纸质杆件的抗弯能力增强结构设计 20页

'纸质杆件的抗弯能力增强结构设计1设计说明书1.1设计构思构思是设计的灵魂。要将模型设计为悬臂结构，考虑模型制作的白卡纸力学性能，借用“塔吊”的思想对我们的设计进行构思，本次模型采用空间桁架结构体系，结构布置简单明了，稳定性好，荷载传递路线清晰，构件受力合理。充分利用白卡纸抗拉性能好的优点。1.1.1造型构思（1）材料强度分析最弱，因此，总的设计思路是尽可能降低荷载产生的弯矩。由表1，表2可看出白卡纸的主要优点在于它具有较强的抗拉性能；经试验，白卡纸制成的杆件抗压性能也较强。因此，结构体系的杆件受力应以杆件受拉和受压为主。表1230克白卡纸弹性模量名称种类层数弹性模量(MPa)230克白卡纸156.92148.2表2230克白卡纸极限应力名称类型层厚(mm)拉应力(N/mm2)压应力(N/mm2)备注230克白卡纸0.322.27.0受压计算时需考虑长细比对稳定的影响（2）结构功能要求所设计结构模型应能为承载板提供承载平面，承载平面必须在支承平面以上。5 模型最低加载荷载不能少于5kg，最大加载荷载不能大于20kg（不包含挂篮系统重量），且必须承载20s；模型竖向或横向最大挠度不大于跨度的1/10。（3）结构立面形式的选择结构最重要的功能，就是承受其生命全过程中可能出现的各种荷载。因此，在选择结构立面形式中，为了能满足结构承载能力要求，我们做了以下几个方案分析：图1立面形式比选方案一、造型简单，但受力不合理。方案二：传力直接，但质量大，不美观。方案三、稳定性较好，质量较轻，充分利用纸带很好的抗拉性能，实用性强，但传力略复杂，纸带的张拉难道大。但经过反复试验和甄选，由构思中得到启发，充分考虑白卡纸的材料性质，以结构功能要求为基本出发点，从多种形式对比中，决定以桁架作基本形式，考虑稳定性等方面的因素，最终选择折弦式桁架作为结构的立面形式。如图2所示。5 图2最终模型（4）构件截面的选择由白卡纸材料性质及结构的功能要求决定了构件宜以受拉、压为主，而白卡纸的受拉性能较好，且拉杆不存在稳定性问题。因此，构件的截面形式的选择应从受压性能最优的截面形式开始考虑。可供选择时常见截面有圆形截面、方形截面、矩形截面等。上弦杆主要承受较大的轴心压力。从圆形、方形、矩形截面中考虑，圆形的受压性能优于方形，方形优于矩形。但是，考虑到模型制作时圆形截面节点的处理难度较大（如图3所示），因此，上弦杆选方形截面为宜。腹杆主要承受拉力和压力，但所受力的大小较上弦杆小得多。因此，考虑到腹杆与上弦杆、腹杆与下弦杆之间节点的连接方面，为了便于节点处理，腹杆截面选为与上弦外包尺寸相等的方形截面（仅白卡纸层数不同）。下弦杆以受拉为主，且拉杆不存在失稳的问题。因此，根据白卡纸抗拉性能较强的优势，适当减小下弦杆的截面面积，故将其选为高度小于宽度的矩形截面，也易于进行节点处理。5 图3圆形截面杆件连接示意图1.1.1结构体系的选择结构体系的选择主要从结构的整体稳定性出发。该体系为图1所示的两榀桁架，通过横系杆在节点处将其连接成整体，并利用纸带做成拉条支撑弦杆，增强结构的稳定性。这样，整个结构能够具有较大的横向、纵向的稳定性，使结构不至因偏心导致整体的倾覆。1.2模型设计图纸1.2.1结构作品效果图效果图15 效果图2图4方案效果图1.2.2节点处理示意图节点图图5A节点处理示意图5 图6B节点处理示意图其他节点图7其他节点的处理1.3小组成员工作分工说明结构构思设计：全组三人运用草图大师制图：老卢运用力学求解器求解：叶总承载能力验算：许工5 1计算书1.1计算计算简图结构的计算简图如图8所示。1.2杆件编号为了便于运用结构力学求解器软件对结构进行分析计算和数据分析，我们对结构的节点和杆件进行了编号。各杆件的具体位置如图8所示。图8结构计算简图7 1.1.1构件截面尺寸上弦杆：方形，10mm×10mm，厚度10mm下弦杆：矩形10mm×10mm，厚度10mm腹杆：方形，10mm×10mm，厚度10mm拉条：宽10mm，厚度10mm1.1.2材料力学性质参见表1，表2。静载工况下结构的内力分析1.1.3结构内力图：7 图9轴力图（N）图10剪力图（N）7 图11弯矩图（）通过内力分析，可以看出，结构各杆件轴力较均匀，但在节点处发生突变，因此应在薄弱部位（如结构突变、节点处）予以加强，对最不利位置进行特殊处理，增加一定的刚度，防止破坏的发生。1.1.1结构刚度计算模型在竖向荷载作用下，产生相应的位移，如图12所示，为结构主要节点位移变化情况,各节点具体位移值见附录三。7 图12位移图1.1承载能力验算2.3.1强度、稳定性验算经大量试验得到不同长细比下的稳定系数，见表3。表3不同长细比对应的稳定系数长细比λ1020304050607080稳定系数0.930.880.780.660.590.520.480.371，拉杆结构的拉杆均为纸带，计算承受最大轴力的53号杆件的承载力7 满足强度要求1，悬臂杆件悬臂的回转半径i===6.46mm，杆件的计算长度为360mm，==55.71，查表3由内插法得悬臂在荷载作用下最大轴力=229.57（压）+=+=12.78<[]=16MPa3,底柱杆件的回转半径I===4.0mm，杆件的计算长度为200mm，==50，查表3得底柱在荷载作用下最大轴力为=206.54N（压）==10.29<[]=13MPa满足强度要求2.3.2刚度验算竖向荷载下结构变形小，经计算最大竖向挠度为37.66mm<[f]=40mm,满足强度要求。