大学【建筑】- 搜题酱免费题库

第三章图为一两端铰接的焊接工字形等截面钢梁,钢材为Q235。梁上作用有两个集中荷载P=300 kN(设计值),集中力沿梁跨度方向的支承长度为100mm。试对此梁进行强度验算并指明计算位置。解:首先计算梁的截面模量,计算出梁在荷载作用下的弯矩和剪力,然后按照规定的计算公式,分别验算梁的抗弯强度、抗剪强度、局部承压强度和折算应力强度等。/(1)计算截面模量_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln…(2)验算截面强度梁上剪力和弯矩图分布如图所示,由此确定危险点。弯曲正应力B、C两点间梁段弯矩最大,不考虑截面发展塑性_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln剪应力A. B. 两点间梁段和 C. D. 两点间的梁段上的剪力最大 E. _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln F. _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln局部承压 G. ! 两点处没有加劲肋,应验算局部承压应力。 _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln折算应力左截面、右截面处同时存在较大的弯矩、剪力和局部压应力,应计算腹板与翼缘交界处的折算应力。局部承压验算已不满足,此处不必验算折算应力。 P=1500kN(不包含自重),钢材为Q235,梁的跨度及几何尺寸如图所示。试按强度要求确定梁截面。解:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln内力计算 — 梁的支座反力(未计主梁自重):_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 跨中最大弯矩:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln初选截面梁所需要的净截面抵抗矩为:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 梁的高度在净空上无限制,按刚度要求,工作平台主梁的容许挠度为l/400,则梁容许的最小高度为:(参照均布荷载作用) _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 按经验公式,可得梁的经济高度:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln hw=150cm。腹板厚度按抗剪强度:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 考虑局部稳定和构造因素:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln / 取腹板t=14mm。根据近似公式计算所需翼缘板面积:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln h=250~600mm,取b=420mm。翼缘板厚:t=7131/420=,取t=16mm。翼缘外伸宽度:b1=(420-14)/2=203mm。 _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln截面验算截面的实际几何性质: _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln : _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 主梁自重估算: 单位长度梁的质量为:×100×7850×10-6×=m 式中为考虑腹板加劲肋等附加构造用钢使自重增大的系数,则梁的自重为:g=m×=m 由梁自重产生的跨中最大弯矩:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 由梁自重产生的支座剪力:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 跨中最大弯矩:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 弯曲应力:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln … _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln,所选截面符合要求,截面尺寸如图所示。(也可重新选较大截面再进行验算) 支座处最大剪应力:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 次梁处放置支承加劲肋,不需验算腹板的局部压应力。跨中左侧和右侧截面处的弯矩和剪应力均最大,故需验算腹板与翼缘交界处的折算应力: 跨中截面腹板边缘正应力: _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 跨中截面腹板边缘剪应力: _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 跨中截面腹板边缘折算应力:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln I45a轧制工字形钢,钢材为Q235。作用力如图所示,截面无削弱,要求确定构件所能承受的最大轴线拉力。 _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln - I45a型钢的截面特性:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln N/mm2。根据强度条件有:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln P<,所以该压弯构件所能承受的最大轴线拉力为 KN(设计值)。 T形截面的形心、惯性矩、截面抵抗矩系数。 _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 解:相对翼缘外边缘的x′- x′轴,翼缘:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln,_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln;腹板:_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln,_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln,则截面形心到翼缘外边缘的距离: _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln 则_(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln _(2)=dfrac (1)(12)times 8times (800)^3+2times 280times 10times (404)^2=125534293mln;

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