混凝土課后答案第6,7章

1、6-1已知一鋼筋混泥土矩形截面純扭構(gòu)件，截面尺寸bx h=150mm x 300mm ,作用于構(gòu)件上的扭矩設(shè)計(jì)值T=3.60KN.m ,采用C30混泥土，采用HPB235級(jí)鋼筋。試計(jì)算其配筋量。解查表得:2t=1.43N/ mm2yv =210N/ mm2y=210N/ mm取-s=35mmC=25mmb2150263wt(3h-b)(3 300 -150)=2.8125 106mm36 642Acor = bcor .hcor = (150 '50) (300 50) = 2.5 10 mmUcor = 2(bcor hcor) = 2 (100 250) = 700mmyv Ast

2、i取 =1-2 由公式得:T < 0.35 ftW 1.2 ,廠Acors466 2102 5x10= 3.6 106 乞 0.35 1.43 2.8125 1061.2,1.2A1.2 ,12 2.0 2.5 104=& _3.606 二竺L1.432.812506®s取單肢8即Asti二=50.3s些型丄即 0.3178=158mm取 s= 150mmfyAsti.Sf yvAsti Ucor-.fyvAsti Ucor1.2 疋 210 漢 50.3 疋 7002二 Asti282mm由縱箍比可知:fy.s210 1502查附表11取4 10即氐二314mm結(jié)構(gòu)在

3、剪扭作用下，結(jié)構(gòu)受剪及受扭箍筋最小配筋率為:%v.minAsv.minbcor. s= 0.28 出= 0.19 00 亦 0.34 00 210100匯150故滿足最小配筋率。配筋圖如下:4106-2已知一均布荷載作用下鋼筋混泥土矩截面彎、剪、扭構(gòu)件，截面尺寸為b x h=200mmX 400mm。構(gòu)件所承受的彎矩設(shè)計(jì)值M=50KN.m，剪力設(shè)計(jì)值 V=52KN,扭矩設(shè)計(jì)值T=4KN.m。全部采用HPB235級(jí)鋼筋，采用 C20混泥土。試計(jì)算其配筋。解(1)受彎縱筋計(jì)算設(shè)鋼筋按一排布置，取 悅=400 _ 35 = 365mm2查表得：ft=i.iN/mm2c=9.6N/ mm2y=210N

4、/ mm650"01.0 9.6 200 3652= 0.1955=1一、1匚2s =0.2196：1 fcbhofy° 9.6 0.2196 200 365 二 733mm2210(2)受剪及受扭鋼筋計(jì)算截面限制條件驗(yàn)算：h。二九=365mm，hw/b 二 365 / 200：8252=1.459N /mmV T 52 1034 106bhb Wt _200 365 0.8 6.7 106：0.25 cfc =0.25 1.0 9.6 =2.4N/mm2故截面尺寸滿足要求,V T 1.459 N/mm20.7 1.1N / mm2 = 0.25 1.0 9.6 = 0.7

5、7 N / mm2又 bh0 W故需按計(jì)算配置受扭鋼筋受剪鋼筋計(jì)算由公式6-23可得:1.51 0.5 處 Tbh。10.51.552 103 6.7 1064 106 200 365-0.93952Acor =(200 -50) (400 -50) = 52500mm受剪箍筋由公式6-24可得：= 0.213952 10-0.7 (1.5-0.9395) 200 365 1.11.25x210x365受扭箍筋取.=3，由公式6-27可得:= 0.1045每 4 106 -0.35 6.7 106 0.9395 1.1St1.2 ,1.3 210 5.25 104故得腹板單肢箍筋的需要量為s=

6、 0.10450.21392= 0.2112取箍筋直徑為'8( Asvi = 50.3mm)0.21150.30.211-238mm取 s=220mm受扭縱筋:Asti =1.3 50.3 210 1000/210 220 = 297mm2故得腹板縱筋：彎曲受壓區(qū)縱筋總面積為A/ =297/2 =149mm2選用 2 10(A/=157mm2)彎曲受拉縱筋總面積為2 - - 2As =733 297/2 =882mm選用 2 20 2 18(As =883mm )配筋圖如下：1P 82202182202107-1 已知矩行截面柱b=300mm , h=400mm。計(jì)算長(zhǎng)度 L0為3m,

