简支钢梁稳定设计计算书(Mathcad)

2015-12-9A46.492104×=A4b4h4⋅b4tw4−()h04⋅−:=h041.94103×=h04h42tf4⋅−:=h42000:=tf430:=tw418:=b4500:=f处截面mm4I32.8661010×=I3112b3h33⋅b3tw3−()h033⋅−⎡⎣⎤⎦⋅:=mm2A36.006104×=A3b3h3⋅b3tw3−()h03⋅−:=h031.67103×=h03h32tf3⋅−:=h31730:=tf330:=tw318:=b3500:=mm2Ab9.552103×=Abbbhb⋅bbtwb−()hb0⋅−:=hb0396=hb0hb2tfb⋅−:=hb420:=tfb12:=twb12:=bb200:=次梁KNqD0139.65=qD04.99.5⋅3⋅:=恒荷载标准值二、受力计算mm4I44.0061010×=I4112b4h43⋅b4tw4−()h043⋅−⎡⎣⎤⎦⋅:=mm2h01h12tf1⋅−:=h11550:=tf124:=tw116:=b1450:=a处截面N/mm2fce400:=N/mm2fv170:=N/mm2f295:=fy345:=Q345钢N/mm2E206103⋅:=弹性模量一、钢梁尺寸（建筑抗震设计规范GB500112001）−（钢结构设计规范GB500172003）−简支钢梁验算c处右截面mm4I22.2061010×=I2112b2h23⋅b2tw2−()h023⋅−⎡⎣⎤⎦⋅:=mm2A24.851104×=A2b2h2⋅b2tw2−()h02⋅−:=h021.682103×=h02h22tf2⋅−:=h21730:=tf224:=tw216:=b2450:=c处左截面mm4I11.7091010×=I1112b1h13⋅b1tw1−()h013⋅−⎡⎣⎤⎦⋅:=mm2A14.563104×=A1b1h1⋅b1tw1−()h01⋅−:=h011.502103×=9~12015-12-9≤bs130:=厚度bs158.667=≤ts16:=2.加劲肋验算端部支承加劲肋采用钢板成对布置于腹板两侧。每侧宽取bs与中间肋一样()下端支承处刨平后与下翼顶紧。,1）稳定性验算支座反力RP102⋅:=R1.35103×=KNtw0015tw1⋅235fy⋅:=tw00198.078=取tw0200:=mm截面面积A02tw0⋅()tw1⋅2bs⋅ts⋅+:=A01.056104×=mm2惯性矩Iy0ts2bs⋅tw1+()3⋅122tw0⋅tw13⋅12+:=Iy02.817107×=mm4钢梁自重qD1A43⋅Ab9.5⋅+()106−⋅78.5⋅:=qD122.412=KN活qL01.69.5⋅3⋅:=qL045.6=KN荷载设计值P11.2qD0qD1+()⋅1.4qL0⋅+:=P1258.314=KNP21.35qD0qD1+()⋅1.40.7⋅qL0⋅+:=P2263.472=KNP0maxP1P2,():=P0263.472=KN取P270:=KN三、端部支承加劲肋尺寸选择1加劲肋尺寸选择外伸宽度h043040+104.667=9~22015-12-911235fy⋅9.079=b3tw3−()2tf3⋅8.033=翼缘外伸肢11235fy⋅9.079=b4tw4−()2tf4⋅8.033=翼缘外伸肢跨中截面抗震第9.2.12条1验算翼缘局部稳定性五、验算局部稳定故可不计算整体稳定性钢梁受压翼缘上密铺deck板并有牢固相接,能阻止梁受压翼缘的侧向位移.,,四、验算整体稳定mmhf8=加劲肋与腹板焊缝相接焊缝高度满足构造要求()mm1.5tmax⋅6=mma3000:=在次梁处设横向加劲肋间距,0.5h04~2h04按构造要求设横向加劲肋间距,受压翼缘扭转无约束150235fy⋅123.799=h04tw4107.778=80235fy⋅66.026=受压翼缘扭转受约束170235fy⋅140.305=2加劲肋设计校核11235fy⋅9.079=b1tw1−()2tf1⋅9.042=翼缘外伸肢端部截面11235fy⋅9.079