混凝土结构中册习题答案
第11章
11．1 解：1、求支座截面出现塑性铰时的均布荷载q1 首先计算支座截面极限抗弯承载力MuA：
2
C20混凝土查得fc=9.6N/mm2, 3?16 As=603mm
x?Asfy?1fcb?603?300?94mm??bh09.6?200MuAx94?Asfy(h0?)?603?300(465?)?75.6KNm22 A 1 B 按弹性分析：MA?MuA12MuA12?75.6ql2??25.2kNm?, q? 2212l6?q1?25.2kN/m
2、计算跨中极限抗弯承载力Mu1：2?16 As=402mm
2
x?402?30063???63mm, Mu1?402?300?465???52.3kNm
9.6?2002??总弯矩M总?MuA?Mu1?75.6?52.3?127.9kNm 由M总
8M总8?127.9pul2??28.4kN/m ? 得 pu?228l622M总??127.9?85.3kNm 333、若均布荷载同为pu,按弹性计算的支座弯矩
MAe?则调幅系数??MAe?MAu85.3?75.6??0.114
MAe85.3
11．2 解：As1=AsA=644mm2/m， fy=210N/mm2, h0=120-20=100mm
644?210?14.1mm??bh09.6?100014Mu?644?210(100?)?12.58kNm/m
2x?,
?8/10@100
M总?2Mu?25.2kNm/m
8?25.2pu?2?2?12.6kN/m2
ln?14?18M总A
?8/10@100
B
1
11．3 解：塑性铰线位置如图所示。
a
a
l
取出一块梯形板块为隔离体，对铰支座AB取力矩平衡：
B 1(l?a)? 32l?a 4l?a 2A ??l?a?21?l?a??l?a??l?a??m?(l?a)?pu????a?????
23224????????l?a?2a?l?a??l?a?l?a??l?a?m?pu???p??apu?l?2a?????u2488324???? 24m?pu??l?2a??l?a?
第12章
12．1 解：
y3?10.45?0.0756影响线 0.45?4.4y2??0.80861.6y4??0.2676y1?y1
y2 y3
y4 0.45 4.4 1.15 4.4
1.6
?yi?1?0.075?0.808?0.267?2.15Dmax?0.9Pmax?yi?0.9?2.15?115?0.9?247.25?222.5kN18?9.8?10?9.8?115?22.2kN2P22.2Dmin?min?Dmax??222.5?43kNPmax115水平荷载系数??0.12 Pmin?1?0.12?3.94?10??9.8?4.098kN4
4.098Tmax,k??222.5?7.93kN115Tk?
2
12．2 解：
○
1计算柱顶水平集中力Wk：柱顶标高处?z?1.0, 檐口处?z?1.07
Wk?W1k?W2k???0.8?0.5??2.1??0.5?0.6??1.2??1.07?0.45?6??1.3?2.1?0.12??1.07?0.45?6?7.54kN
○2 q1k??s?zw0B?0.8?1.0?0.45?6?2.16kN/m
q2k??0.5?1.0?0.45?6??1.35kN/m
○
3 剪力分配系数计算： Wk n2.13A?14.38?0.148
n?7.2q1k q2k
B19.5?0.369
??10.5?8.410.5?0.2;
A B
C30A??31?0.23??11?0.008?5.757??2.868?0.148?1?????
C0B?3?2.96因只需相对值，故略去1091?0.23??1?0.369?1???H3H3H3?u1A?
E?868?E?;cI2C0AEc?14.38?2.c41.2433
?uH1H1B?E?.5?2.96?E?;c19c57.72
1?1?EcEc?uu3?41.24?57.72??98.963 A?BHH
?A?41.2498.96?0.417， ?57.72B?98.96?0.583 ○
4 计算约束反力RA、RB： 3
3??1?0.24??1??C???0.148?1????11A?3.028?0.8???1?0.23??1??98.96362
?0.148?1????
3??1?0.24??1??C11B???0.369?1?????3.008?0.3718???1?0.23??1??8.11?0.369?1????
RA?q1HC11A?2.16?10.5?0.362?8.21kN???RB?q2HC11B?1.35?10.5?0.371?5.26kN???
?R?8.21?5.26?13.47kN
○5 剪力计算： ?A??R?Wk??0.417??13.47?7.54??0.417?21.01?8.76kN?B??R?Wk??0.583??13.47?7.54??0.583?21.01?12.25kN
A柱顶剪力 VA=8.76-8.21=0.55Kn (?)
B柱顶剪力 VB=12.25-5.26=7kN (?)
○
6 弯矩图： M1A底?2q?V11H2AH?2?2.16?10.52?0.55?10.5?124.85kNm
MB底?12?1.35?10.5?7?10.5?147.8kNm
MA=124.85kN
MB=147.8kNm
4
12．3 解：从前题知 nA=0.148, nB=0.369, ??1 计算剪力分配系数： ○
3.5?0.318 11C0A?
C0B3?2.531??1?0.3183??1?0.148??
3??2.841??1?0.3183??1??0.369?Ec11??H314.38?2.5336.38
Ec11?uB?3??19.5?2.8455.38H?uA?
EE11??(36.38?55.38)c3?91.76c3 （相对值） ?uA?uBHH
?A?36.3855.38?0.4， ?B??0.6 91.7691.762 计算约束反力RA、RB： ○
C3A
1?0.31820.899?1.5??1.5??1.13811.185??1?0.3183??1?0.148??1?0.3180.899?1.5??1.2781.055?1?1?0.3183??1??0.369?2M1 M2
A
B
C3B?1.5?
M1153.2?C3A??1.138?15.85kN???H11
M?131RB?2?C3B??1.278??15.22kN???H11RA??R?15.85?15.22?0.63kN???
3 柱顶剪力： ○
VA?RA??A?R?15.85?0.4?0.63?15.6kN???VB?RB??B?R??15.22?0.6?0.63??15.6kN???98.6kNm
54.6kNm
4 弯矩图： ○
76.4kNm
54.6kNm
18.4kNm 40.6kNm 5