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结构力学实验土木建筑学院实验名称：平面桁架结构的设计实验题号:梯形桁架D2-76姓名:学号：指导老师:实验日期:一、实验目的在给定桁架形式、控制尺寸和荷载条件下，对桁架进行内力计算，优选杆件截面，并进行刚度验算。
①掌握建立桁架结构力学模型的方法，了解静定结构设计的基本过程；②掌握通过多次内力和应力计算进行构件优化设计的方法；③掌握结构刚度验算的方法。
梯形桁架D ；其中结点1到结点7的水平距离为15m；结点1到结点8的距离为2m；结点7到结点14的距离为3m。
选用的是Q235钢，[ɑ]=215MPa。
完成结构设计后按如下步骤计算、校核、选取、设计、优化二、强度计算1）轴力和应力2）建立结构计算模型后，由“求解→内力计算”得出结构各杆件的轴力N（见图3）再由6=N/A得出各杆件应力。
表1内力计算杆端内力值 ( 乘子 = 1)--------------------------------------------------------------------------------------------杆端 1 杆端 2------------------------------------- ------------------------------------------ 单元码轴力剪力弯矩轴力剪力弯矩--------------------------------------------------------------------------------------------1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000002 51.9230769 0.00000000 0.00000000 51.9230769 0.00000000 0.000000003 77.1428571 0.00000000 0.00000000 77.1428571 0.00000000 0.000000004 67.5000000 0.00000000 0.00000000 67.5000000 0.00000000 0.000000005 39.7058823 0.00000000 0.00000000 39.7058823 0.00000000 0.000000006 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000007 -54.0000000 0.00000000 0.00000000 -54.0000000 0.00000000 0.000000008 -52.0383336 0.00000000 0.00000000 -52.0383336 0.00000000 0.000000009 -77.3140956 0.00000000 0.00000000 -77.3140956 0.00000000 0.0000000010 -81.1798004 0.00000000 0.00000000 -81.1798004 0.00000000 0.0000000011 -81.1798004 0.00000000 0.00000000 -81.1798004 0.00000000 0.0000000012 -67.6498337 0.00000000 0.00000000 -67.6498337 0.00000000 0.0000000013 -39.7940198 0.00000000 0.00000000 -39.7940198 0.00000000 0.0000000014 -54.0000000 0.00000000 0.00000000 -54.0000000 0.00000000 0.0000000015 66.4939824 0.00000000 0.00000000 66.4939824 0.00000000 0.0000000016 -41.5384615 0.00000000 0.00000000 -41.5384615 0.00000000 0.0000000017 33.3732229 0.00000000 0.00000000 33.3732229 0.00000000 0.0000000018 -21.8571428 0.00000000 0.00000000 -21.8571428 0.00000000 0.0000000019 5.27613031 0.00000000 0.00000000 5.27613031 0.00000000 0.0000000020 -18.0000000 0.00000000 0.00000000 -18.0000000 0.00000000 0.0000000021 19.7385409 0.00000000 0.00000000 19.7385409 0.00000000 0.0000000022 -31.5000000 0.00000000 0.00000000 -31.5000000 0.00000000 0.0000000023 42.0090820 0.00000000 0.00000000 42.0090820 0.00000000 0.0000000024 -47.6470588 0.00000000 0.00000000 -47.6470588 0.00000000 0.0000000025 62.0225709 0.00000000 0.00000000 62.0225709 0.00000000 0.00000000结构轴力图表2桁架四类杆内力与应力计算表3所得各类杆件性质上弦杆 下弦杆 直腹杆 斜腹杆 初选截面 截面D*t （mm ）63.5-2 60-2 42-2 45-2.5 截面面积（mm 2）386.4 364.4 251.3 333.8 最大轴力（KN ）-81.180 77.143 -54.000 66.494 最大应力（MPa ）210.1 211.7 214.9 199.2 调整 截面 截面型号63.5-2 60-2 42-2 45-2.5 截面面积（mm 2）386.4 364.4 251.3 333.8 最大轴力（KN ）-81.180 77.143 -54.000 66.494 最大应力（MPa ）210.1 211.7 214.9 199.2上弦杆 下弦杆 直腹杆 斜腹杆 EA(KN)77283.1873513.27 50265.48 62046.45 EI(KN*m 2) 36.5814.06 10.0812.15三、强度校核根据0.9[ɑ]≤6≤[ɑ]；对于Q235钢，[6]=215MPa；参考公式：A=0.25π[D2+-（D-2t）2];I=π[D4-(D-2t)4]/64.对截面进行强度校核。