2.3.3承载力估算1，强度、稳定条件控制的最大承重材料抗压强度为=7N/m，荷载作用下悬臂受压杆件最不利，临界应力=5.43N/m，由此推出=20x=25.78kg2，刚度条件控制的最大承重20kg荷载下，最大挠度f=37.66mm。本设计容许最大变形[f]=40mm,则变形控制的最大承重=20x=21.24kg。考虑制作误差等缺陷影响，取安全系数。则=min｛｝/=22.30kg这说明，在保证强度、稳定性和刚度的条件下，本悬臂结构具有足够的承载力。1.1破坏形式的估计对模型的特点及以上计算的受力分析，粗略估计该模型的破坏形7 式主要有以下两种：（1）偏心产生的整体倾覆由于模型的主体结构处于支座上方，重心较高，制作误差及加载过程中的偏差致使模型存在偏心作用，从而使模型发生横向的整体倾覆。（2）局部损坏导致结构破坏由以上的受力分析可看出上弦杆压应力较大，最接近其极限压应力，故在无偏心以及制作误差较小的情况下，上弦杆将最早达到屈服，从而引起结构的破坏。7 附录一结构力学求解器输入源代码7结点,1,0,0结点,2,100,0结点,3,100,200结点,4,100,400结点,5,100,600结点,6,100,650结点,7,190,650结点,8,280,650结点,9,370,650结点,10,460,650结点,11,550,650结点,12,460,600结点,13,370,600结点,14,280,600结点,15,190,600结点,16,0,200结点,17,0,400结点,18,0,600结点,19,0,650结点,20,-90,650结点,21,-180,650结点,22,-180,600结点,23,-90,600结点,24,50,770结点,25,25,710结点,26,75,710结点,27,550,700结点,28,-180,0单元,21,22,1,1,0,1,1,0单元,21,20,1,1,0,1,1,0单元,20,19,1,1,0,1,1,0单元,19,6,1,1,0,1,1,0单元,6,7,1,1,0,1,1,0单元,7,8,1,1,0,1,1,0单元,8,9,1,1,0,1,1,0单元,9,10,1,1,0,1,1,0单元,22,23,1,1,0,1,1,0单元,23,18,1,1,0,1,1,0单元,18,5,1,1,0,1,1,0单元,5,15,1,1,0,1,1,0单元,15,14,1,1,0,1,1,0单元,14,13,1,1,0,1,1,0单元,13,12,1,1,0,1,1,0单元,10,11,1,1,0,1,1,0单元,11,12,1,1,0,1,1,0单元,20,23,1,1,0,1,1,0单元,18,19,1,1,0,1,1,0单元,6,5,1,1,0,1,1,0单元,7,15,1,1,0,1,1,0单元,8,14,1,1,0,1,1,0单元,9,13,1,1,0,1,1,0单元,10,12,1,1,0,1,1,0单元,21,23,1,1,0,1,1,0单元,23,19,1,1,0,1,1,0单元,19,5,1,1,0,1,1,0单元,5,7,1,1,0,1,1,0单元,7,14,1,1,0,1,1,0单元,14,9,1,1,0,1,1,0单元,9,12,1,1,0,1,1,0单元,11,27,1,1,1,1,1,1单元,27,10,1,1,1,1,1,1单元,19,25,1,1,0,1,1,1单元,25,24,1,1,1,1,1,18 单元,24,26,1,1,1,1,1,1单元,26,6,1,1,1,1,1,0单元,2,3,1,1,0,1,1,0单元,25,26,1,1,0,1,1,0单元,3,4,1,1,0,1,1,0单元,4,5,1,1,0,1,1,0单元,1,16,1,1,1,1,1,1单元,16,17,1,1,0,1,1,0单元,17,18,1,1,0,1,1,0单元,1,2,1,1,0,1,1,0单元,1,28,1,1,0,1,1,0单元,3,16,1,1,0,1,1,0单元,4,17,1,1,0,1,1,0单元,1,3,1,1,0,1,1,0单元,3,17,1,1,0,1,1,0单元,17,5,1,1,0,1,1,0单元,24,27,1,1,0,1,1,0单元,24,21,1,1,0,1,1,0单元,28,22,1,1,0,1,1,0结点支承,28,3,0,0,0结点支承,1,3,0,0,0结点支承,2,3,0,0,0单元荷载,16,3,1,0,1,90单元材料性质,1,54,1,1,0,0,-1813 附录二支架结构内力输出值内力计算杆端内力值(乘子=1)杆端1杆端2单元码轴力剪力弯矩轴力剪力弯矩-----------------------------------------------------------------------------------------------1137.754868-0.00000000-0.00000000137.754868-0.000000000.000000002-55.6305055-0.000000000.00000000-55.6305055-0.00000000-0.000000003-55.63050550.00000000-0.00000000-55.63050550.000000000.000000004208.6356090.00000000-0.00000000208.6356090.000000000.000000005