7、作用軸向力設(shè)計(jì)值N=300KN，彎矩設(shè)計(jì)值 M=150KN.m，混泥土強(qiáng)度等級(jí)為 C20，鋼筋采用HRB335級(jí)鋼 筋。設(shè)計(jì)縱向鋼筋 As及As/的數(shù)量。解查表得:2c=9.6N/ mm2y =300N/ mm取-s=40mmho 二 h _ as =360mme0 二 M / N 二 0.5 mea 二 20mme = ea +q = 520mmV l0 /h =7.55n-要考慮1 =0.5fcA/N =0.5 9.6 300 400/300 103 =1.92 1 取 廣1取 2 “.0-11i400e/ho(lo/h)2 1 2-121400 520/360(7.5)11.03e MO

8、3 520 =535.6。.九二0.3 360屬于大偏心受壓e h)/2-as =535.6 180-40 =675.6mm取 x = bgr fr由 N e二 a cf bx0 h / 2) y sf A0 -hs 得)a氏二 Ne-a/cbh2 b(V0.5 b)/ fy (% -as)二 560.9mm；Amin =0.02Dh= 0.02 300 400 = 240mmfAs Asmin選用 4 上 14 As =615mm由Ne= acf Hh(1 - 0. 5 ) y f s A(h s得a)卜 - 2:s =Ne-fy A(h0-as )/印小館=0.385=1 - .,1 -2

9、： s =1-0.48 = 0.52h0 =0.52 360 =187.2 2as' =80mm由N二印小入 fy人甘人得A =印 fcbhbfy As / fy9.6 300 360 0.5 300 6153002343nm2選用5 i 25 A =2454mm截面配筋圖如下:1111117-eo tn_3 r12tl44jOTl5 254J47-2 已知條件與題7-1相同，但受壓鋼筋已配有 4 16的HRB335級(jí)的縱向鋼筋。 數(shù)量。解設(shè)計(jì)As查表得:2c=96N/ mm2y =300N/ mm取血=-s =40mmh。= h - as =360mme0 = M / N = 0.5

10、 mea = 20mme=ea eb = 520mm：Io/h =7.55要考慮=0.5fcA/N =0.5 9.6 300 400/300 103取2 "0"息（皿，1. 21400 520/360(7.5) 1 一1.03e "°3 520 =535.6。肌=0.3 360屬于大偏心受拉e二 e m/2-as =535.6 180-40 = 675.6mm.M = fy A (h0-as )= 77.184 106 N.mm6M1 =Ne-M ”=131.184 10 N.mm由N e二 a cf bxc h / 2) y f A) -hs 得)aA

11、 二 Ne-a/cbh)2 b(1 - 0.5 b)/ fy (怙 - as)二 560.9mm,Asmin =0.0230.02 300 400 = 240mnfAs Asmin卜 2選用 414 As =615mms =0.7729由 Ne= acf 3(1- 0. 5 ) y f s A( h s得a)As1 = M / iy s h= 1 5 7 2m m3300=1572 300 804 一300 10 -1376mm22選用3 I 25人=1473mm截面配筋圖如下:3 254 147-3已知條件同題7-1相同，但受壓鋼筋已配有416的HRB335級(jí)鋼筋的縱向鋼筋。設(shè)計(jì)As數(shù)量。已

12、知矩行截面柱 b=600mm，h=400mm。計(jì)算長(zhǎng)度混泥土強(qiáng)度等級(jí)為 C30，縱筋采用 HRB400級(jí)鋼筋。，柱上作用軸向力設(shè)計(jì)值 N=2600KN,彎矩設(shè)計(jì)值 M=78KN.m，混泥 土強(qiáng)度等級(jí)為 C30，鋼筋采用HRB400級(jí)鋼筋。設(shè)計(jì)縱向鋼筋 As及As/的數(shù)量，并驗(yàn) 算垂直彎矩作用平面的抗壓承載力。解查表得:2c=14.3N/ mm2y =300N/ mm2y=360N/ mm取-s = - s =40mm h° - h - as =560mme0 = M / N =30mm+15 I。/ h =10 5ea = 20mm n- 要考慮e 二e。二 50mm1 =0.5fc

