《钢筋混凝土结构课程设计》.doc

1、2单向板结构设计2.1板的设计2. 1.1板的计算按塑性分析法计算内力。2. 1. 2荷载恒荷载标准值：20mm水泥砂浆面层0.02？ X 20kN / in3 = OAkN / m180mm钢筋混凝土板0.08W × 25kN / = 2.0W / m215mm厚石灰砂浆抹灰0.015m ×lkN w3 = 0.255归V / m2gk=2.655kNm2活荷载标准值Clk =7.5kNm2横荷载设计值g = 1.2× 2.655 = 3.186ZjV / Ilr活荷载设计值q = 1.3×7.5 =9.15kN / m2合计2.1.3内力计算g +

2、q = 2.936/JV / m2次梁的截面20OnmI×AOOmm,板在墙上的支撑长度为120” ,则板的讣算跨度 为：=/ + = 1.9-02-+ = 1.72h0 ,r 2 2 2÷- = 1.9-0J2- + -= 1.74”2 2 2/. 0 = 1.72?Z中间跨 /o = 1.9-O.2 = 1.7n跨度差(1.72-1.7)1.7 = 1.2%<10%说明可按等跨连续板讣算内力。取Im宽板作为 计算单元，计算简图如图2-1所示。A L 一L_卜 179CL 3 J卜 17C2 y1± 丄* _I 17C9 !图2-1计算简图连续板各截面的弯

3、矩讣算见表2-1。表21连续板各截而弯矩计算截面1边跨跨内B离端第二支座2中间跨跨内C中间支座弯矩计算系数1111"111614计算跨度人0 =1.72zIQ = 1.72/ZO = 1 HmIQ = 1.7/nM= %(g+q)/：3.48-3.482.34-2.672.1.4截面承载力计算h = 1 OOO/n/fhh = 80w?,o =80-20 = 60mm o C30 混凝土，fc =14. 3 Nmm2。HPB300钢筋，s=270kNnr,连续板各截面的配筋计算见表2-2。表2-2连续板各截面配筋计算截面位豐边区板带（1-2, 56轴线间中间区板帶（25轴线间）边跨跨

4、内离端第二支座离端 第二 支跨 跨内、中间 跨跨 内中间支座边跨跨内离端第二支座离端第二跨跨内.中间跨跨内中间支座M ( kN)3.483.482.342673.483.480.8 × 2.34=1.870.8 × (-2.67)=-2.14_ M% Qj城0.0670.0670.0450.0520.0670.0670.0360.041 = -2ai0.0690.0690.0460.0540.0690.0690.0370.042A _ Mb 纨 S 219219146172219219118134选配钢筋06/817006/8170061900616006/817006/8

5、17006200。6200实配钢筋而积228228149177228228141141支座截而的受压区高度系数纟均小于0.35,满足弯矩调幅的要求：Pmin = (0.2%,45/ /v)ux = 45/,/v =45x1.43/270x100% = 0.238%所以，A nUn = Pninbh = 0.238% Xl(X)O × 80 = 190AmmI2.1.5板的裂缝验算裂缝宽度验算属于正常使用极限状态，采用荷载的标准组合。按弹性方法计算截面弯矩，考虑可变荷载的最不利布置，有Mk =afigk+allqk式中 8k 折算永久荷载标准值，gk = gk + qJ2 = 2.65

6、5 + 7.5/2 = 6.405ArTV/mqk折算可变荷载标准值，qk =OA/2 = 7.5/2 = 3.75RN/”？q 五跨连续板满布荷载下相应截面的弯矩系数，按有关表格查的；勺一五跨连续板最不利荷载布置下相应的弯矩系数，按有关表格查的。山荷载标准组合产生的跨中和支座弯矩：Mk = (0.078X6.405 + 0.1×3)×l .7202kN /m = 2.32W /mMBk = -(0.105 × 6.405 + 0.119×3)×l .7202 kN / m = -3Q5kN / mMlk = (0.033 X 6.405 +

7、0.079 ×3)×1.72W/m = 1.30kN / mMCk = -(0.079 × 6.405 + 0.111×3)×1.72W = -2.42kN / m= (0.046 × 6.405 + 0.085 ×3)×1.72 kN m = .59kN / m受弯构件的受力特征系数t=l9,光面钢筋的相对粘结特征系数 = 0.7, C30混凝土抗拉强度标准值人=2O1N/7F；保护层厚度c=15mm<20mm,取c=20mm, Ir算过程见表2-3,裂缝宽度均小于一类环境规范规定值。表2-3板的裂缝宽度验

