青岛理工大学青岛理工大学混凝土结构设计原理第11章梁板结构

1、Af01l1q240221401138453845EIlqEIlqfA 40140221llqq qqq 21qqlllqqlllq24024014012 21EIEI 当当Aqq /1qq /20102/ ll0120821988082813210102.l/l ，时时，当当 qqlllqqlllq24024014012 qq /1qq /20102/ ll0120821988082813210102.l/l ，时时，当当 qqlllqqlllq24024014012 4124401025384384138455q

2、lEIEIfKKEIll ，得，402222114412010212121212384115=3843841155EIlKKKKEIEIKKllKKKKKKK K4012244010212=lKllKK同理，(a) 两对边简支矩形板(b) 两对边简支矩形板的弯曲形状无梁密肋楼盖单向板密肋楼盖17.1 梁板结构形式17.1 梁板结构形式威斯康星州约翰逊制蜡公威斯康星州约翰逊制蜡公司试验楼司试验楼赖特，赖特，1950p忽略了次梁、主梁、柱的竖向变形对板、次梁、主梁内力忽略了次梁、主梁、柱的竖向变形对板、次梁、主梁内力的影响；的影响；p柱子的竖向位移主要是柱子的轴向变形，在通常的内力分柱子的竖向位移

3、主要是柱子的轴向变形，在通常的内力分析中都是可以忽略的；析中都是可以忽略的；p 忽略主梁的变形导致次梁跨中弯矩偏小，主梁跨中弯矩增忽略主梁的变形导致次梁跨中弯矩偏小，主梁跨中弯矩增大。主要和主梁和次梁的线刚度有关。准确的分析要按照大。主要和主梁和次梁的线刚度有关。准确的分析要按照交叉梁系交叉梁系来计算，较复杂。来计算，较复杂。 板和次梁之间的内力同次梁和主梁。板和次梁之间的内力同次梁和主梁。p实际上忽略了次梁对实际上忽略了次梁对板、主梁对次梁、柱对板、主梁对次梁、柱对主梁的转动约束能力；主梁的转动约束能力；p计算支座转角大于实计算支座转角大于实际支座转角；际支座转角；p导致边跨跨中正弯矩导致边

4、跨跨中正弯矩计算值大于实际值；计算值大于实际值；p而支座负弯矩计算值而支座负弯矩计算值小于实际值小于实际值 。 a1 (a) 支承于墙上的单向板 l01=ln1+h1.1ln1 l02=ln2+h1.1ln2 ln1 ln2 a2 a2 2,21ha 两者取小者 2,22ha 两者取小者 h (b) 支承于墙上的梁 l01=ln1+(a1+a2)/21.05ln1 ln1 ln2 a2 a2 2,21ha 两者取小者 2,22ha 两者取小者 h a1 l02=ln2+a21.05ln2 较小值和（)ahl)al.(nn2202512121中心到中心的距离较小值和（)aal)al.(nn220

5、25121121中心到中心的距离 b1 (c) 与次梁整浇的单向板和与主梁整浇的次梁 l01=ln1+(b1+b2)/2 l02=ln2+b2 ln1 ln2 b2 b2 h qgg21qq21qgg41qq43ABCDEF12345ABCDEF12345ABCDEF12345ABCDEF12345ABCDEF12345ABCDEF12345(a)1、3、5 跨跨中最大正弯矩的活荷载布置 A B C D E F 1 2 3 4 5 (b)2、4 跨跨中最大正弯矩的活荷载布置 A B C D E F 1 2 3 5 (c) B 支座最大负弯矩和最大剪力的活荷载布置 A B C D E F 1 2

6、 3 4 5 2m2m2m2m2m2m 80 40 120 40 80 90 30 90 30 90 90 30 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 80 40 120 40 80 90 30 90 30 90 90 30 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m

