应力比法
例题3.1：有一个三杆件组成的超静定桁架，外形尺寸如图所示，作用荷载P 1或P 2，（P 1与P 2不同时作用），P 1=P 2=20kN ，[σ+]=200MPa ，[σ-]=150MPa 。

试求A 1，A 2，A 3。

程序框图
计算各杆件的应力比K i =σi /[σ]
结构内力分析，确定最不利工
况下的各杆件内力给出初始设计值，令A i =1优化杆件面积A=K i A
判断优化之后的应力比K i 是否接近1
输出优化的结果A*，W
是
i =i +1
否
应力比法计算框图
源程序（Fortran 语言编写）
PROGRAM main
REAL u1,u2,u3,p,A1,A2,A3,K1,K2,K3,w !定义实型
变量
PRINT*,'请输入荷载大小P ：'READ *,P
PRINT*,'请输入初始假定1杆的截面面积A1,A2：'READ *,A1,A2
PRINT*,'请输入控制误差e ：'READ *,e
PRINT*,'请输入超松弛因子B ：'
A 2
A 1
A 3
10
10
10
P 1
P 2图
READ*,B
do while（abs（1-K1）>e.or.abs（1-K2）>e.or.u3>150）!两杆件应力比同时接近1时，即可跳出循环，同时对第3杆件进行判断
i=i+1!统计计算次数
u1=10*P*（SQRT（2.0）*A1+A2）/（SQRT（2.0）*A1*A1+2*A1*A2）!计算杆件1的拉应力
u2=10*P*（SQRT（2.0）*A1）/（SQRT（2.0）*A1*A1+2*A1*A2）!计算杆件2的拉应力
u3=10*P*（A2）/（SQRT（2.0）*A1*A1+2*A1*A2）!计算杆件3的拉应力
K1=u1/200!1杆件的应力比
K2=u2/200!2杆件的应力比
w=2*sqrt（2.0）*A1+A2
PRINT*,A1,A2,K1,K2,w
A1=A1*K1**B!杆件优化，B为超松弛因子
A2=A2*K2**B
end do!结束do-while循环语句
PRINT*,'优化之后杆件的面积'
PRINT*,A1,A2
PRINT*,'应力比'
PRINT*,K1,K2
PRINT*,'循环次数'
PRINT*,i
PRINT*,'材料总量'
PRINT*,w
End
运行结果
请输入荷载大小P：
20
请输入初始假定1杆的截面面积A1,A2：
1
1
请输入控制误差e：
0.01
请输入超松弛因子B：
1.7
1.000000 1.0000000.70710680.4142136 3.828427
0.55478470.2235020 1.475393 1.148285 1.792670
1.0746510.28272580.80436840.6782025 3.322299
0.74223440.1461088 1.200588 1.053892 2.245465
1.0127700.15974610.89734940.8073077 3.024292 0.84245260.1110188 1.093777 1.000543
2.493835 0.98112490.11112140.94888060.8785229 2.886162 0.89739568.9161582E-02 1.0456930.9770499 2.627380 0.96821318.5710943E-020.97537230.9179140 2.824231 0.92802707.4096836E-02 1.0228910.9682269 2.698954 0.96442937.0139192E-020.98853360.9401844 2.797957 0.9457053 6.3157208E-02 1.0117870.9661620 2.738016 0.9647332 5.9567291E-020.99493410.9533124 2.788245 0.9564397 5.4917119E-02 1.0062820.9670205 2.760137 0.9666769 5.1873840E-020.99798770.9615037 2.786049 0.9633724 4.8524946E-02 1.0035080.9689950 2.773354 0.9691240 4.5995113E-020.99940890.9669582 2.787092 0.9681504 4.3441493E-02 1.0020810.9712642 2.781784 0.9715776 4.1340746E-02 1.0000440.9708340 2.789377 0.9716502
3.9311964E-02 1.0013270.9734769 2.787554 0.9738431 3.7555914E-02 1.0003060.9737524 2.792000 0.9743496 3.5895567E-02 1.0009140.9755017 2.791772 0.9758636 3.4413472E-02 1.0003950.9760559 2.794572 0.9765183 3.3024438E-02 1.0006760.9773052 2.795035 0.9776402 3.1760458E-02 1.0004060.9779413 2.796945 0.9783155 3.0578662E-02 1.0005300.9788947 2.797673 0.9791970 2.9489651E-02 1.0003860.9795263 2.799077 0.9798390 2.8470624E-02 1.0004350.9802936 2.799874 0.9805633 2.7523423E-02 1.0003540.9808851 2.800975 0.9811528 2.6635038E-02 1.0003680.9815271 2.801754 0.9817671 2.5804013E-02 1.0003200.9820679 2.802661 0.9823008 2.5022337E-02 1.0003190.9826197 2.803389 0.9828334 2.4287520E-02 1.0002880.9831091 2.804160 0.9833143 2.3594243E-02 1.0002800.9835922 2.804827 0.9837832 2.2939907E-02 1.0002590.9840339 2.805499 0.9842165 2.2320751E-02 1.0002500.9844624 2.806105 0.9846339 2.1734385E-02 1.0002340.9848617 2.806700 0.9850252 2.1178015E-02 1.0002240.9852455 2.807250 0.9854001 2.0649562E-02 1.0002120.9856071 2.807782
0.9857546 2.0146860E-02 1.0002020.9859535 2.808282 0.9860938 1.9668141E-02 1.0001920.9862821 2.808763 0.9864160 1.9211676E-02 1.0001840.9865967 2.809217 0.9867243 1.8775983E-02 1.0001750.9868965 2.809654 0.9870184 1.8359650E-02 1.0001680.9871835 2.810069 0.9873003 1.7961426E-02 1.0001600.9874578 2.810468 0.9875696 1.7580139E-02 1.0001540.9877210 2.810849 0.9878280 1.7214743E-02 1.0001480.9879731 2.811214 0.9880759 1.6864259E-02 1.0001420.9882150 2.811565 0.9883136 1.6527789E-02 1.0001360.9884477 2.811901 0.9885423 1.6204514E-02 1.0001310.9886709 2.812224 0.9887619 1.5893662E-02 1.0001260.9888859 2.812535 0.9889735 1.5594538E-02 1.0001210.9890928 2.812834 0.9891771 1.5306485E-02 1.0001170.9892921 2.813122 0.9893734 1.5028900E-02 1.0001130.9894843 2.813399 0.9895627 1.4761223E-02 1.0001080.9896696 2.813667 0.9897452 1.4502930E-02 1.0001050.9898486 2.813925 0.9899215 1.4253538E-02 1.0001010.9900215 2.814174优化之后杆件的面积
0.9900920 1.4012595E-02
应力比
1.0001010.9900215
循环次数
57
材料总量
2.814174
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