?FAC??3P
稳定性：
bh30.1?0.53Iz???1.04267?10?6m4
1212hb30.5?0.13Iy???41.667?10?6m4
1212Pcr??2EACIACLAC2??2?200?109?1.04267?10?682?32.128kN
?P?18.55kN
强度：
?AB?FAB2P??????50?106MPaAAB0.05?0.150?106P??125kN400F3P?AC?AC??????50?106MPa
AAC0.05?0.150?106P??144.3kN2003取P??125kN刚度：
FAC2LACFi2LiFAB2LABU????2EABAAB2EACAACi2EiAi?P?FiLi?????Fi??Li??(F)????i?????P?i2EiAi?i??P??EiAi?Fi(N) 2
单元 ?Fi ?P2 Li 6 8 Ai 0.05 0.05 ??F??LFi?i??i??P??EiAi?? ?AB AC 2P ?3P 2.4?109P 2.4?109P ?3 ?P?(2.4?109P)?(2.4?109P)?4.8?109P????0.0005?P???10.417kN94.8?10P=min{Pcr,P?,P?}?10.417kN
9-21
xAPBCD2m 解：（1）当P位于AB跨中时FAC?FBD? 计算AC杆的柔度：
P 2a4454 A?45?45 mI???341718.75mm4 ?2025m12122 i? ?AC?IA?341718.75?13.0mm
2025?li?1?2 故AC杆为细长杆 ?153.8?4?P13?1?30?2EA3.142?200?109?2025?10?6 Pcr,A???168.72kN C?2153.842计算BD杆的柔度： A?2?D2??d2??502???404?42?706.5m m
I??D4??d464IA??4??504???4064?181040.6245 mm i? ?BD?181040.625?16mm
706.5?li?0.?72?87.5??P
16?1?3022 Pcr,BD?235?0.00668??235?0.00668?87.5?183.86kN 由
P?168.72kN,可以求出当P位于AB杆中点时， 2结构的许用荷载为：?P??2?168.72?337.44kN
（2）由Pcr,AC?168.72kN，Pcr,BD?183.86kN知，当AC,BD都达到临界值时，荷
载P为最大，此时x值为：
x183.86 ?x?0.5l2 ?l?x168.72?P?max?168.72?183.86?352.58kN
（3）当P位于A端时，结构的许用荷载最小：?P?min?168.72kN