1、1 轴向拉压弯 曲 扭 转2q3内力内力 右截面正向右截面正向 左截面正向左截面正向 微段变形（正）微段变形（正）yxx顺时针错动顺时针错动FS向上凹向上凹M45解：解：1）求约束反力：）求约束反力： 受力如图。受力如图。2) 截面法求内力截面法求内力( 取坐标如图取坐标如图) 0 xa:aaaA B 3F 45 yx0F 2MMFSxFFN0FN=0; FS=- -F; M=- -Fx6a x2a: 2a x3a: 2) 截面法求内力截面法求内力0 xa: FN=0; FS=- -F; M=- -FxaaaA B 3F 45 yx0F MMFSxFFN0MMFSxFFN03FFMMFSxFF
2、N0 3F F3FFN=- -F；FS=3F- -F=2FM=3F(x-a)- -Fx=F(2x-3a)FN=- -F；FS=3F- -F- -3F=- -F M=3F(x-a)-Fx-3F(x-2a) =F(3a-x)7a x2a: FN=- -F； FS=2F M=F(2x-3a)0 xa: FN=0; FS=- -F; M=- -F x 2a x3a: FN=- -F ；FS=- -F M=F(3a-x)3P B45 x0FFAxFAyFBAMFaFa+-x2F+-FS -FFx-FNFx8aaaA B 3F 45 yx0F xF0MMFSFN910q11MM= aM=M0M12MMz1
3、3aa 缩短，缩短，bb伸长，变为弧形，伸长，变为弧形，AABBaabbMMaaMM14若梁由纵向纤维组成，则其变形若梁由纵向纤维组成，则其变形是伸长或缩短。是伸长或缩短。凹部纤维凹部纤维aa 缩短，凸部缩短，凸部bb纤维伸纤维伸长，总有一层纤维既不伸长又不长，总有一层纤维既不伸长又不缩短，此层称为中性层。缩短，此层称为中性层。AABBaabbaaMM15xyz中性轴中性轴s smax压压16ozybhydyoyzd( () )222IIdAzydAIyzAAr rr r+ += =+ += = = yzrdA = =AzdAyI2642/4dIIIzyp pr r= = = =17yx18y
4、xz19maxss=zWMmaxmax压压拉拉ssssyxzzWMIMy= = =maxmaxs s20L=1.2mOAMPaWMz11710227. 1104 .1443maxmax= = = = =- -s s21x63max31010101283 = = = =s sMbWz2283max3s sMb 6max3s sMb 272max3s sMb maxs2324mzbhFSIFSht tt t5 . 12382max= = = =maxt tt t FS25AB1m1m6/2maxmaxs ss s = =bhM6331015010664b23Smaxmaxt tt t = =bhF
5、mb182. 06321060410103bmb035. 026maxmaxss=zzWMIMymax压压smax拉拉sFS2728l/4xyBAFlCFAl/2l/4FD(a)xyBAFCFA1FB1l/2(b)l/4xyBAFA2FB2FD(c)29LEIbLFabzA6)( + +- -= =q qLEIaLFabzB6)(+ += =q qxyBAFCl/2l- - -4/3(6222/LbLEIFbL/2 yzLx- -= = =)30LEIbLFabzA6)( + +- -= =q qLEIaLFabzB6)(+ += =q qxyBAFD3l/4l- - -4/3(6222/Lb
6、LEIFbL/2 yzLx- -= = =)31xyBAFCl/2lxyBAFD3l/4ll/4xyBAFCl/2l/4FDl- - - -32maxyymaxqq33LAxBycmmb25. 81025. 8101202104532363=-326max322s sMbbhWbhz = = = =34zBEIqLy84-=25084maxLyEIqLyyzB=EqLbbbbhIz82503212)2(123433=cmmb92. 81092. 8210200825031010324933=-LAxBy35maxmaxss=zWM),(maxmaxyLfEIMyz=36 = =AzdAyI2maxsmaxs3738maxmaxss=zzWMIMymax压压smax拉拉s39