7、 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 20bVMMb集中荷载）或均布荷载）(VV(b)qg(VVbb 2pL P My Mu Ly fy fu-fy P yfufpL P My Mu Ly fy fu-fy P yfuf pL P My Mu Ly fy fu-fy P yLyuudx)(0f ff f pyuuL)(ff2m2m2m2m2m2m GG= =3 30 0k kN N QQ

8、= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 80 40 120 40 80 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 90 30 90 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 90 90 30 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 80 40 120 40 80 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m

9、2m 2m 90 30 90 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 90 90 30 30 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 120 90 40 40 90 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m

10、 2m 2m 2m 2m 2m 120 90 40 40 90 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 120 90 40 40 90 80 40 120 40 80 6 60 0 6 60 0 6 60 0 6 60 0 GG= =3 30 0k kN N QQ= =3 30 0k kN N 2m 2m 2m 2m 2m 2m 120 90 40 40 90 80 40 120 40 80 6 60 0 6 60 0 6 60 0 6 60 0 kN52/ )8090(P GG= =3 30 0k kN N QQ= =3 3

11、0 0k kN N 2m 2m 2m 2m 2m 2m 120 90 40 40 90 80 40 120 40 80 6 60 0 6 60 0 6 60 0 6 60 0 kN52/ )8090(P eaeMMM 20/l20/lFF001880163Fl.FlMe 0011560325Fl.FlM 20/l20/lFF001880163Fl.FlMe 0011560325Fl.FlM 0150Fl.Ma 011750Fl.M 0150Fl.Ma 20201880150188000.Fl.Fl).(MMMeae 0001101750150214121Fl.Fl.FlMMMMa 20/l20

12、/lFF001880163Fl.FlMe 0011560325Fl.FlM 0150Fl.Ma 011750Fl.M 。eM)(M 1)MM(M.Mrl 210210)MM(M.Mrl 21021020l )qg(Mm 0l )QG(Mm nvl )qg(V )QG(nVv 111 111 161 141 161 墙 0.50 0.55 0.55 0.55 0.55 141 111 161 141 161 梁 241 0.50 0.55 0.55 0.55 0.55 141 111 161 141 161 柱 161 nvml )qg(Vl )qg(M 2020l )qg(Mm 111 111

13、 161 141 161 墙 141 111 161 141 161 梁 161 eM)(M 1310/bVM)(Me )MM(M.Mrl 21021011142020l )qg(Ml )qg( 16202020l )qg(Ml )qg( (b) 板角附近板带的扭转 (a) 弯曲变形形状 Sx1 Sx2 Sx2 Sy2 Sy1 Sy2 lx ly 四边简支 2)(xlqgM系数17.4 双板计算 2)(xlqgM系数AAgqg+q/2q/2q/2q/2q/2q/2AAgqg+q/2q/2q/2q/2q/2q/2 支座附近板带 Asx/2 支座附近板带 Asx/2 跨中板带 Asx lx/4 l

14、x/4 (lxly )/2 lx 跨中板带 Asy 支座附近板带 Asy/2 支座附近板带 Asy/2 ly lx/4 lx/2 lx/4 (a) 短向弯矩图 (b) 长向弯矩图 ly lx(b) 板底裂缝板底裂缝(a) 板面裂缝板面裂缝 负塑性铰线 正塑性铰线 11 22 2 2 1 1 自由边 (a) (b) mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx x11xl22 mx mx mx my my my x x ly-2x lx lx/2 lx/

15、2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 212)2(xlmUyxxyxlxlm4)2(22)( yxxlmmUxyxxllmm2)( 13)( xyylmmUxlmmxyy1)( 12424xyxlmxmU mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx x11xl22212)2(xlmUyxxyxlxlm4)2(22)( yxxlmmUxyxxllmm2)( 13)( xyylmm

16、Uxlmmxyy1)( 12424xyxlmxmUxlmlxmxyxx224 mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx x11xl22xyyxyyxxyxxlmmlmxlmmlmlU)(21)(22 )2(23122xlllxqWyxx)23(6xllqyx0ddxq mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx

17、 mx xlx5 . 0 xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122 mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 0ddxqxlx5 . 0 xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122xyyyxxxyyyxxxyyyxxlmMlmMlmMlmMlmMlmM , , , ,yyxxyxxyxMMMMMMllql 22)3(122 mx mx mx my my my x x ly

18、-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122xynll xymmxxxmmm yyymmm 212132222xxlmnnnq mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122212132222xxl

19、mnnnq0 xxmm0 yymm2121322xxlmnnq mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 0 xxmm0 yymm2121322xxlmnnq mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 0 xxmm0 yymm2121322xxlmnnq xyxyyxyxxyyxxyxlmlmlmlml

20、mlmllql 22)3(122xynllxymmxxxmmm yyymmm 212132222xxlmnnnq mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122212132222xxlmnnnq21nmmxy5 . 25 . 1 yyyyxxxxmmmmmmmm mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1

21、my 1 1 1 1 my my my =1 2 22 2 mx mx mx 12lln xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(12221nmmxy5 . 25 . 1 yyyyxxxxmmmmmmmmqlnnnmxx122222132 mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 12lln (a) lylx /2 lx /4 lx /4 lx /4 lx /4 lx /2 Asx/2 Asx Asy Asy/2

22、xxxyxyyxxxxxyxxlmlmlmMlmnlmllmM4322241222xxmlnnnq212132232412qlnnnmxx122232412132yyxxyxxyxMMMMMMllql 22)3(122 (a) lylx /2 lx /4 lx /4 lx /4 lx /4 lx /2 Asx/2 Asx Asy Asy/2 xxmlnnnq212132232412xxmlnnq21229)(21 (4 (a) lylx /2 lx /4 lx /4 lx /4 lx /4 lx /2 Asx/2 Asx Asy Asy/2 xxmlnnnq212132232412xxmlnn

23、q21229)(21 (4 lylx /2 lx /4 lx /4 lx /4 lx /4 lx /2 Asx Asy Asx Asy mx mx mx my my my x x ly-2x lx lx/2 lx/2 A B C D E F =1 my 1 1 1 1 my my my =1 2 22 2 mx mx mx 2481322xxlmnnq212132222xxlmnnnq1)(23() 13)(12(2nnnn B1 B2 B2 B3 B4 B4 B3 B4 B4 21nmmxy5 . 25 . 1 yyyyxxxxmmmmmmmmqlnnnmxx122222132xyxyyxy

24、xxyyxxyxlmlmlmlmlmlmllql 22)3(122 B1 B2 B2 B3 B4 B4 B3 B4 B4 21nmmxy5 . 25 . 1 yyyyxxxxmmmmmmmmqlnnnmxx122222132xmymxmxm ymym xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122 B1 B2 B2 B3 B4 B4 B3 B4 B4 21nmmxy5 . 25 . 1 yyyyxxxxmmmmmmmmxmymxmxm ymym xyxyyxyxxyyxxyxlmlmlmlmlmlmllql 22)3(122 a a q/2 q/2 q/2 2

25、161qa a a q/2 q/2 q/2 2161qa 22161)2/(81qaaqmmyx2121322xxulmnnqqqu231/1/xyxymmlln a a q/2 q/2 q/2 2161qa 22161)2/(81qaaqmmyxqqu23 a a q/2 q/2 q/2 2161qa a a a/4 a/4 a/4 a/4 A A q/2 q q 2645qa q/2 2641qa q/2 B B a a a/4 a/4 a/4 a/4 A A B B q/2 q q 2645qa q/2 2641qa q/2 2645qa2645qa2645qa2645qa2645qa a a a/4 a/4 a/4 a/4 A A B B 2645qa2645qa2645qa2645qa2645qaqqu89 a a q/2 q/2 a a a/4 a/4 a/4 a/4 A A B B qqu89qqu23 q ba/2 q q q/2 q/2 a/4 a/4 a a/4 a/4 a b 281qamy2641qamy q ba/2 q q q/2 q/2 a/4 a/4 a a/4 a/4 a b 281qamy2641qamy2321q