支撑、系杆计算

Sheet1 材料表 型号 截面面积(cm2) ix0(cm4) iy0(cm4) 56x36x3 2.74 0 单角钢 56x3 3.34 2.20 1.10 63x4 4.98 2.46 1.26 70x4 5.57 2.74 1.41 75x5 7.41 2.92 1.50 80x5 7.91 3.13 1.60 56x3 3.34 2.20 1.10 125x8 19.75 90x6 10.64 3.51 1.80 63x4 4.98 2.46 1.26 100x6 11.93 3.91 2.00 70x4 5.57 2.74 1.41 110x7 15.20 4.30 2.20 75x5 7.41 2.92 1.50 125x8 19.75 4.88 2.50 80x5 7.91 3.13 1.60 不等肢角钢 90x6 10.64 3.51 1.80 56x36x3 2.74 1.80 1.03 100x6 11.93 3.91 2.00 63x40x4 4.06 2.02 1.14 110x7 15.20 4.30 2.20 70x45x4 4.55 2.25 1.29 125x8 19.75 4.88 2.50 75x50x5 6.13 2.39 1.44 80x50x5 6.38 2.57 1.42 90x56x5 7.21 2.90 1.59 100x63x6 9.62 3.21 1.79 100x80x6 10.64 3.17 2.40 110x70x6 10.64 3.54 2.00 125x80x7 14.10 4.02 2.30 双角钢 2L56x3 6.69 1.75 2.29 2L63x4 9.96 1.96 2.59 2L70x4 11.14 2.18 2.86 2L75x5 14.73 2.33 3.10 2L80x5 15.84 2.48 3.28 2L90x6 21.27 2.79 3.71 2L100x6 23.86 3.10 4.09 2L110x7 30.39 3.41 4.52 2L125x8 39.50 3.88 5.14 不等肢角钢长并 2L56x36x3 5.49 1.80 1.31 63x4 0 2L63x40x4 8.12 2.02 1.46 2L70x45x4 9.09 2.28 1.64 2L75x50x5 12.25 2.39 1.85 2L80x50x5 12.75 2.57 1.82 2L90x56x5 14.42 2.90 2.03 2L100x63x6 19.23 3.21 2.29 0 2L100x80x6 21.27 3.17 3.11 2L110x70x6 21.27 3.54 2.55 2L125x80x7 28.19 4.02 2.92 不等肢角钢短并 2L56x36x3 5.49 1.03 2.53 2L63x40x4 8.12 1.14 2.87 2L70x45x4 9.09 1.29 3.18 2L75x50x5 12.25 1.44 3.38 2L80x50x5 12.75 1.41 3.65 2L90x56x5 14.42 1.59 4.10 2L100x63x6 19.23 1.79 4.56 2L100x80x6 21.27 2.40 4.33 2L110x70x6 21.27 2.01 5.00 2L125x80x7 28.19 2.30 5.68支撑、系杆计算 支撑、系杆计算 一、概况 工程地点：云南昆明 地面粗糙度: B 类 材料表 场地类别：II类 型号 截面面积(mm2) ix0(mm) iy0(mm) 基本风压： 0.30 kN/m2 （50年一遇） 单角钢 抗震设防烈度：6度,设计基本地震加速度值为0.05g 56x3 334.00 22.00 11.00 风荷载体型系数按《建筑结构荷载规范》GB50009-2001取值 63x4 498.00 24.60 12.60 支撑、隅撑受压构件长细比限值： [λ1]= 220 70x4 557.00 27.40 14.10 支撑、隅撑受拉构件长细比限值： [λ2]= 400 75x5 741.00 29.20 15.00 钢材采用Q235钢， [σ]=fy= 215 N/mm2 80x5 791.00 31.30 16.00 二、厂房支撑、系杆计算简图 90x6 1064.00 35.10 18.00 100x6 1193.00 39.10 20.00 110x7 1520.00 43.00 22.00 125x8 1975.00 48.80 25.00 不等肢角钢 56x36x3 274.00 18.00 10.30 63x40x4 406.00 20.20 11.40 70x45x4 455.00 22.50 12.90 75x50x5 613.00 23.90 14.40 80x50x5 638.00 25.70 14.20 90x56x5 721.00 29.00 15.90 100x63x6 962.00 0.40 17.90 100x80x6 1064.00 31.70 24.00 110x70x6 1064.00 35.40 20.00 125x80x7 1410.00 40.20 23.00 双角钢 2L56x3 669.00 17.50 22.90 2L63x4 996.00 19.60 25.90 2L70x4 1114.00 21.80 28.60 2L75x5 1473.00 23.30 31.00 2L80x5 1584.00 24.80 32.80 2L90x6 2127.00 27.90 37.10 2L100x6 2386.00 31.00 40.90 1.