5-2.一跨度为4.5m的工作平台简支梁,承受均布荷载设计值28kN/m(静载不包自重),采用普通轧制工字钢I32a,钢材Q235,验算强度、刚度和整体稳定。跨中无侧向支撑点。解:I32a轧制工字钢的主要参数如下:自重mNg/46.5168.97.520,32.692cmWxmmtw5.9,.5.27cmSIxxIX=11076cm4,r=11.5cm,t=15mm,b=130mm加上自重后取最大弯矩和剪力设计值分别如下:mkNlgqlM44.725.42.1516.028812.181812202maxkNV39.645.42.1516.0215.42821max1.强度验算抗弯强度:满足22333max21567.99102.69205.1101044.72mmNfmmNWrMxx抗剪强度:满足223max12565.24105.95.271039.64mmNfmmNtISVvwxx局部承压强度:mmtrhy5.16155.11假定支承长度a=100mmkNVFmmhaLyZ39.6413325.161002max支座处满足22321596.501335.91039.640.1mmNfmmNLtFzwc2.刚度验算:按荷载标准值计算有mNmkNq/85.23/85.23516.02.128mmlmmEIqlV1825058.5101107610206450085.23384538454344max3.稳定性验算:(因为136.341304500bl)由题意可知跨中无侧向支承点,均布荷载作用于上翼缘I32a,6.083.0,5.4bml查表,可得73.0282,007.1'bb可得2236'max2153.143102.69273.01044.72mmNfmmNWMxb故整体稳定性满足要求。5-5.图5-55所示简支梁,中点及两端均设有侧向支承,材料为Q235,设梁的自重为1.1kN/m,分项系数为1.2,在集中荷载F=110kN作用下,分项系数为1.4,问该梁能否保证其整体稳定性?解:梁受压翼缘侧向自由长度1l与其宽度的比值162030060001bl故应进行整体稳定计算(1).截面特征值cmy2.331108.080130)5.0801(1101408.0805.01301cmy8.482.331801242323235.929575.08.481101101214018.48808.0808.01215.02.33130130121cmIx4333.2333110121301121cmIy4312250301121cmI4323.83110121cmI319.27992.335.92957cmyIWxx21041108.080130cmAcmAIiyy74.41043.233358.12674.46001yyil(2).最大弯矩:mkNM76.485124.111041122.11.1812max(3).求整体稳定系数ybyXybbfhtWAh2354.414320212h=82cm,8.096.03.23332250211IIIb736.0196.028.0128.0bb2235mmNfy跨度中点有一个侧向支撑点,集中荷载作用在上翼缘75.1b6.058.2235235736.0824.4158.12619.27998210458.126432075.122b96.0282,007.1'bb可得(4).验算整体稳定性满足2236'max2157.180109.279996.01076.485mmNfmmNWMxb5-7.某平台的梁格布置如图5-56所示。铺板为预制钢筋混凝土板,焊接于次梁上。平台永久荷载(包括铺板自重)为6kN/m2,分项系数为1.2;可变荷载为20kN/m2,分项系数为1.3。钢材Q235,E43型焊条,手工焊。要求:(1)选择次梁截面;(2)选择主梁(焊接组合梁)截面,设计梁沿长度的改变,设计翼缘焊缝,设计加劲肋。解:1.由于预制钢筋混凝土板与次梁上翼缘焊接,可保证整体稳定性,故只需考虑刚度和强度。1).最大弯矩设计值mkNM25.311533.12081532.168122max2).型钢需要的净截面抵抗矩nreqW3336max7.1378107.137821505.11025.311cmmmfrMWxnreq选用I45a,自重mkNmNg788.092.7878.94.80031430cmWx,cmSImmtcmIxxwx6.38,5.11,322404r=13.5cm,t=18.0mm,b=150mm加上自重后的最大弯矩设计值(跨中)maxM和最大剪力设计值(支座)maxV如下:mkNM2.31452.1788.08125.3112maxkNV4.25152.1788.0533.1202.11621max3).截面验算:(1).强度抗弯强度:满足2236max/215/3.20910143005.1102.314mmNfmmNWMXX抗剪强度:满足223max/125/7.565.11386104.251mmNfmmNtISVvwXX局部承压强度:mmtrhy5.31185.13假设支承长度mmhalmmayz5.1785.315.21005.2,100满足223/215/3.12275.1785.11104.2510.1mmNfmmNltFzwc(2).