图示三根压杆均为细长(大柔度)压杆,且弯曲刚度均为EI。三根压杆的临界载荷Fcr

练习题库2022-08-02  34

问题 图示三根压杆均为细长(大柔度)压杆,且弯曲刚度均为EI。三根压杆的临界载荷Fcr的关系为(  )。A.Fcra>Fcrb>FcrcB.Fcrb>Fcra>FcrcC.Fcrc>Fcra>FcrbD.Fcrb>Fcrc>Fcra

选项 A.Fcra>Fcrb>Fcrc
B.Fcrb>Fcra>Fcrc
C.Fcrc>Fcra>Fcrb
D.Fcrb>Fcrc>Fcra

答案 C

解析 欧拉公式Fcr=π^2EI/(μl)^2,μl越大则Fcr越小,图a中μl=1×5=5m;图b中μl=2×3=6m;图c中μl=0.7×6=4.2m,经比较可知Fcrc>Fcra>Fcrb。
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