习题课2-静定平面桁架的内力计算

静定平面桁架的内力计算习题课2一、找出桁架的零杆(1)FP8根零杆FP00000000一、找出桁架的零杆(2)5根零杆FP00000FP(3)FPFP12根零杆FPFP0000000000012根零杆(4)FPA000000000000FPA(5)aaaaFPFPABCD6根零杆aaFPFPaaFP2FPFPFN1ABCD000000由于荷载反对称，该桁架除下部水平链杆AB外，其余杆件受力反对称，故。0=NCDF(6)FP6根零杆FP000000附属部分7根零杆(7)FP0000000FP二、用简捷方法求桁架指定杆轴力(1)FPFPFPaa/2aa/2ABCDEFGHa/2a/212111.501.5()NPNPFaFaFF⋅+⋅==−压II-II左：220/200.5DyPyPMFaFaFF=+==−∑I-I下：250.51.118()1NPPFFF=−⋅=−压简单桁架1.5FPFPFPFPaa/2aa/21.5FPABCDEFGHa/2a/2ⅡⅡⅠⅠ12125解：0CM=∑(2)ddddFPACDBd1323FP2FP331)020()2)0()3)0()CNPPNPxNPyyCPMFdFdFdFFFFFFFF=+−======↑∑∑∑拉拉I-I右：联合桁架FNFyB=2FPddddFPACDBdⅡⅡⅠⅠ1FyC=FPFyA=FPFxA=2FP323FP2FP解：FNFyB=2FPddddFPACDBdⅡⅡⅠⅠ1FyC=FPFyA=FPFxA=2FP323FP2FP1210()()032()DNPPyNPPPMFFdFdFFFFF==−⋅=−==−=−∑∑压压II-II左：整体平衡：10(322)()2ByAPPPPPMFFdFdFdFdFd==+⋅−−=↑∑(3)AFDEC12FPFPaa/2aa/2a/2aB00ENMF==∑1)I-I右：02=NF2)结点C：1102()yyPNPFFFFF===∑拉3)结点F：FP0A-FP-FP-FPFDEC12FPFPPF2FNaa/2aa/2FPa/2aⅠⅠ00B联合桁架解：(4)FP4m4mFPFPFPABFC2134EDGH4m4m3m3m1220()0()33DNPxNPMFFFFF====−∑∑拉压1)I-I右：2)结点E：FP4m4mFPFPFP4FP6.67FP6.67FPABFCFN2134ⅡⅠEⅡDGH4m4m3m3mⅠ2222550()346xxPNxPFFFFFF====∑拉简单桁架解：FPFN2E23PF5534340343xPyPPNFFFFFF==⋅==4)结点D：FPFN3FN5D2FP2FP/3FP4m4mFPFPFP4FP6.67FP6.67FPABFCFN2134ⅡⅠEⅡDGH4m4m3m3mⅠ410(48)2()6FNPPPMFFFF−==+=−∑压3)II-II右：0xF=∑(5)FPddddCABd12FPFPdC1)结点C：结构与荷载均对称，两斜杆轴力为零。20()yNPFFF==∑拉2)结点A：11200.5()2yyPNPFFFFF==−=−∑压4)或取I-I左：11120()22yyPNPFFFFF==−=−∑压3)结点B：FPddddCABdⅠⅠ11.5FP1.5FP02FPFPdC000复杂桁架解：(6)FPaaFPFPFP1CABaaa3a110(2)0.6()5ANPPPMFFaFaFa−==⋅+⋅=−∑拉作如图封闭截面，取ABC部分为隔离体:FPaaFPFPFP1CABaaa3a联合桁架解：(7)FPaaaFPA1BaaaC11120(2)33525()()233AyPPNPPMFFaFaFFF==−⋅=−=−=−∑压I-I下：联合桁架解：125FPaaaFPFPFP0A1BaaaCⅠⅠ1NF1xF1yFB(8)aaaa2FP2FPABCD121)I-I右：02xxBCPyBCPNBCPFFFFFFF====∑2)结点B：04yNBDPFFF==−∑复杂桁架3FPFPBFNBDFNBC10223222202()SNPPNPFFFFFF=⋅+⋅−⋅==−∑压解：aa3FP3FPaaS12FP4FP2FPFNABCDⅠⅠ12S24FPDFN2CFN1=2FP2NCBPFF=2NCAPFF=3)结点D：4)结点C：2222040222()SNPNPFFFFF=−⋅==∑拉1002()xNCANCByNPFFFFFF====∑∑拉(9)aaFPFPFPCADB21aaa12103()310(333)2()3DNPPCNPPPMFFaFaMFFaFaFa==⋅===⋅−=∑∑拉拉I-I左：复杂桁架3FPaa3FP3FPFPFPFPCADB21ⅠⅠaaa解：(10)aaaaABCD1FP110()22AxCPPMFFaFa==⋅=←∑11110()224DNPPMFFaFa==⋅=∑拉I-I上：复杂桁架解：整体平衡：aaFPaa0.75FP0.5FP0.25FPABCDⅠⅠ1FP习题：3-9(c)(d)(f)、3-26