181.020523-0.000000000.00000000181.020523-0.00000000-0.000000006-58.26117720.00000000-0.00000000-58.26117720.000000000.000000007-58.26117720.000000000.00000000-58.26117720.000000000.000000008-297.542877-0.000000000.00000000-297.542877-0.00000000-0.0000000090.00000000-0.000000000.000000000.00000000-0.00000000-0.0000000010-201.857965-0.000000000.00000000-201.857965-0.00000000-0.0000000011-201.8579650.00000000-0.00000000-201.8579650.000000000.0000000012-229.471537-0.000000000.00000000-229.471537-0.00000000-0.0000000013-229.471537-0.000000000.00000000-229.471537-0.000000000.00000000149.810163510.00000000-0.000000009.810163510.000000000.00000000159.810163510.00000000-0.000000009.810163510.000000000.0000000016-129.49532445.00000000.00000000-129.495324-45.00000000.0000000017148.086639-0.000000000.00000000148.086639-0.00000000-0.00000000180.000000000.00000000-0.000000000.000000000.000000000.0000000019-21.2136312-0.000000000.00000000-21.2136312-0.00000000-0.0000000020-66.4468870-0.000000000.00000000-66.4468870-0.00000000-0.00000000210.000000000.00000000-0.000000000.000000000.000000000.00000000220.00000000-0.000000000.000000000.00000000-0.00000000-0.0000000013 23-0.000000000.00000000-0.00000000-0.000000000.000000000.0000000024-138.3843680.00000000-0.00000000-138.3843680.000000000.0000000025-115.458608-0.000000000.00000000-115.458608-0.00000000-0.0000000026115.4586080.00000000-0.00000000115.4586080.000000000.0000000027-164.6354480.00000000-0.00000000-164.6354480.000000000.0000000028-136.864216-0.000000000.00000000-136.864216-0.00000000-0.0000000029136.864216-0.000000000.00000000136.864216-0.00000000-0.0000000030-136.8642160.00000000-0.00000000-136.8642160.000000000.0000000031136.8642160.00000000-0.00000000136.8642160.000000000.0000000032116.917229-0.04431110-0.00000000116.917229-0.04431110-2.2155548433-192.2514490.02151937-2.21555484-192.2514490.02151937-0.0000000034-41.97259790.06564636-0.00000000-41.97259790.065646364.2670133935-42.0339300-0.081550764.26701339-42.0339300-0.08155076-1.0337858836-72.01810710.08155076-1.03378588-72.01810710.081550764.2670133937-71.9567750-0.065646364.26701339-71.9567750-0.065646360.0000000038-206.5412370.00000000-0.00000000-206.5412370.000000000.00000000390.15946354-0.000000000.000000000.15946354-0.00000000-0.0000000040-206.5412370.000000000.00000000-