结构力学实验报告实验内容：平面桁架结构设计实验目的：在给定桁架形式，控制尺寸以及荷载条件下，对桁架进行内力和应力计算，优选截面，并进行刚度验算。
实验步骤：选定桁架如图所示，其控制参数如图所述。
1234567891011121314( 1 )( 2 )( 3 )( 4 )( 5 )( 6 )( 7 )( 8 )( 9 )( 10 )( 11 )( 12 )( 13 )( 14 )( 15 )( 16 )( 17 )( 18 )( 19 )( 20 )( 21 )( 22 )( 23 )( 24 )( 25 )初选截面尺寸：选取尺寸 强度验算各杆轴力内力计算杆端内力值 ( 乘子 = 1)-----------------------------------------------------------------------------------------------杆端 1 杆端 2 ---------------------------------------- ------------------------------------------单元码 轴力 剪力 弯矩 轴力 剪力 弯矩 -----------------------------------------------------------------------------------------------1 48214.2857 0.00000000 0.00000000 48214.2857 0.00000000 0.000000002 67500.0000 0.00000000 0.00000000 67500.0000 0.00000000 0.000000003 67500.0000 0.00000000 0.00000000 67500.0000 0.00000000 0.000000004 67500.0000 0.00000000 0.00000000 67500.0000 0.00000000 0.000000005 54000.0000 0.00000000 0.00000000 54000.0000 0.00000000 0.000000006 30681.8181 0.00000000 0.00000000 30681.8181 0.00000000 0.000000007 -7500.00000 0.00000000 0.00000000 -7500.00000 0.00000000 0.000000008 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000009 -48510.9918 0.00000000 0.00000000 -48510.9918 0.00000000 0.00000000 10 -67915.3885 0.00000000 0.00000000 -67915.3885 0.00000000 0.00000000 11 -54332.3108 0.00000000 0.00000000 -54332.3108 0.00000000 0.00000000 12 -30870.6311 0.00000000 0.00000000 -30870.6311 0.00000000 0.0000000013 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000014 -7500.00000 0.00000000 -0.00000000 -7500.00000 0.00000000 -0.0000000015 17142.8571 0.00000000 0.00000000 17142.8571 0.00000000 0.0000000016 -0.00000000 0.00000000 0.00000000 -0.00000000 0.00000000 0.0000000017 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000018 13500.0000 0.00000000 0.00000000 13500.0000 0.00000000 0.0000000019 25909.0909 0.00000000 0.00000000 25909.0909 0.00000000 0.0000000020 -61080.8263 0.00000000 0.00000000 -61080.8263 0.00000000 0.0000000021 -25803.4169 0.00000000 0.00000000 -25803.4169 0.00000000 0.0000000022 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000023 -19091.8830 0.00000000 0.00000000 -19091.8830 0.00000000 0.0000000024 -34857.1168 0.00000000 0.00000000 -34857.1168 0.00000000 0.0000000025 -48452.2854 0.00000000 0.00000000 -48452.2854 0.00000000 0.00000000 桁架内力与应力计算在本次计算中直接应用每一杆中的轴力进行应力计算，根据控制应力0.9[σ]进行计算，直接确定各个杆件的最优截面尺寸，避免二次验算，计算结构如表格所示单元尺寸单元尺寸单元尺寸单元尺寸单元尺寸1 34-2.5 6 38-2.5 11 38-2.5 16 30-2 