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1、通过软件计算得出各杆件的应力。具体计算如下：正放四角锥网架，网格尺寸a = 4.0m，网架高度h = 3.0m。有一下弦节点，汇交有四根弦杆，最大 轴心拉力N1 = 76.242KN;四根斜腹杆，最大轴心拉力N2 = 278.09KN;最大轴心压力N3 = -147.05KN; 采用无缝钢管杆件，焊接空心球节点，均为Q235钢。设计符合要求的焊接空心球节点。解：(1)计算有关几何特性弦杆集合长度l = 4.0m，计算长度l0 = 0.9l = 3.6m。腹杆几何长度l = (a/2)2 + (a/2)2 + h2 = 22 x 2 + 32 = 4.12m计算长度l0 = 0.8l= 3.3m
2、.在该网架中一根弦杆与两根斜腹杆组成等腰三角形。该三角形中腹杆与 腹杆间的夹角为91 =2sin-i(2000/4120) = 58.08。= 1.01369rad；弦杆与腹杆间的夹角92 = (180 - 91)/2 = 60.96= 1.0640rad。(2) 杆件截面选择1、下弦杆：按最大轴心拉力N1 = 76.242KN确定截面。经过试算，四根下弦杆均采用076x 3.8的 圆钢管，A = 861.9mm2，i = 25.6mm。验算刚度、强度：入=l0/i = 3600/25.6 = 140.625 A = 250a = NJAn = 76242/861.9 = 88.458N/mm
3、2 / = 210N/mm22、斜腹杆：按最大轴心拉力N2 = 278.09KN，最大轴心压力N3 = - 147.05KN确定截面。经试算，四根斜腹杆均采用0114x6的圆钢管，A = 1382mm2，i = 38.9mm。验算刚度、强度、稳定:入=l /i = 3300/38.9 = 84.83 A = 250a = N2/An = 278090/1382 = 201.2N/mm2 / = 210N/mm2 由入 f /235 = 84.83 210/235 = 80.19，查表得(a 类截面)甲= 0.781；yN3/(A) = 147.05/(0.781 x 1382) = 136.2
4、4N/mm2 / = 210N/mm2(3) 确定空心球外径D = (d1 + 2a + d2)/9计算，取a = 15mm。需考虑以下三种情况：1、弦杆与腹杆之间d1 = 76mm，d2 = 114mm，9 = 92 = 1.0640rad，D = (76 + 2 x 15 + 114)/1.064 = 207mm。2、腹杆与腹杆之间d1 = d2 = 114mm，9 = 91 = 1.01369rad，D = (114 + 2 x 15 + 114)/1.01369 = 255mm。3、两根相互垂直的弦杆之间d1 = d2 = 76mm，9 = n/2 = 1.5708rad，D = (7
5、6 + 2 x 15 + 76)/1.5708 = 115.86mm。比较以上计算结果，并考虑焊接空心球规格，最后选择空心球外径D = 300mm。通过承载力计算，取空心球壁厚t = 25，适当。1.714tPmax= 1.714 x 6 = 10.284mm，取t = 12mm球内不设加劲肋。D/t = 300/12 =(4) 验算焊接空心球承载力1、按式Ntmax M Nt = 0.55nttdnf 验算。nt = 1.0，t = 12mm，f = 210N/mm2。A、弦杆：岑二=N1 = 76.242KN，d = 48mmNtmax = 76.242Kn Nt = 0.55nttdnf
6、 = 0.55 x 1.0 x 12 x 76 x n x 210 x 10-3 = 330.92N/mm2 哉必斜腹杆：Nmax = N2 = 278.09KN，d = 114mmNt= 278.09KNT Nt = 0.55nttdnf = 0.55 x 1.0 x 12 x 114 x n x 210 x 10-3 = 496.38N/mm22、 受压空心球承载另t按照公式Ncmax Nc = nc(400td 13.3t2d2/D)验算。nc = 1.0，t = 12mm，D = 300mm。由N=N；X= 147.05KN，d= 114mm得：CNZ：x = 147.05KN N = (400td - 13.3t2d2/D)cmax= 1.0 xC(400Cx 12 x 114 - 13.3 x 122 x 1142/300) x 10-3 = 464.23KN验算满足条件。
