4+4*。1二0.574Nu=1915900E+48864=1148.59kNvN=1200kN軸向承載力不滿足要求6-19某對(duì)稱I形截面截面尺寸bXh=120mmX600mm,bf二bf'=500mm,h=h'=120mm計(jì)算長(zhǎng)度l0=5.0m采用C30混凝土,HRB400級(jí)縱筋和HPB235級(jí)箍筋，承受軸向壓力設(shè)計(jì)值N=125kN，彎矩設(shè)計(jì)值M=200kN?m,試求采用對(duì)稱配筋時(shí)的縱筋截面面積As=Asz=?,并會(huì)配筋截面圖。6-20已知一承受軸向壓力設(shè)計(jì)值N=1500kN,彎矩設(shè)計(jì)值M=150kN?m的對(duì)稱I形截面，計(jì)算長(zhǎng)度l0=14.20m，截面尺寸bXh=150mmX800mm,bf二bf'=400mm,h=h'=120mm，采用C25混凝土,HRB335級(jí)縱筋和HPB235級(jí)箍筋，試求采用對(duì)稱配筋時(shí)的縱筋截面面積As=As‘=?,并繪配筋截面圖。6-21某鋼筋混凝土框架柱，截面為矩形，bXh=400mmX600mm,柱凈高H0=4.80m,計(jì)算長(zhǎng)度l0=6.30m,采用C25混凝土,HRB335級(jí)縱筋和HPB235級(jí)箍筋，若該柱柱端作用的內(nèi)力設(shè)計(jì)值M=420kN?m,N=1250kN,V=350kN，試求該截面配筋并繪配筋截面圖。（采用對(duì)稱配筋,取as二as'=40mm）解：6-22已知矩形截面柱bXh=400mmX600mm,采用C30混凝土,HRB500級(jí)鋼筋對(duì)稱配筋，計(jì)算長(zhǎng)度l0=4.0m,承受兩組內(nèi)力設(shè)計(jì)值：QM=343kNm,N=1530kN；QM=345kN-m，N=2500kN。試判斷哪一組內(nèi)力對(duì)配筋起控制作用，求對(duì)稱配筋時(shí)的縱筋截面面積As=As'=?解：f=11.9N/mm2,fy=435N/mm2,fy'=410N/mm2,Fb=0.482,as二as'=40mhi=560mm，00=4000/600=6.67hN—afbhg+-ff-A—1x11.9m400m560x0.517=1378115N=137812kNvN=1530Nb1c0bIyy丿sVN=2500kN該柱在這兩