屋面水平支撑计算 (屋面水平荷载由第一道屋面水平支撑承担) 2L110x7 3039.00 34.10 45.20 风荷载标准值ωk=μsμzω0 2L125x8 3950.00 38.80 51.40 10米以下:ωk1=μsμz1ω0= 0.80 X 1.00 X 0.30 = 0.24 kN/m2 不等肢角钢长并 10.5米:ωk2=μsμz2ω0= 0.80 X 1.05 X 0.30 = 0.25 kN/m2 2L56x36x3 549.00 18.00 13.10 12.3米：ωk2=μsμz3ω0= 0.80 X 1.10 X 0.30 = 0.26 kN/m2 2L63x40x4 812.00 20.20 14.60 P1= 0.24 X 3.50 X 5.00 X 1.4 + 0.25 X 3.5 X 0.50 X 1.4 = 6.50 kN 2L70x45x4 909.00 22.80 16.40 P2= 0.24 X 6.50 X 5.00 X 1.4 + 0.25 X 6.5 X 1.13 X 1.4 = 13.51 kN 2L75x50x5 1225.00 23.90 18.50 P3= 0.24 X 6.50 X 5.00 X 1.4 + 0.25 X 6.5 X 1.67 X 1.4 = 14.75 kN 2L80x50x5 1275.00 25.70 18.20 P4= 0.24 X 7.00 X 5.00 X 1.4 + 0.26 X 7.0 X 2.30 X 1.4 = 17.62 kN 2L90x56x5 1442.00 29.00 20.30 P5= 0.24 X 6.50 X 5.00 X 1.4 + 0.25 X 6.5 X 1.67 X 1.4 = 14.75 kN 2L100x63x6 1923.00 32.10 22.90 P6= 0.24 X 6.50 X 5.00 X 1.4 + 0.25 X 6.5 X 1.13 X 1.4 = 13.51 kN 2L100x80x6 2127.00 31.70 31.10 P7= 0.24 X 3.50 X 5.00 X 1.4 + 0.25 X 3.5 X 0.50 X 1.4 = 6.50 kN 2L110x70x6 2127.00 35.40 25.50 计算可得支座反力： R1= 21.78 kN R2= 43.57 kN R3= 21.78 kN 2L125x80x7 2819.00 40.20 29.20 受力最大的斜杆： cosα= 0.789 Ncosα=(R1-P1) N=(R1-P1)/cosα= 19.38 kN 不等肢角钢短并 选用φ 18 圆钢做水平支撑: Ae= 254 mm2 2L56x36x3 549.00 10.30 25.30 则σ=N/Ae= 76.1390280401 N/mm2 ≤ [σ]= 215 N/mm2 2L63x40x4 812.00 11.40 28.70 满足要求! 2L70x45x4 909.00 12.90 31.80 2.柱间支撑、系杆计算 2L75x50x5 1225.00 14.40 33.80 2.1B/F轴上柱支撑2号杆计算 2L80x50x5 1275.00 14.10 36.50 在风压力作用下传至柱间支撑的荷载R1= 21.78 kN kN 2L90x56x5 1442.00 15.90 41.00 则在风吸力作用下传至柱间支撑的荷载R1'=R1X X 0.5 / 0.8 = 13.62 kN 2L100x63x6 1923.00 17.90 45.60 故可知传至柱间支撑的荷载R1+R1'= 35.40 kN 2L100x80x6 2127.00 24.00 43.30 该力由 4 副柱间支撑共同承担 则RA= (R1+R1')/ 4 = 8.85 kN 2L110x70x6 2127.00 20.10 50.00 Aa杆长 LAa= 9000 mm AB杆长 LAB= 4000 mm Ab杆长 LAb= 9850 mm 2L125x80x7 2819.00 23.00 56.80 sinβ= 9000 / 9850 = 0.914 所以斜杆所受力N=RA/sinβ= 9.69 kN 钢管 选用 2L100x6 做上柱支撑， ix= 31.0 mm iy= 40.9 mm A= 2386 mm2 102x2 933 35 则λx=0.5LAb/ix= 4925 / 31.0 = 159 ≤ [λ2]= 400 108x3 989.6 37.13 则λy=0.8LAb/iy= 7880 / 40.9 = 193 ≤ [λ2]= 400 114x3 1046.2 39.25 