8、算截而1B2C32.32-3.051.30-2.421.59AV / Innr228228149149149sq =Mk Q.S7h0As(Nmnr)202.9266.8170.6317.5208.6Pze=AMr0.010.010.010.010.01肖=1.1-0.65几 SQM0.4560.6100.3340.6890.474deq =d / V (mm)11.4311.438.578.578.57r =7(1.9+O.O8)(mm)<Pie129.44129.44106.56106.56106.56WmaX = a“IHq / E,(mm)0.1080.1910.0550.210

9、0.095注：几 vO.Ol,取几=0.01。2.1.6板的挠度验算截面的短期刚度由下式确左：B ESAXhI)1.15肖+ 0.2+ &汝一l + 3.5z式中，他=CQ=210x10'3x104=7,矩形截而f =0,各截面的短周期刚度如下表所示。截而1B2C3AS / mm 22192191461461460.4560.6100.3340.6890.474P = Ibho0.00370.00370.00240.00240.0024B10ll7V1.8821.5671.6121.0101.305山上表可见，禺与$很接近，满足0.5Bi<¾<2Bh

10、89;混凝土结构设计规范可 取整跨刚度目为计算挠度，这样的简化使挠度计算大为方便。长期刚度按下式确定吐苗硕好询千新關XK)J64"Nz其中，MI(Z = (0.078 +0.1%)/； = (0.078X7.965+ 0.1x3)x1.7221= 2J25kN.nigk =gk+ 丄 Wqqk) = 2.655 + - (0.8 × 7.5) = 7.965W / m2 21Clk= 1x0.8x75 = 3/.第一跨挠度最大.对于等跨连续板可只验算该跨挠度。永久荷载班满布，可变荷载你在1, 3, 5跨布置，又相应表格査的相应的挠度系数分别是0.644× IO-2

11、和0973><10一2,于是挠 度：0644xl(2g/B0.973x104? J4B0.644×102×2.655×172048.64 X 10,°0.973×102×75×17204+8.64xlOK)=8.45mm<200=S.6mm2.2次梁的设计2.2.1次梁计算次梁按考虑塑性内力重分布方法计算。2. 2. 2荷载恒荷载设计值Ill 板传来 1.9m ×3.186kN / m = 6.05JW / m2次梁自重 1.2xO2"x(O.4m-O.O8?)x25kN/F=1.92k

12、N/r梁侧抹灰 12×0.015m×(OAm一0.08)×7kN/my ×2 = 0.2OkN/ Hrg =8.17kNm2山板传来活荷载设计值q = .9m×9.15kN / ms = 18.5Inr合计g + q = 26.67kN / m22. 2.3内力计算汁算跨度边跨O 25爪4额-02L心4.555?厶+斜4555zn+字心4.675加1.025 = 4.669m > 4.675m 取 0§75中间跨h = Z= 4.8m 0.25m = 4.55m跨度差(°675-4.55)4.55 = 2.7%v10%

13、,说明可按等跨连续梁计算内力。计算简图如图22所示。s+q = 26.67kNm2I r 3 I匚丄=r:丄/刁刁二1彳E=J）图22计算简图连续次梁各截面弯矩及剪力计算分别见表2-4>表2-5o表24连续次梁弯矩计算截面1边跨跨中B离端第二支座2中间跨跨中C中间支座弯矩计算系数1111111614计算跨度人0 = 4.675m0 = 4.675/»Z0 = 4.55/?/0 = 4.55mM=%(g+q)j53.00-53.0034.51-39.44表25连续次梁剪力计算截面A边支座B （左） 离端第二支座B （右）离端第二支座C中间支座剪力计算系数0.450.60.550.

14、55净跨度J0 =4.6750 =4.675Z0 =4.550=4.55V=av(g + q)l;54.6774.8166.7466.742. 2. 4正截面承载力计算正截面承载力计算时，支座按矩形截面计算，跨中按T形截面计算，翼缘宽度 JR . =1/=1 × 48=160Omm , 乂 + 片=200 +1700 = 190Omm ,故取 bf = 160OmnI一类环境，梁的混凝土保护层厚度要求为25m,单排钢筋截面有效高度取 /0=365mmo判别T型截面类型： IIt80ajcbfhj （代）一 ）= 1.0x14.3×1517×80×（365

15、一一） = 564.02JVzn > 5300kNm2 2各跨跨中均属于第一类T型截面。次梁的正截面承载力过程见表2-6O表2-6次梁正截而受弯承载力汁算截而边跨跨中(1)离端第二支座(B)离端第二跨跨中(2)中间跨跨中(3)中间支座(C)弯矩设计值(kN.m )53.0053.0034.51 39.44_ Mctsa、f尿0.1600.1600.0910.104 = -2a0.1750.1750.0960.110选配钢筋 564.21044334.0383实际配筋5 I 123 I 223124<|：12AS =565A5 = 1140AS =339Aj =452计算结果表明均小