21 30-22 38-3.5 7 38-2.5 12 30-2 17 30-2 22 30-23 38-3.5 8 38-2.5 13 30-2 18 30-2 23 30-24 38-3.5 9 34-2.5 14 30-2 19 30-2 24 30-25 38-2.5 10 38-3.5 15 30-2 20 30-3 25 38-2.5 各个单元计算单元编号杆件轴力杆件应力截面选择截面面积1 48214.29 249.169434-2.5 247.2752 67500 348.837238-3.5 379.1553 67500 348.837238-3.5 380.1554 67500 348.837238-3.5 381.1555 54000 279.069838-2.5 278.6756 30681.82 158.562438-2.5 279.6757 -7500 -38.759738-2.5 280.6758 0.00000004 2.06718E-1038-2.5 281.6759 -48511 -250.703 34-2.5 282.675 10 -67915.4 -350.984 38-3.5 380.155 11 -54332.3 -280.787 38-2.5 278.675 12 -30870.6-159.538 30-2.0 175.84 13 0 0 30-2.0 176.84 14 -7500 -38.7597 30-2.0 177.84 15 17142.86 88.59358 30-2.0 178.84 16 0.0000004 2.06718E-09 30-2 179.84 17 0.000000147.23514E-10 30-2. 180.84 18 13500 69.76744 30-2 181.84 19 25909.09 133.8971 30-2 181.84 20 -61080.8 -315.663 38-3.5 380.155 21 -25803.4 -133.351 30-2.0 181.84 22 -0.00000022-1.137E-09 30-2.0 181.84 23 -19091.9 -98.6661 30-2.0 181.84 24 -34857.1 -180.14 30-2.0 181.84 25-48452.3-250.39938-2.5282.675杆件轴力图1234567891011121314( 1 )( 2 )( 3 )( 4 )( 5 )( 6 )( 7 )( 8 )( 9 )( 10 )( 11 )( 12 )( 13 )( 14 )( 15 )( 16 )( 17 )( 18 )( 19 )( 20 )( 21 )( 22 )( 23 )( 24 )( 25 )48214.2967500.0067500.0067500.0054000.0030681.82-7500.00-48510.99-67915.39-54332.31-30870.63-7500.0017142.8613500.0025909.09-61080.83-25803.42-19091.88-34857.12-48452.29结构变形示意图yx12345678 91011121314 ( 1 )( 2 )( 3 )( 4 )( 5 )( 6 )( 7 ) ( 8 )( 9 )( 10 )( 11 )( 12 )( 13 )( 14 )( 15 )( 16 )( 17 )( 18 )( 19 ) ( 20 )( 21 )( 22 )( 23 )( 24 )( 25 )位移计算以及挠度验算单元挠度验算f MAX<=0.045据此验算各单元的挠度(与下表中的位移进行验算，据此验算得到位移符合要求杆端位移值( 乘子= 1)-----------------------------------------------------------------------------------------------杆端1 杆端2---------------------------------------- ------------------------------------------单元码u -水平位移v -竖直位移-转角u -水平位移v -竖直位移-转角-----------------------------------------------------------------------------------------------1 0.00000000 0.00000000 -0.00794179 0.00179940 -0.01191268 -0.007941792 0.00179940 -0.01191268 -0.00482434 0.00313460 -0.01914918 -0.004824343 0.00313460 -0.01914918 -0.00132530 0.00446981 -0.02113713 -0.001325304 0.00446981 -0.02113713 0.00154073 0.00580502 -0.01882603 0.001540735 0.00580502 -0.01882603 0.00529618 0.00810825 -0.01088176 0.005296186 0.00810825 -0.01088176 0.00725451 0.00941690 0.00000000 0.007254517 0.00941690 0.00000000 0.00470440 0.00000811 -0.00042652 0.004704408 0.00688396 -0.01134398 -0.00742048 0.00564722 -0.00021326 -0.007420489 0.00688396 -0.01134398 -0.00509448 0.00626168 -0.01914918 -0.0050944810 0.00626168 -0.01914918 -0.00122578 0.00512255 -0.02113713 -0.0012257811 0.00512255 -0.02113713 0.00207557 0.00331437 -0.01818625 0.0020755712 0.00331437 -0.01818625 0.00586763 0.00101973 -0.00953110 0.0058676313 0.00101973 -0.00953110 0.00606972 0.00000811 -0.00042652 0.0060697214 0.00000000 0.00000000 -0.00564722 0.00564722 -0.00021326 -0.0056472215 0.00179940 -0.01191268 -0.00435820 0.00688396 -0.01134398 -0.0043582016 0.00313460 -0.01914918 -0.00234530 0.00626168 -0.01914918 -0.0023453017 0.00446981 -0.02113713 -0.00043516 0.00512255 -0.02113713 -0.0004351618 0.00580502 -0.01882603 0.00149439 0.00331437 -0.01818625 0.0014943919 0.00810825 -0.01088176 0.00386647 0.00101973 -0.00953110 0.0038664720 0.00688396 -0.01134398 -0.00693617 0.00000000 0.00000000 -0.0069361721 0.00626168 -0.01914918 -0.00417214 0.00179940 -0.01191268 -0.0041721422 0.00512255 -0.02113713 -0.00132530 0.00313460 -0.01914918 -0.0013253023 0.00512255 -0.02113713 0.00099785 0.00580502 -0.01882603 0.0009978524 0.00331437 -0.01818625 0.00376837 0.00810825 -0.01088176 0.0037683725 0.00101973 -0.00953110 0.00529155 0.00941690 0.00000000 0.00529155 13.绘制材料表材料表构件类型杆件号截面（mm) 长度（mm) 数量重量（KG)每个共计m³合计上弦杆38-2.5281.6751509 3 0.001275 34-2.5282.6751509 1 0.00042738-3.5380.1551509 2 0.00114738-2.5278.675030-2.0176.84030-2.0177.840下弦杆34-2.5247.2751500 1 0.000371 38-3.5379.1551500 3 0.00170638-3.5380.1551500 038-3.5381.1551500 038-2.5278.6751500 2 0.00083638-2.5278.6751500 0直腹杆38-2.5280.6751000 1 0.000281 30-2.0177.841167 6 0.00124530-2.0178.841333 1 0.00023830-2179.841500 1 0.0002730-2.180.841667 1 0.00030130-2181.841833 1 0.00033330-2181.842000 1 0.000364斜腹杆38-3.5380.1551803 1 0.00068530-2.0181.842005 1 0.00036530-2.0181.842121 1 0.00038630-2.0181.842245 1 0.00038630-2.0181.842368 1 0.00040838-2.5282.6752500 1 0.0004310.011776 G=78.5*0.011776=0.92446KN=924.46N=92.446KG实验总结：通过本次试验，对于结构力学求解器有了更好的理解和运用，尤其是对于结构力学求解器进行桁架结构设计有了更加深刻的应用，同时也发现自己在试验中也存在一定的不足和经验的缺乏，比如方程式的应用，函数的应用等等，这些问题都需要自己以后去解决。
平面桁架程序：#include "stdio.h"#include "math.h"#define unitmax 30#define pointmax 30#define matermax 10#define Pmaxnum 20#define bindmax 20main(){int unit[unitmax][4],bind[bindmax][3],number[5];float point[pointmax][2],material[matermax][2],P[Pmaxnum][3];float allarray[pointmax*2][pointmax*2];void readdata(int unit[unitmax][4],float point[pointmax][2],int number[5],int bind[bindmax][3],float material[matermax][2],float P[Pmaxnum][3]);void all(float point[pointmax][2],int unit[unitmax][4],float material[matermax][2], int number[5],float allarray[][pointmax*2]);void equa(float allarray[][pointmax*2],float P[Pmaxnum][3],int bind[][3],int number[]);void result(int unit[unitmax][4],float point[pointmax][2],int number[5],float material[matermax][2],float