206.5412370.00000000-0.0000000041-206.5412370.00000000-0.00000000-206.5412370.000000000.0000000042-21.21363120.00000000-0.00000000-21.21363120.000000000.0000000043-21.2136312-0.00000000-0.00000000-21.2136312-0.00000000-0.0000000044-21.21363120.00000000-0.00000000-21.21363120.000000000.00000000450.000000000.000000000.000000000.000000000.000000000.00000000460.000000000.000000000.000000000.000000000.000000000.00000000470.00000000-0.000000000.000000000.00000000-0.00000000-0.00000000480.00000000-0.000000000.000000000.00000000-0.00000000-0.00000000490.000000000.000000000.000000000.000000000.00000000-0.0000000050-0.00000000-0.000000000.00000000-0.00000000-0.00000000-0.00000000510.000000000.00000000-0.000000000.000000000.000000000.0000000052169.7311700.00000000-0.00000000169.7311700.000000000.0000000013 53176.5871460.00000000-0.00000000176.5871460.000000000.0000000054137.7548680.00000000-0.00000000137.7548680.000000000.00000000---------------------------------------------------------------------------------------------13 附录三支架结构变形输出值位移计算杆端位移值(乘子=1)杆端1杆端2单元码u-水平位移v-竖直位移θ-转角u-水平位移v-竖直位移θ-转角1464801.52789540.6644-946.156991417493.67782652.9209-946.1569912464801.52789540.6644-674.187825459794.78128863.7601-674.1878253459794.78128863.7601-473.918005454788.036-13788.8603-473.9180054454788.036-13788.8603-1134.58226475651.597-127247.086-1134.582265475651.597-127247.086-2541.53192491943.444-355984.960-2541.531926491943.444-355984.960-3404.54439486699.938-662393.955-3404.544397486699.938-662393.955-3194.80416481456.432-949926.330-3194.804168481456.432-949926.330-3236.36777454677.573-1241199.43-3236.367779417493.67782652.9209-597.657342417493.67728863.7601-597.65734210417493.67728863.7601-462.132654399326.460-12728.1787-462.13265411399326.460-12728.1787-1111.96563379140.664-123924.742-1111.9656312379140.664-123924.742-2578.44686358488.225-355984.960-2578.4468613358488.225-355984.960-3404.54439337835.787-662393.955-3404.5443914337835.787-662393.955-3194.80416338718.702-949926.330-3194.8041615338718.702-949926.330-3159.48757339601.616-1234280.21-3159.4875716454677.573-1241199.43-32017.7210443022.993-1389044.3228732.278917443022.993-1389044.32-1801.87159339601.616-1234280.21-1801.8715918459794.78128863.7601-846.022081417493.67728863.7601-846.02208119399326.460-12728.1787-1109.23150454788.036-13788