16、于0.35,符合塑性内力重分布的条件。A() = 339/(200X400) = 0.42% > PmIn = (0.2%,45flfy)ux =45v =45×1.43/300 = 0.22% ,满足最小配筋率的要求。2. 2. 5斜截面受剪承载力计算计算内容包括：截而尺寸复核、腹筋计算和最小配筋率验算。(1) 验算截面尺寸IlW = ¾-hf = 365-SO = 265mtn,hw/b = 265/200 = 1.2 <4» 截而尺寸按下式验算：O250JM)=O.25xl.0xl4.3x250x365 = 362.2OkN>½n

17、ax =74.8IkN 截而尺寸满足要求。(2) 计算所需腹筋采用06双箍，计算支座B左侧截而，Vlil=I2.S9kN a由斜截而受剪承载力计算公式确 左箍筋间距s:1°人九九1.0×270×l.48×365杯VV -0.7ftbhI) 748IO-0.7×1.43×2×365调幅后受剪承载力应加强，梁局部范囤内将计算的箍筋而积增加20%0先调幅整箍筋间距，S = 0.8x5725.7 = 458056M，大于箍筋最大间距 20Omm,最后取 s=200nmo(3) 验算最小配箍率弯矩调幅时要求的配箍率下限为0.3/4 =

18、0.3×1.43270 = 1.58×103,实际配箍率 p,=A, /(加)= 100.48(200×250) = 250xl(2t ,满足最小配箍率的要求。2. 26次梁的裂缝宽度验算次梁的折算永久荷载g* =6.808 +14.23/4 = 10.373/"?；折算可变荷载 .3乞=14.23x二= 10.67灯V/八变形钢筋的相对粘度特征系数v = 1.0混凝上的保护层厚度 4c=25mm荷载标准值下弹性分析的荷载弯矩系数=1.9,裂缝宽度的汁算过程见表2-7,各截面的裂 缝宽度均满足要求。表2-7次梁的裂缝宽度验算截而1B2C341.00-51

19、.5524.54-41.4828.65AV / H ln r565565339402339sq =Mk /0.87VJ(A(ZW2)24532308.45227.96324.94266.14PHW0.01410.01410.01000.01010.0100V = ll-0.65几/QQg0.7220.7990.6290.7020.609deq =(IlV (mm)12121212124-0(1.9q+O.O8'*z)(mm)Pre115.59115.59143.5142.54143.5VvmaX = CtCrlcrsq Z C 仙)0.2080.2640.1950.2760.221由荷

20、载标准组合产生的跨中和支囘E弯矩：Mk = (0.078 × 10.37 + 0.1×10.67) × 4.675叹N / m = 4 LOokN / IrIMIik = -(0.105×1037 + 0.119×10.67) × 4.6152 kN / In = -5155kN / mM2k = (0.033 X1037 + 0.079 × 10.67) × 4.5502 kN / m = 24.54W / mMek = -(0.079 X1037 + 0.111×10.67) X 4.5502kN /

21、 m = -41 ASkN / InMyk = (0.046 × 1037 + 0.085 X 10.67) X 4.5502 kN / m = 28.65W / m2. 2. 7次梁的挠度验算按等刚度跨度连续梁讣算边跨跨中挠度。短期刚度：BEM1.15/ + 0.2 + M P- + 3.5f2.0 × 105× 565 ×3652y N mm2 = 1.145×10l3N ? I IC nn 6×7.14×83×10'1.15× 0.772+0.2+1 + 3.5x1.675其中,P = AS

22、lbh° = 565/(200×365) = 8.3×10"3;, =Ev =2.0×IO5 ×2.8×IO4 = 7.14：( -b)hf _ (16-200)×80=1.04 / oZA)200×365长期刚度:BSa)+ ,5I2(2匚)7.00 小 EOJ9.267“M 加41.00英中，Ms = (0.078X9.654+0.1 ×8.538)×4.6752 = 35.2kNmgk =gk+ () = 6.808 + l×0.8× 14.23 = 9.65

23、4JW / mqk =扌匕你=X 0.8 X14.23 = 8.538W / m挠度系数与板相同，挠度:0.644 × 10240.973x10-2%/4J0.644Xb X6.808X46754 十 0.973"“丄23675.737讪V丄=23.375M2009.267 × IO129.267 XIO122.3主梁的设计2.3.1主梁计算主梁按弹性理论设计。23.2荷载为简化计算，将主梁自重及梁侧抹灰重量等效为集中荷载。荷载设讣值：由次梁传来 & 17 X 4.8=39.22 kN主梁自重 1.2×0.25× (0.65-0.08)

24、 ×1.9×17×2=8.3kN梁侧抹灰 1.2×0.015× (0.65-0.08) × 1.9× 17×2=0.67jWVG=48.02A7V活荷载设计值：由次梁传来Q=1&5×4.8=88.8 WG+Q= 136.82 W2.33计算简图主梁端部支承在砖墙上，支承长度为370mm；中间支承在柱上，钢筋混凝上柱截而为35Omm × 35Omm :墙、柱为主梁的钱支座，主梁连续梁计算。图23计算数计算跨度:0 35=5.7-0.12-=5.405,o=l.O25n÷ = l.