13、A/N =0.5 14.3 300 600/260 103 =4.95 1 取 1取2 TO=11140g/hb11400 50/5602(10) 1 = 1.8屬于小偏心受壓e =1.8 50 = 90 ：0.3h° =0.3 560 = 168mm對(duì)AS合力中心取矩e =h/2-as -(&-ea) =300-40-10 = 250mmA =Ne -a/cbhg-h/2)/fy (g-as ) =2600 103 -14.3 300 600 (560-300)/360 5202=A 0取 A； = 0.02Dh = 0.02 300 600 = 360mmM1 =Ne-M

14、 ' =131.184 106N.mm2選用 216As=402mma'=hsfyAs(1-as/ho)/aifcbh°( b -=-0.75 :：: 2 -12_aifNbho2', asfyAs(as/ho)/aifcbho( b - . _ ho-b =1.6 -0.518 =1.082 e = e h0/2 - as =1.8 50 280 -40 二 330mm由 Nepfcb2 (1 - /2)(館-Q)得A 二Neyfcbh2 (1-0.5 )/fy (h。-as) =1214.6nmf 0.02?h2選用 4也 20As =1256mm抗壓承載

15、力驗(yàn)算：l0/h =10 查表 3-1 得，°. 98訂= As/bh0 =1256/300 560 =0.75°0 ：3°0Nu =0.9 (fcA fyA) = 0.9 0.98 (14.3 300 600 360 1256)=2.67 103kN 260CkN所以平面外承載力滿足要求。截面配筋圖如下：n-要考慮7-4 已知矩行截面柱 b=600mm， h=300mm。計(jì)算長(zhǎng)度 L0 = 4m ,受壓區(qū)已配有 216的鋼筋，柱上作用軸向力設(shè)計(jì)值N=780KN,彎矩設(shè)計(jì)值 M=390KN.m，混泥土強(qiáng)度等級(jí)為C30，鋼筋采用HRB400級(jí)鋼筋。設(shè)計(jì)配筋數(shù)量。解查

16、表得:2c=14.3N/ mm2y =360N/ mm2y =360N/ mm取-s - - s =40mmho - h _ as =560mmea 二 20mme 二 ea e0 二 520mmt e0 二 M / N = 500mm；15 l0/h =6.675仃0.5fcA/N =0.5 14.3 300 600/780 105 =1.65 1 取取 2 ".01'(的1 1400(6.67：2 1九036” B =1.°36沢520= 538.72a 0.3恰=0.3沃 560 = 168mm 屬于大偏心受壓e=y +h/2-as'=538.7300

17、-40 = 798.72mmM J fy A (h0-as ) =360 402 520 = 75.2544 106N.mmM1=Ne-M =780 1 03 538.72 - 75.2544 1 06 = 344.9472 1 06N.mm2:s M/aJcbg344.9472 1014.3 300 56 廠 O.256*"3838s =0.84932As1 = M1/ fy sh= 201 5mm3二 2015360 402 一780 10 二 250mm2 譏nbh = 360mm23602選用2 16 As =402mm截面配筋圖如下:7-5 已知矩行截面柱 b=600mm

18、, h=400mm。計(jì)算長(zhǎng)度L0 = 4.5m,受壓區(qū)已配有 2 25的鋼 筋，柱上作用軸向力設(shè)計(jì)值N=468KN,彎矩設(shè)計(jì)值 M=234KN.m，混泥土強(qiáng)度等級(jí)為C30，鋼筋采用HRB400級(jí)鋼筋。設(shè)計(jì)配筋數(shù)量。解f2 f2 f2查表得：fc=14.3N/ mm y =360N/ mm y=360N/ mmt e0 = M / N = 500mm?15 l0/h =7.55取-s i s =40mm h。- h - as =560mme = ea e0 二 520mmea = 20mm仃 0.5fcA/N =0.5 14.3 400 600/468 105 =3.67 1 取取 2 &quo

19、t;.0-111400=i/h）1400 520/560（7.5）1-1.043140*/%B =1.043漢 520 = 542.360.3恰=0.3匯 560 = 168mm 屬于大偏心受壓e = y +h/2-as'542.3毋 300-40 = 802.36nmM ' = fy A （h0-as ） =360 1964 520 = 367.6608 106N.mmM1=Ne-M =468 1 03 802.36 - 367.6608 1 06 = 7.84368 1 06N.mmM/aJcb%2784368014.3 400 56C?=0.004£Qsmax