allarray[][pointmax*2]);readdata(unit,point,number,bind,material,P);all(point,unit,material,number,allarray);equa(allarray,P,bind,number);result(unit,point,number,material,allarray);}/******************************************************************/ void readdata(int unit[unitmax][4],float point[pointmax][2],int number[5],int bind[bindmax][3],float material[matermax][2],float P[Pmaxnum][3]){FILE *fp;int pointnum,unitnum,maternum,Pnum,bindnum,no_use,i,j,k,n,m;if((fp=fopen("data.txt","r"))==NULL){printf("data file can't be opened,please create it");exit(0);return;}for(i=0;i<=4;i++)if(fscanf(fp,"%d",&number[i])==EOF){printf("file error");fclose(fp);}pointnum=number[0];unitnum=number[1] ;maternum=number[2];Pnum=number[3];bindnum=number[4];for(i=0;i<pointnum;i++)fscanf(fp,"%d %f %f",&k,&point[i][0],&point[i][1]);for(i=0;i<unitnum;i++)if(fscanf(fp,"%d %d %d %d\n",&unit[i][0],&unit[i][1],&unit[i][2],&unit[i][3])==EOF) {printf("file error\n");fclose(fp);}for(i=0;i<maternum;i++)if(fscanf(fp,"%d %g %g\n",&k,&material[i][0],&material[i][1])==EOF){printf("file error\n");fclose(fp);}for(i=0;i<Pnum;i++)fscanf(fp,"%d %f %f %f\n",&k,&P[i][0],&P[i][1],&P[i][2]);for(i=0;i<bindnum;i++)if(fscanf(fp,"%d %d %d %d\n",&k,&bind[i][0],&bind[i][1],&bind[i][2])==EOF){printf("file error\n");fclose(fp);}fclose(fp);return;}/*OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOPPPPPPPPPPPPPPPPP*/void all(float point[pointmax][2],int unit[unitmax][4],float material[matermax][2],int number[5],float allarray[][pointmax*2]){float unitarray[2][2][4],allar[pointmax*2][pointmax*2]; int i,j,ii[2],r,s,v,w,kk;float xi,xj,yi,yj,E,A,L,EAL,SRF,CRF,SS,CC,CS;FILE *wp;wp=fopen("out.txt","w");for(v=0;v<2*number[0];v++)for(w=0;w<2*number[0];w++)allarray[v][w]=0.0;kk=0;for(kk=0;kk<number[1];kk++){i=unit[kk][1];j=unit[kk][2];ii[0]=i;ii[1]=j;xi=point[i-1][0];yi=point[i-1][1];xj=point[j-1][0];yj=point[j-1][1];L=sqrt((xj-xi)*(xj-xi)+(yj-yi)*(yj-yi));E=material[unit[kk][3]-1][0];A=material[unit[kk][3]-1][1];EAL=E*A/L ;SRF=(yj-yi)/L;CRF=(xj-xi)/L;SS=SRF*SRF;CC=CRF*CRF;CS=SRF*CRF;for(r=0;r<=1;r++)for(s=0;s<=1;s++){{if(r==s){unitarray[r][s][0]=EAL*CC;unitarray[r][s][1]=EAL*CS;unitarray[r][s][2]=EAL*CS;unitarray[r][s][3]=EAL*SS;}else{unitarray[r][s][0]=-EAL*CC;unitarray[r][s][1]=-EAL*CS;unitarray[r][s][2]=-EAL*CS;unitarray[r][s][3]=-EAL*SS;}}}for(v=0;v<=1;v++)for(w=0;w<=1;w++){allarray[2*ii[v]-2][2*ii[w]-2]+=unitarray[v][w][0]; allarray[2*ii[v]-2][2*ii[w]-1]+=unitarray[v][w][1];allarray[2*ii[v]-1][2*ii[w]-2]+=unitarray[v][w][2];allarray[2*ii[v]-1][2*ii[w]-1]+= unitarray[v][w][3];}for(v=0;v<number[0]*2;v++)for(w=0;w<number[0]*2;w++)allar[v][w]=0;for(v=0;v<=1;v++)for(w=0;w<=1;w++){allar[2*ii[v]-2][2*ii[w]-2]+=unitarray[v][w][0];allar[2*ii[v]-2][2*ii[w]-1]+=unitarray[v][w][1];allar[2*ii[v]-1][2*ii[w]-2]+=unitarray[v][w][2];allar[2*ii[v]-1][2*ii[w]-1]+= unitarray[v][w][3];}}fclose(wp);return;}/***********************************************************************/void