刚度验算:按荷载标准值计算:mmkNgk/8.78320788.036mmlmmEIlgVXk2025050002507.910322401020650008.78384538454344max所以满足要求。2.主梁的设计1).截面选择次梁传来集中荷载设计值kNF7.50252.1788.0533.12032.16最大弯矩设计值(不包括主梁自重)为:mkNM3.452410150045007.5021075007.5022433max最大剪力设计值:kNV4.10057.502421max需要的截面抵抗矩(按翼缘厚度20mm,2/215mmNf)3336max210431021043215103.4524cmmmfMWX梁的最小高度:根据容许挠度得-查表95,4001lvmmlh1000151015153min或mmvllfh10044001285000150002151285000min梁的经济高度为:cmWhcmWhxexe16330210437307166210431.31.3335252取腹板高度mmhmmhW1590,1550约为梁高腹板厚度(按mmtw20)mmhtmfhVtwwvww3.11111550112.51251550104.10052.12.14max取mmtw12,需翼缘面积mmhbmmhthWAwxf318~530159051~3151~3110055615901215901021044623取上下翼缘宽为500mm,厚度为20mm,则yffmmA235132.1220/24410000205002则可按部分截面发展朔性进行抗弯强度计算截面验算:42325.16048375.7825021551212135525021155cmIcmAx36.201862cmhIWxx375.145375.382.15.775.78250cmS梁自重(取刚重力密度为76.933/mkN):mkNg/7.293.761035540最大剪力设计值(支座处)kNV8.1029157.22.1214.1025max最大弯矩设计值(跨中)kNM71.4615157.22.181552.45242max抗弯强度:满足236max/2157.217106.2018605.1107.4615mmNWrMXx抗剪强度:满足=22433max/125/2.6112105.16048371075.11453108.1029mmNfmmNtISVvwx局部承压强度:拟设置支承加劲肋,不必验算。梁截面改变:梁在左右半跨内各改变截面一次,采用改变翼缘宽度的方法。变截面处离支座的距离为:mblx5.2615变截面处弯矩,剪力设计值:kNVmkNFM6.101714.23545.225.205.27.22.1215.22121需截面的抵抗矩:33361111880107.118792151014.2554cmmmfMW需翼缘面积:223211455.792121552.15.7911880222cmhIhWAw取改变后翼缘尺寸:,2301mmb,201mmt2211464600cmmmbt变截面后截面验算:3114311181529393155.782232121552.1cmhIWcmI抗弯强度(变截面处):满足22611/215/9.2051181505.11014.2554mmNmmNWrMXx抗剪强度(支座处):满足224331max3/125/9.6512109393151075.7214108.102975.721475.385.772.15.78223mmNmmNtIsVcmSx折算应力:243311114121'1/6.321210939315103611106.101736115.78223/7.2001591559.205mmNtISVcmSmmNhhww21222212/5.2362151.1/5.2086.3237.2003mmNfmmNli刚度验算,荷载折算成均布荷载满足则mmlmmWmkNqk8.4235041613461110939315105.16048372.31105.160483710206384150007.1995,615.15.2/7.1997.225788.02063344434max整体稳定可以保证167.8230200011bl翼缘焊缝计算mmIVSfhxwff77.110939315103611108.10291604.114.114331mmthmmthfmmf4.14122.12.17.6205.15.1minmaxmin取,8mmhf可满足要求。加劲肋的设计:一、腹板加劲肋的设计:已知截面尺寸:腹板-155012mm,翼缘-50020mm(跨中),-23020mm(端部)17
本文标题:钢结构第六章例题
链接地址:https://www.777doc.com/doc-1986296 .html