=b2tw2−()2tf2⋅9.042=翼缘外伸肢N/mm2f295=R103⋅φA0⋅139.419=φ0.917=稳定系数φ1α1λn2⋅−λn0.215≤if12λn2⋅α2α3λn⋅+λn2+()α2α3λn⋅+λn2+()24λn2⋅−−⎡⎢⎣⎤⎥⎦⋅λn0.215if:=λn0.379=λnλy0πfyE⋅:=α30.300:=α20.965:=α10.65:=b类截面类别GB500172003第132页注1公式−λy029.081=λy0h01iy0:=长细比mmiy051.648=iy0Iy0A0:=回转半径mmhf8:=取mmtmax16=tmaxmaxtw1ts,():=mmhf02.075=hf0R103⋅()40.7⋅h01220⋅−10−()⋅ffw⋅:=焊缝高度N/mm2ffw160:=角焊缝强度3）支承加劲肋与腹板焊缝相接N/mm2fce400=R103⋅Ace383.523=mm2Ace3.52103×=Ace2bs20−()⋅ts⋅:=承压面积2）端面承压计算9~32015-12-9集中力均为次梁传来且次梁处设加劲肋。,σcab0:=σabσcrab⎛⎜⎝⎞⎟⎠2τabτcrab⎛⎜⎝⎞⎟⎠2+0()2+0.205=1.0≤满足要求2）中间II区格bc段剪力Vbc945:=KN弯矩Mb3645:=Mc6480:=平均弯矩MbcMbMc+2:=Mbc5.063103×=KNm⋅σbcMbc106⋅I2h022⋅:=σbc192.98=N/mm2τbcVbc103⋅h02tw2⋅:=τbc35.114=N/mm2因双轴对称截面梁的受压翼缘扭转受到约束λb2h02tw2177⋅fy235⋅:=λb20.72=σcrbcfλb20.85≤if10.75λb20.85−()⋅−⎡⎣⎤⎦f⋅0.85λb21.25≤if1.1fλb22⋅λb21.25if:=σcrbc295=N/mm2ah021.784=3验算腹板局部稳定性1）支座区格ab段剪力Vab1215:=KN弯矩Ma0:=Mb3645:=平均弯矩MabMaMb+2:=Mab1.822103×=KNm⋅σabMab106⋅I1h012⋅:=σab80.069=N/mm2τabVab103⋅h01tw1⋅:=τab50.558=N/mm2因双轴对称截面梁的受压翼缘扭转受到约束λb1h01tw1177⋅fy235⋅:=λb10.643=σcrabfλb10.85≤if10.75λb10.85−()⋅−⎡⎣⎤⎦f⋅0.85λb11.25≤if1.1fλb12⋅λb11.25if:=σcrab295=N/mm2ah011.997=λs1h0141tw1⋅45.34h01a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah011≤ifh0141tw1⋅5.344h01a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah011if:=λs11.102=τcrabfvλs10.8≤if10.59λs10.8−()⋅−⎡⎣⎤⎦fv⋅0.8λs11.2≤if1.1fvλs12⋅λs11.2if:=τcrab139.754=N/mm29~42015-12-9τcd22.455=N/mm2因双轴对称截面梁的受压翼缘扭转受到约束λb3h03tw3177⋅fy235⋅:=λb30.635=σcrcdfλb30.85≤if10.75λb30.85−()⋅−⎡⎣⎤⎦f⋅0.85λb31.25≤if1.1fλb32⋅λb31.25if:=σcrcd295=N/mm2ah031.796=λs3h0341tw3⋅45.34h03a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah031≤ifh0341tw3⋅5.344h03a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah031if:=λs31.069=τcrcdfvλs30.8≤if10.59λs30.8−()⋅−⎡⎣⎤⎦fv⋅0.8λs31.2≤if1.1fvλs32⋅λs31.2if:=τcrcd143.029=N/mm2集中力均为次梁传来且次梁处设加劲肋。