20、= 0.38382.s =0.998As1 二 M1/ iy sh = 7843680 / 360 0. 998 5i6i®n 393As二 250mm2，' minbh2選用3218人763mm截面配筋圖如下fyAs= 2015360 402 -780 103607-6已知條件同題7- 1,設(shè)計(jì)對(duì)稱配筋的鋼筋數(shù)量。 解取-s - - s =40mmh° - h - as =360mme° = M / N =0.5mea =20mm二 e= ea +/= 520mmV l0 /h =7.55n-要考慮查表得:2c=9.6N/ mm2y =300N/ mm廠

21、 0.5fcA/N =0.5 9.6 300 400/300 101.92 1 取 廣1= 1.0=1121400 520/360（7.5） 1 1.03e九03 520 =535.6 0.肌=0.3 360屬于大偏心受壓e二 e hb/2-as =535.6 180-40=675.6mmx 二 N/acfb300 3 0 / 9. 6 3002: s ： x ： bh0 = 0.55 360 = 180mm3A Ne-aifcbx(h)-x/2) 300 10 675.6- 9.6 300 104.17 (360-52.085) fy"(h°-&)300320 -

22、 2 2二 人=A； =1058.9 mm >As.mi =240mm t2選用 4 20 A； = As = 1256mm7-7已知條件同題7-3,設(shè)計(jì)對(duì)稱配筋的鋼筋數(shù)量。 解2 2 2查表得：fc=14.3N/mm1 y =300N/ mm y=360N/ mm取-s - - s =40mmh。- h - as =560mme0 = M / N =30mmea = 20mme 二 ea e0 =50mm15 l0/ h =105n-要考慮1 =0.5fcA/N =0.5 14.3 300 600/260 103 =4.95 1 取 1取2 TO"丄 M)2"品茨0

23、(102 8e九8 50 = 9° ：0.亦0 =0.3 56° = 168mm屬于小偏心受壓七_(dá)N印仗帕1+戸_ _2bNe-0.43a1fcbh。a1 fcbh0(一1 - b)(h0 -a；)2600 103 -0.518 14.3 300 560320.518 = 1.1832600 103 330-0.43 14.3 300 560214.3 400 560(0.8-0.518) 520A = A=Ne-a1fcbh02 (1-0.5 )/fy (% - a$) = 1097.6mf 0.02bh選用 4也 20 As =1256mm抗壓承載力驗(yàn)算：L = As/

24、bho =1256/300 560 =0.75°0 ：3°0Nu =0.9 (fcA fy As )=0.9 0.98 (14.3 400 600 360 1256)=2.67 103kN 2600kN 所以平面外承載力滿足要求。7-8 已知矩行截面偏心受壓構(gòu)件，b=300mm, h=500mm , as= as/= 35mm, l0 = 4.0m，米用對(duì)稱配筋 As = As = 804mm2(4雄16),混泥土強(qiáng)度等級(jí)為 C30，縱筋采用 HRB400級(jí)鋼 筋。設(shè)軸向力沿長(zhǎng)邊方向的偏心矩e)=120mm，求此柱的受壓承載力設(shè)計(jì)值。解查表得:2c=14.3N/ mm2y

25、=360N/ mm取-s - - s =35mmh° - h _ as =465mm取 ea =20mme =ea=120 +20 =140mm0.3佗=139.5按大偏心受壓計(jì)算15 l0/h =85取 1 二1 ,2 =1.0=11140*/怙(l°/h)2 1 2=121400 140/465(8)1 1.152"兀 +厲/2-as=376.28mmN = a f bx yf sA yfiA4. 3 300 x(1)oooo oooooooNe二 acf bx0 h / 2) y sf A0 -hs )a=N 376.2814.3 300 (465-X/2)

26、 360 804 430由(1) (2)解得：N=1550.88kN x = 315. 2r2m所以此柱的受壓承載力設(shè)計(jì)值為1550.883KN7-9已知矩形截面偏心受壓構(gòu)件b x h= 400mm x 600mm , L0 = 6.0m，截面配筋：As/ =1256mm2(4 20), As = 1964mm2(4 25)。混泥土強(qiáng)度等級(jí)為 C30，縱筋為 HRB400 級(jí) 鋼筋。as= as/= 40mm，軸向力沿長(zhǎng)邊方向偏心矩e0=100mm。求該受壓構(gòu)件的受壓承載力設(shè)計(jì)值N。解查表得:2c=14.3N/ mm2y =360N/ mm取-s = - s =40mmho = h _ as