b= 100 mm t= 6 mm loy = 7880 mm 121x3 1112.1 41.73 b / t = 16.67 ≤ 0.58loy/b = 46 127x3 1168.70 43.85 λyz = λy(1+0.475*b4/(loy2*t2) = 186 ≤ [λ2]= 400 133x3 1225.20 45.97 σ=N/A= 4.0593814817 N/mm2 ≤ [σ]= 215 N/mm2 140x4 1709.00 48.1 满足要求! 2.2B/F轴中柱支撑4号杆计算 纵向水平荷载 RB= 8.85 kN bc杆长 LBC= 1500 mm 4号杆长 L= 2120 mm mm cosβ= 1500 / 2120 = 0.708 所以斜杆所受力N=RB/2cosβ= 6.26 kN 选用 56x3 角钢做中柱支撑， ix0= 22.0 mm iy0= A= 11.0 mm A= 334 mm2 则λx=0.9L/ix0= 1908 / 22.0 = 87 ≤ [λ1]= 220 则λy=0.9L/iy0= 1908 / 11.0 = 173 ≤ [λ1]= 220 b= 56 mm t= 3 mm loy = 1908 mm b / t = 18.67 ＞ 0.54loy/b = 18 λyz = 4.78*b/t*(1+loy2*t2/13.5*b4)= 111 ≤ [λ1]= 220 查表得φx= 0.487 σ=N/(φxA)= 38.4779341433 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.3B/F轴下柱支撑6号杆计算 纵向水平荷载 RC= 4.30 kN 6号杆长 L= 5220 mm sinθ= 1500 / 5220 = 0.287 斜杆所受力N= 6.54 kN 选用 2L100x80x6 长肢相连 ix= 31.7 mm 33 iy= 31 mm A= 2127 mm2 则λx=L/ix= 5220 / 31.7 = 165 ≤ [λ1]= 220 0 则λy=L/iy= 5220 / 31.1 = 168 ≤ [λ1]= 220 查表得φx= b2= 80 mm t= 6 mm loy = 5220 mm b2 / t = 13.33 ≤ 0.48loy/b2 = 31 λyz = λy(1+1.09*b24/(loy2*t2)= 165 ≤ [λ1]= 220 查表得φx= 0.262 σ=N/Aφx= 11.7356991354 N/mm2 ≤ [σ]= 215 N/mm2 2.4B/F轴屋顶系杆1号杆计算 系杆Aa受力 RA= 8.85 kN 选用φ 133X3 焊管做系杆， i= 46.0 mm A= A= 1225 mm2 则λ=L/i= 9000 / 46.0 = 196 ≤ [λ1]= 220 查表得φx= 0.186 σ=N/(φxA)= 38.8344046967 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.5B/F轴中间系杆3号计算 Bb杆受拉力 RB= 8.85 kN 选用 2L100x80x6 短肢相连 ix= 24.0 mm iy= 43.3 mm A= 2127 mm2 则λx=L/ix= 3000 / 24.0 = 125 ≤ [λ1]= 220 则λy=L/iy= 9000 / 43.3 = 208 ≤ [λ1]= 220 查表得φx= 查表得φx= 0.19 b1= 100 mm t= 6 mm loy = 9000 mm b2 / t = 16.67 ≤ 0.48loy/b2 = 39 λyz = λy = 208 ≤ [λ1]= 220 σ=N/(φxA)= 21.8985567763 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.6B/F轴中间系杆5号杆计算 Cc系杆受力 Rc= 4.30 kN 选用 2L100X80X6 短肢相连 ix= 24.0 mm iy= 43.3 mm A= 2127 mm2 则λx=L/ix= 3000 / 24.0 = 125 ≤ [λ1]= 220 则λy=L/iy= 9000 / 43.3 = 208 ≤ [λ1]= 220 查表得φx= b1= 100 mm t= 6 mm loy = 9000 mm 查表得φx= 0.19 b2 / t = 16.67 ≤ 0.48loy/b2 = 39 λyz = λy = 208 ≤ [λ1]= 220 σ=N/(φxA)= 2.0216267043 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.7D轴上柱支撑8号杆计算 在风压力作用下传至柱间支撑的荷载R2= 43.57 kN kN 则在风吸力作用下传至柱间支撑的荷载R2'=R2X X 0.5 / 0.8 = 27.23 kN 故可知传至柱间支撑的荷载R2+R2'= 70.80 kN 该力由 4 付柱间支撑共同承担 则RE= (R2+R2')/ 4 = 17.70 kN