equa(float allarray[][pointmax*2],float P[Pmaxnum][3],int bind[][3],int number[]) {int i,j,k,n,m;float op;FILE *wp;wp=fopen("out.txt","w");for(i=0;i<number[4];i++){ if(bind[i][1]==0){for(j=0;j<2*number[0];j++){allarray[2*bind[i][0]-2][j]=0.0;allarray[j][2*bind[i][0]-2]=0.0;}allarray[2*bind[i][0]-2][2*bind[i][0]-2]=1.0;}if(bind[i][2]==0){ for(j=0;j<2*number[0];j++){allarray[2*bind[i][0]-1][j]=0.0;allarray[j][2*bind[i][0]-1]=0.0;}allarray[2*bind[i][0]-1][2*bind[i][0]-1]=1.0;}}for(i=0;i<2*number[0];i++)allarray[i][2*number[0]]=0.0;for(i=0;i<number[3];i++){allarray[2*(int)P[i][0]-2][2*number[0]]=P[i][1];allarray[2*(int)P[i][0]-1][2*number[0]]=P[i][2];}n=2*number[0];for(k=0;k<n;k++){ op=allarray[k][k];for(m=k;m<=n;m++)allarray[k][m]=allarray[k][m]/op;for(i=k+1;i<n;i++){op=allarray[i][k];for(m=k;m<=n;m++)allarray[i][m]=allarray[i][m]-allarray[k][m]*op;}}for(k=n-1;k>=0;k--){for(i=k-1;i>=0;i--){op=allarray[i][k];for(m=n;m>=0;m--)allarray[i][m]=allarray[i][m]-allarray[k][m]*op;}}return;}/*_____________________________________________________________________________ ___*/void result(int unit[unitmax][4],float point[pointmax][2],int number[5],float material[matermax][2],float allarray[][pointmax*2]){int i,j,k,kk,ii;float disXi,disXj,disYi,disYj,xi,xj,yi,yj,EAL,E,A,L,SRF,CRF,N;FILE *wp;if((wp=fopen("out.txt","a"))==NULL){printf("data file can't be opened,please create it");exit(0);return;}printf("\n");for(kk=0;kk<number[1];kk++){i=unit[kk][1];j=unit[kk][2];xi=point[i-1][0];yi=point[i-1][1];xj=point[j-1][0];yj=point[j-1][1];L=sqrt((xj-xi)*(xj-xi)+(yj-yi)*(yj-yi));E=material[unit[kk][3]-1][0];A=material[unit[kk][3]-1][1];EAL=E*A/L ;SRF=(yj-yi)/L;CRF=(xj-xi)/L;disXi=allarray[2*i-2][2*number[0]];disYi=allarray[2*i-1][2*number[0]];disXj=allarray[2*j-2][2*number[0]];disYj=allarray[2*j-1][2*number[0]];printf("the unit=%d i=%d j=%d\n",unit[kk][0],i,j);printf("disXi=%f disYi=%f disXj=%f disYj=%f \n",disXi,disYi,disXj,disYj);N=-EAL*(CRF*(disXi-disXj)+SRF*(disYi-disYj));printf("the inner force=%f\n",N);fprintf(wp,"the unit=%d i=%d j=%d\n",unit[kk][0],i,j);fprintf(wp,"disXi=%f disYi=%f disXj=%f disYj=%f \n",disXi,disYi,disXj,disYj); fprintf(wp,"the inner force=%f\n",N);}return;}数据：10 17 1 1 21 0.0 0.02 0.0 1.03 1.0 1.04 1.0 0.05 2.0 1.06 2.0 0.07 3.0 1.08 3.0 0.09 4.0 1.010 4.0 0.01 12 12 23 13 1 3 14 1 4 15 3 4 16 3 5 17 3 6 18 4 6 19 5 6 110 5 7 111 6 7 112 6 8 113 7 8 114 7 9 115 7 10 116 8 10 117 9 10 11 2.1e9 0.0025 1 3 0 -501 1 0 02 10 1 0。