.8603-1109.2315020475651.597-127247.086-1930.21865379140.664-123924.742-1930.2186521491943.444-355984.960-2669.10436358488.225-355984.960-2669.1043622486699.938-662393.955-2977.28301337835.787-662393.955-2977.2830123481456.432-949926.330-2854.75460338718.702-949926.330-2854.7546024454677.573-1241199.43-2301.51912339601.616-1234280.21-2301.5191213 25464801.52789540.6644-738.331496417493.67728863.7601-738.33149626417493.67728863.7601-538.061676454788.036-13788.8603-538.06167627454788.036-13788.8603-1183.67654379140.664-123924.742-1183.6765428379140.664-123924.742-2502.41118491943.444-355984.960-2502.4111829491943.444-355984.960-3328.50872337835.787-662393.955-3328.5087230337835.787-662393.955-3118.76848481456.432-949926.330-3118.7684831481456.432-949926.330-3083.45189339601.616-1234280.21-3083.4518932443022.993-1389044.32-1339.53667510922.975-1383198.46-1394.9255433510922.975-1383198.46-1394.92554454677.573-1241199.43-1508.9782034454788.036-13788.8603-1414.32110535824.428-50509.5943-1275.6431635535824.428-50509.5943-1275.64316606437.013-82891.3941-1170.5632736606437.013-82891.3941-1170.56327535832.401-107238.707-1065.4833837535832.401-107238.707-1065.48338475651.597-127247.086-926.805446380.000000000.00000000-413.08247482616.4948-41308.2474-413.08247439535824.428-50509.5943-1134.58226535832.401-107238.707-1134.582264082616.4948-41308.2474-328.227949148262.084-82616.4948-328.22794941148262.084-82616.4948-1154.39289379140.664-123924.742-1154.39289420.000000000.00000000-413.08247482616.4948-4242.72625-413.0824744382616.4948-4242.72625-328.227949148262.084-8485.45250-328.22794944148262.084-8485.45250-1255.32187399326.460-12728.1787-1255.32187450.000000000.000000000.000000000.000000000.000000000.00000000460.000000000.000000000.000000000.000000000.000000000.000000004782616.4948-41308.2474-370.65521182616.4948-4242.72625-370.65521148148262.084-82616.4948-741.310423148262.084-8485.45250-741.310423490.000000000.00000000-413.08247482616.4948-41308.2474-413.0824745082616.4948-41308.2474-328.227949148262.084-8485.45250-328.22794951148262.084-8485.45250-1154.39289379140.664-123924.742-1154.3928952606437.013-82891.3941-2576.85177510922.975-1383198.46-2576.8517753606437.013-82891.3941-841.837026464801.52789540.6644-841.837026540.000000000.00000000-695.822795417493.67782652.9209-695.82279513'