27、=560mm取 ea =20mme =ea +60 =100 +20 =120mm c 0.3h0 = 168mm按小偏心受壓計(jì)算15 l0/ h =105-要考慮£=0.2 + 2.7e/% =0.779 ,1.0=1(lo/h)212T(10f 1 0.779=1.26140*/%1400140/465e/e +佗/2 as=411.2mmN 二 a f bx yfs .A.(1)(2)Ne= Qcf bxc h / 2) y f A)池.)a.(1)( 2)解得:X =112mm(舍去)x2 = 358. mm= 2470.30&N : a,fcb14.3 400 60

28、0 = 3432kN所以此柱的受壓承載力設(shè)計(jì)值為2470.306KN7-10 已知矩形截面偏心受壓構(gòu)件bx h= 400mm x 600mm , L0 = 6.0m,在截面上作用一偏心力 N = 75KN，其偏心矩分別為 e0=20mm , 40mm , 60mm , 80mm , 120mm , 150mm, 180mm , 200mm。試分別求設(shè)計(jì)以上8種情況下截面的配筋數(shù)量。采用對(duì)稱配筋(As=As/),混泥土強(qiáng)度等級(jí)為 C30 ,縱筋采用HRB400級(jí)鋼筋。并繪出用鋼量隨偏心矩變 化的關(guān)系圖。解2 f2查表得：fc=14.3N/mm y=360N/ mmF取-s 一 - s =40mm

29、h° - h - as =560mm取ea =20mm二 e=ea +e0 = 2 0+ 2 0 4r0n同理可得 e = 40mm,60mm,80mm,120mm,150mm,180mm,200mm,時(shí)e = 60mm,80mm,100mm,140mm,170mm, 200mm,220mm 并分別取為ei,e2,劭，e4, £5&6 &7, e815 I。/ h =105-要考慮=1.0, 2=1.0= 1.2, 8 "182Ne 75 103 280fy（h0 - as ）360520=73mm : i minbh = 480mm勺=0.5fc

30、A/N =0.5"4.3 24000075燈03 =22.881，取勺"（的2*1 0/5（10）2 I同理可得：2 ".667, 3 =1.5, 4 =1.4, 5 "286, 1.236, 7怡=2 40 =80 ： O.oh。二168mm同理可求得前4組e O.3bh0后4組的ne >0.3bh0同理可得：= 360.02 mm, e3 = 380mm, e4 = 400mm, e5 = 440.04mm, q = 470.12 mm, e7 =500 mm, q = 520.04mm 由于是對(duì)稱配筋計(jì)算 NbNb =4 fcbh0 b =1

31、4.3 400 0.518 560 =1659.2kN N = 75kN 屬于大偏心受壓.取 x = 80mmx=N/afcb=75 1 03/14.3 400 1.0 = 13.11 ： 2a$ = 80mmip2r2r2r2As2 =As2= 64mmAs3=人3= 57 mm 4=49mm人5=As5= 33mmr2p2r2As6=As6 =11mm Ai = Ai = 4mmA$8 =1mm2:?m bh = 480mmF2選用 3 16 As = As = 603mm7-11知工字形截面柱尺寸如圖7-36所示，計(jì)算長(zhǎng)度L0 = 6.0m，軸向力設(shè)計(jì)值 N=650KN,彎矩設(shè)計(jì)值 M=

32、226.2KN.m，混泥土強(qiáng)度等級(jí)為 C25，鋼筋采用 HRB335級(jí)鋼筋。設(shè)計(jì) 對(duì)稱配筋的數(shù)量。解2查表得：fc=i.9N/mm圖 7 - 362y =360N/ mm取-s = - s =40mmho = h - as =660mm ea =20mm或ea =h/30 = 23.3mm 取 ea = 2 3. mmej= ea e0 = 348 23.3 = 371.3mm*15 lo/h=1O 5要考慮勺=0.5fcA/N =0511.911872065010P=1.O9>1，取 £ =1.0, J =1.0=111400=/h0(l°/h)2 ! 2=11400 371.3/660(8.57)_