25、O25×5.4O5÷ = 5.715wf I UbLZ 0.37 0.35IQ = /”1 = 5.405 H1= 5.765/z?2 2 2 2取最小值0 =5.715m中间跨:In =5.7-0.35 = 5.35nZo =In +b = 5.35 + 0.35 = 5.7In跨度差(5.715-5.7) 5.7=0.26%<10%,则可以按等跨连续梁讣算。主梁的计算简图见图2-3。2.3.4内力计算及包络图内力讣算可采用等跨连续梁的内力系数进行计算，跨中和支座截面最大弯矩及 剪力按下式计算：M =kfilQ+ k2QlV =kfi + k2Q不同截面下的弯矩及剪

26、力的计算见表2-8、表2-9。表2-8主梁弯矩计算项次荷载简图kMkM(IkMBkkMhkMCG GG GG G/ /4 /0.2440.155-0.2670.0670.067-0.267-73.27II.13.1PTT-T66.9642.54-73.2718.3818.38Q Q(J Q/ ii /0.2890.244-0.133-0.133-0.133-0.133÷ ÷-4146.67123.83-67.4167.31-67.31-67.41I /-0.044-0.089-0.1330.2000.200-0.133=_+丄÷-22.32-45.17-67.41

27、101.23101.23-67.41。：)QQ¢(i /0.229116.220.126-0.3110.0964&590.170-0.089-45.11T ：+丄斗63.94-157.6486.05G 3-0.089/3 -0.059-0.089070.096-0.311-15.06-29.94-157.644 - ÷- : 4-45.1186.054&59基本不利®+<g)213.63166.37-140.684&93-48.93-140.68®+44.64263-140.68119.61119.61-140.68G)+&

28、#169;183.18106.48-230.9166.97104.43-118.38®+51.912.6-11838104.4366.97-230.91内 力序号计算简图k 石kk ELJLJLJ_>1人IfIi0.73335.20-1.267-60.841.00048.02Q 3Q SLJLJ_.1 & ! M 1； i10.86676.90-1.134-100.70000 QQ QM1_<： jJ0.68961.18-1.311-116.421.222108.51QQ9 U< ?< iJ b IJ-0.089-7.90-0.089-7.900.78

29、869.97最不 利内 力+112.1-161.544&02+96.38-177.26156.53+27.3-68.74117.993 0.1J/F表29主梁剪力值讣算1 1&丄1 c ：、八刁 ×>÷- oe 3 (S 口+”+二丄P11 Z Z .L2C>2.3.5主梁正截面受弯承载力计算跨内按T形截而计算，其翼缘宽度为:咕卄卜 5700 = 1900" VgFooMb + 2hf =250+12x8 = 1210取bf. =12IOmm,取人)=500-60 = 440" <>判别T形截而类型： ht80q

30、fcb. IIf(o-) = 1.0×14.3×1210×80× (440 一 )2 2= 553.69AAS? > 21267kN 加故属于第一类T形截而。b0.35Mb = Mnm - = -230.91 + (88.8 + 48.02) X 2 2= -203.55Wm主梁正截面承载力的计算截而1B2弯矩设计值(炒/加)213.63-203.55119.614&93as= M / a J(blf (mm2)0.0640.2940.0320.063 =0÷1-2)0.96690.82000.98370.9674A- M5 fy

31、/A1673.81880.5871.6362.6选配钢筋6 T 206 I 2031 202<| 20实配钢筋面积(mm2 )188418849426282.3.6主梁斜截面受剪承载力的计算(1) 验算截面尺寸九=人)一儿=440-80 = 360/77/77,IliV /? = 360/3 = 1.2 < 4 ,截而尺寸按下式验算：0.25fbhO =0.25×1.0×14.3×250×440 = 437.93W>Vnm =177.26W截而尺寸满足要求。(2) 计算所需腹筋采用06150双箍AVeS =0.7ftbl +1.0fw 亠 =0.7×l.43×250×440 + 1.0×270× 440×l.48/150 = 189.69WSVA = 112.1kN < V9Vf = 77.26kN<VesyHr = 156.33W < Vj知 B 截面上的剪力与/刚好，现配两根弯起，2020,而积为62Smnr O验算最小配箍率Q = A(V / (加)=100.48/(250