Ee杆长 LEe= 9000 mm EF杆长 LEF= 5800 mm Ef杆长 LEf= 10710 mm sinβ'= 9000 / 10710 = 0.840 所以斜杆所受力N=RE/sinβ'= 21.06 kN 选用 2L100X6 做上柱支撑， ix= 31.0 mm iy= 40.9 mm A= 2386 mm2 则λx=0.5LAb/ix= 5355 / 31.0 = 173 ≤ [λ2]= 400 则λy=0.8LAb/iy= 8568 / 40.9 = 209 ≤ [λ2]= 400 b= 100 mm t= 6 mm loy = 8568 mm b / t = 16.67 ≤ 0.58loy/b = 50 λyz = λy(1+0.475*b4/(loy2*t2) = 202 ≤ [λ2]= 400 σ=N/A= 8.8 ≤ [σ]= 215 N/mm2 满足要求! 2.8D轴中柱支撑10号杆计算 纵向水平荷载 RF= 17.70 kN BC杆长 LBC= 1500 mm 4号杆长 L= 2120 mm mm cosγ'= 1500 / 2120 = 0.708 所以斜杆所受力N=RF/2cosγ'= 12.52 kN 选用 56x3 做中柱支撑， ix0= 22.0 mm iy0= A= 11.0 mm A= 334 mm2 则λx=0.9L/ix0= 1908 / 22.0 = 87 ≤ [λ1]= 220 则λy=0.9L/iy0= 1908 / 11.0 = 173 ≤ [λ1]= 220 b= 56 mm t= 3 mm loy = 1908 mm b / t = 18.67 ＞ 0.54loy/b = 18 λyz = 4.78*b/t*(1+loy2*t2/13.5*b4)= 111 ≤ [λ1]= 220 查表得φx= 0.487 σ=N/(φxA)= 76.9558682866 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.9D轴下柱支撑12号杆计算 纵向水平荷载 RG= 6.20 kN 12号杆长 L= 5220 mm sinθ'= 1500 / 5220 = 0.287 所以斜杆所受力N= 21.58 kN 选用 2L100X80X6 长肢相连 ix= 31.7 mm 33 iy= 31 mm A= 2127 mm2 则λx=L/ix= 5220 / 31.7 = 165 ≤ [λ1]= 220 则λy=L/iy= 5220 / 31.1 = 168 ≤ [λ1]= 220 查表得φx= b2= 80 mm t= 6 mm loy = 5220 mm b2 / t = 13.33 ≤ 0.48loy/b2 = 31 查表得φx= 0.262 λyz=λy(1+1.09*b24/(loy2*t2)= 165 ≤ [λ1]= 220 σ=N/(φxA)= 38.7170404505 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.10D轴屋顶系杆7号杆计算 屋顶系杆受力 RE= 17.70 kN 选用φ 133X3 焊管做系杆， i= 45.8 mm A= A= 1225 mm2 则λ=L/i= 6000 / 45.8 = 131 ≤ [λ1]= 220 查表得φx= 0.387 σ=N/(φxA)= 37.3352897748 N/mm2 ≤ [σ]= 215 N/mm2 2.11D轴中间系杆9号杆计算 Ff杆受力 RF= 17.70 kN 选用 2L100X80X6 短肢相连 ix= 24.0 mm iy= 43.3 mm A= 2127 mm2 则λx=L/ix= 3000 / 24.0 = 125 ≤ [λ1]= 220 则λy=L/iy= 9000 / 43.3 = 208 ≤ [λ1]= 220 查表得φx= b1= 100 mm t= 6 mm loy = 9000 mm b2 / t = 16.67 ≤ 0.48loy/b2= 39 查表得φx= 0.19 λyz = λy = 208 ≤ [λ1]= 220 σ=N/(φxA)= 43.7971135526 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 2.12B/F轴中间系杆11号杆计算 Gg系杆受力 RG= 6.20 kN 选用 2L100X80X6 短肢相连 ix= 24.0 mm iy= 43.3 mm A= 2127 mm2 则λx=L/ix= 3000 / 24.0 = 125 ≤ [λ1]= 220 则λy=L/iy= 9000 / 43.3 = 208 ≤ [λ1]= 220 查表得φx= b1= 100 mm t= 6 mm loy = 9000 mm b2 / t = 16.67 ≤ 0.48loy/b2= 39 λyz = λy = 208 ≤ [λ1]= 220 查表得φx= 0.19 σ=N/(φxA)= 15.3415980006 N/mm2 ≤ [σ]= 215 N/mm2 满足要求! 用钢量统计 1(水平支撑轴线面积为1140m2）