,σccd0:=σcdσcrcd⎛⎜⎝⎞⎟⎠2τcdτcrcd⎛⎜⎝⎞⎟⎠2+0()2+0.572=1.0≤满足要求4）中间IV区格de段剪力Vde405:=KNλs2h0241tw2⋅45.34h02a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah021≤ifh0241tw2⋅5.344h02a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah021if:=λs21.21=τcrbcfvλs20.8≤if10.59λs20.8−()⋅−⎡⎣⎤⎦fv⋅0.8λs21.2≤if1.1fvλs22⋅λs21.2if:=τcrbc127.826=N/mm2集中力均为次梁传来且次梁处设加劲肋。,σcbc0:=σbcσcrbc⎛⎜⎝⎞⎟⎠2τbcτcrbc⎛⎜⎝⎞⎟⎠2+0()2+0.503=1.0≤满足要求3）中间III区格cd段剪力Vcd675:=KN弯矩Mc6480:=Md8505:=平均弯矩McdMcMd+2:=Mcd7.492103×=KNm⋅σcdMcd106⋅I3h032⋅:=σcd218.265=N/mm2τcdVcd103⋅h03tw3⋅:=9~52015-12-9σdeσcrde⎛⎜⎝⎞⎟⎠2τdeτcrde⎛⎜⎝⎞⎟⎠2+0()2+0.819=1.0≤满足要求5）中间区格ef段剪力Vef135:=KN弯矩Me9720:=Mf10125:=平均弯矩MefMeMf+2:=Mef9.922103×=KNm⋅σefMef106⋅I4h042⋅:=σef240.254=N/mm2τefVef103⋅h04tw4⋅:=τef3.866=N/mm2因双轴对称截面梁的受压翼缘扭转受到约束λb4h04tw4177⋅fy235⋅:=λb40.738=σcreffλb40.85≤if10.75λb40.85−()⋅−⎡⎣⎤⎦f⋅0.85λb41.25≤if1.1fλb42⋅λb41.25if:=σcref295=N/mm2ah041.546=弯矩Md8505:=Me9720:=平均弯矩MdeMdMe+2:=Mde9.113103×=KNm⋅σdeMde106⋅I3h032⋅:=σde265.458=N/mm2τdeVde103⋅h03tw3⋅:=τde13.473=N/mm2因双轴对称截面梁的受压翼缘扭转受到约束λb4h03tw3177⋅fy235⋅:=λb30.635=σcrdefλb40.85≤if10.75λb40.85−()⋅−⎡⎣⎤⎦f⋅0.85λb41.25≤if1.1fλb42⋅λb41.25if:=σcrde295=N/mm2ah031.796=λs4h0341tw3⋅45.34h03a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah031≤ifh0341tw3⋅5.344h03a⎛⎜⎝⎞⎟⎠2⋅+⋅fy235⋅ah031if:=λs41.069=τcrdefvλs40.8≤if10.59λs40.8−()⋅−⎡⎣⎤⎦fv⋅0.8λs41.2≤if1.1fvλs42⋅λs41.2if:=τcrde143.029=N/mm2集中力均为次梁传来且次梁处设加劲肋。,σcde0:=9~62015-12-9N/mm2ffw160=≤120.7⋅hf上⋅Vmax103⋅Sf1⋅I1⎛⎜⎝⎞⎟⎠202+⋅69.727=F00:=有固定集中力处有顶紧上翼缘的支承加劲肋时,mm3Sf18.24106×=Sf1b1tf1⋅h1tf1−()2⋅:=上翼缘毛截面对梁中和轴的面积矩KNVmax1.215103×=VmaxVab:=mmhf上6:=焊缝高度第7.3.1条根据GB500172003−六、验算腹板和上翼缘的焊缝强度满足要求1.0≤σefσcref⎛⎜⎝⎞⎟⎠2τefτcref⎛⎜⎝⎞⎟⎠2+0()2