牛腿、节点刚接柱脚计算(带公式程序)
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一、计算资料(灰色为修改内容)牛腿尺寸(单位:mm)上翼缘宽bf1300上翼缘厚t110腹板宽ts8下翼缘宽bf2200下翼缘厚t210腹板高度hw180荷载竖向压力设计值F=80kN柱边与竖向压力距离e=0.5m 材料钢材为Q235-B焊条为E43焊接形式手工焊焊缝质量三级角焊缝焊角尺寸hf(mm)=10牛腿翼缘和柱的连接采用对接焊缝(坡口焊)连接,腹板和柱的连接采用角焊缝连接。
二、牛腿强度的计算作用于牛腿根部的弯炬M和剪力VM=F*e=40.00kN.mV=80kN钢牛腿设计的净截面积An An=bf1*t1+bf2*t2+ts*hw=6440mm2上翼缘板中心至截面形心轴处的距离y y=(ts*hw*0.5*(hw+t1)+bf2*tf2*(hw+0.5*tf1))/An=78.70mm 形心轴以上面积对形心轴的面积矩SS=(y-0.5*t1)*ts*0.5*(y-0.5*t1)+t1*bf1*y=257811.1531mm3净截面的惯性矩In腹板中心距与y的距离a=(0.5*hw+0 .5*t1-y)In=t1*bf1*y*y+t2*bf2*y*y+ts*hw*hw*hw/12+ts*hw*a*a=35235826.1mm4净截面的上、下抵抗矩Wn1、Wn2Wn1=In/(y+0.5*t1)=420999.48mm3Wn2=In/(hw+t1+0.5*t2-y)=302962mm3边的正应力σσ=M/ Wn2=132.03N/mm2<215 N/mm2,满足要求截面形心轴处的剪应力ττ=VS/(Itw)=73.17N/mm2<215 N/mm2,满足要求截面腹板下端抵抗矩W’n2W’n2=In/(hw+0.5*t1-y)=331461.76mm3下翼缘对形心轴的面积矩S1S1=t2*bf2*(hw+0.5*t1+0.5*t2-y)=222608.7mm3腹板下端的正应力σ1σ1= M/W’n2=120.68 N/mm2腹板下端的剪应力τ1τ=VS1/(It w)=63.18 N/mm2腹板下端的折算应力√(σ12+3τ12)=162.90N/mm2<1.1*215N/mm2,满足要求三、 牛腿与柱的连接焊缝计算:于牛腿翼缘竖向刚度较差,一般不考虑承担剪力。
柱脚计算一、GZ1柱脚计算(5-17轴):查得节点处的最不利内力组为:M=227.51KN ·MN=381.1KN柱底最大剪力为:V=64.34KN ,所对应的轴力为:N=175.6KN,则,柱底板与混凝土柱之间产生的磨擦力为F=0.4N=70.24KN>V=64.34KN,柱底抗剪满足!柱脚计算简图如附图二所示假定砼柱的强度等级为C20,则 fc=10N/mm 2按构造要求,底板尺寸取为:B ×L=310x900则底板所受的最反力为:2291.765.62632max min/10/28.763.09003101048.3046900310106.1756mm N f mm N BL M BL N c =<=±=⨯⨯⨯±⨯⨯=+=-σ经计算,砼柱抗压强度满足!如图所示,经计算,底板各区格所受的反力为:2221/67.4,/29.6mm N mm N ==σσ底板所受的最大弯矩为:1.对三边简支板:b 1=100,a 1=250b 1/a 1=0.40查得β2=0.04392221max 23/2170325091.70439.0mm N a M =⨯⨯==σβ2.对四边支承板b 1=250,a 1=100b 1/a 1=2.5查得α=0.1103222114/693810029.61103.0mm N a M =⨯⨯==ασ3.对四边支承板b 1=500,a 1=125b 1/a 1=4查得β2=0.12502221223/912112567.41250.0mm N a M =⨯⨯==σβ则:mm t mm f M t 25,213002170366max min ==⨯==取 靴梁计算:靴梁所承担的均布线荷载为:q=155×7.91=1226N/mm 2,则:Nql V mm N ql M 2452002001226/1052.24200122621212622=⨯==⨯=⨯⨯== 取-500x12x900,则:2222262/175/3.61500122452005.15.1/300/41500121052.2455mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 靴梁与柱底板采用双面角焊缝:mmh mm t h mmt h f f f 125.7255.15.14.14122.12.1max min min max ===≥=⨯=≤取施焊时不采用引弧板,则焊缝计算长度为:l W =200-10=190mm22/200/8.761902127.02452007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 靴梁与柱翼缘板采用h f =12mm 的单面角焊缝,其焊缝计算长度为:l W =500-10=490mm22/200/60490127.02452007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 柱底板加劲肋计算:柱底板加劲肋所承担的均布线荷载为:q=6.29x100=629N/mm 2则:N ql V mm N ql M 786252506292121/1091.425062981812622=⨯⨯==⨯=⨯⨯== 取-250x10x500则:2222262/175/6.2350010786255.15.1/300/82.9500101091.455mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 底板加劲肋与底板连接时采用h f =8mm 的单面角焊缝,其计算长度为: l W =250-10=240mm22/200/5.5824087.0786257.0mm N f mm N l h V w f w f =<=⨯⨯==τ 底板加劲肋与靴梁连接时采用h f =6mm 的单面角焊缝,其计算长度为: l W =500-10=490mm22/200/2.3849067.0786257.0mm N f mm N l h V w f w f =<=⨯⨯==τ 锚栓计算:受压区计算长度:mm x 48965.691.791.7900=+⨯=底板形心到受压区合力线的距离为:mm a 28734892900=-= 锚栓轴线到受压区合力线的距离为:mm y 6373489100900=--= 则锚栓所受的最大拉力为: KN y Na M N t 399637287106.175105.30436=⨯⨯-⨯=-= 采用2M48-Q235钢锚栓,查得其单个锚栓所能承担的最大拉力为:[N t ]=206.2KN>N t =399/2=200KN锚栓支承加劲肋计算:每个锚栓支承加劲肋所承受的剪力为:V=400/4=100KN取-195x10x400 则:22/175/5.37400101000005.15.1mm N f mm N th V V =<=⨯⨯==τ 锚栓支承加劲肋与靴梁采用h f =6mm 的双面角焊缝连接,其计算长度为: l W =400-10=390mm 则:22222223222/200/4.486.30)22.18.45(/6.30239067.0101007.0/8.45239067.05.971000067.06mm N f mm N mm N l h V mm N l h Ve w f f f f w f f w f f =<=+=+⎪⎪⎭⎫ ⎝⎛=⨯⨯⨯⨯===⨯⨯⨯⨯⨯==τβστσ 锚栓支承加劲肋与顶板的连接采用h f =6mm 双面角焊缝,其计算长度为: l W =195-10=185mm 则:22/200/4.64218567.01000007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 锚栓支承垫板的计算:mm N Qa M ∙⨯=+⨯⨯==4105.152)556(22004141 采用-100x25x160则:22432/300/24452082.1105.152;520825)50100(61mm N f mm N W M mm W n n =<==⨯⨯===⨯-⨯=γσ经计算,柱脚安全二、GZ1柱脚计算(4轴):查得节点处的最不利内力组为:M=376.32KN ·MN=109.53KN柱底最大剪力为:V=64.34KN ,所对应的轴力为:N=175.6KN,则,柱底板与混凝土柱之间产生的磨擦力为F=0.4N=70.24KN>V=64.34KN,柱底抗剪满足!柱脚计算简图如附图三所示假定砼柱的强度等级为C20,则 fc=10N/mm 2 按构造要求,底板尺寸取为:B ×L=310x900则底板所受的最反力为:2238.960.82632max min/10/99.839.09003101032.37669003101053.1096mm N f mm N BL M BL N c =<=±=⨯⨯⨯±⨯⨯=+=-σ经计算,砼柱抗压强度满足!如图所示,经计算,底板各区格所受的反力为:2221/38.5,/38.7mm N mm N ==σσ底板所受的最大弯矩为:1.对三边简支板:b 1=100,a 1=250b 1/a 1=0.40查得β2=0.04392221max 23/2573625038.90439.0mm N a M =⨯⨯==σβ2.对四边支承板b 1=250,a 1=100b 1/a 1=2.5查得α=0.1103222114/814010038.71103.0mm N a M =⨯⨯==ασ3.对四边支承板b 1=500,a 1=125b 1/a 1=4查得β2=0.12502221223/1050812538.51250.0mm N a M =⨯⨯==σβ则:mm t mm f M t 25,233002573666max min ==⨯==取 靴梁计算:靴梁所承担的均布线荷载为:q=155×9.38=1454N/mm 2,则:Nql V mm N ql M 2908002001454/101.29200145421212622=⨯==⨯=⨯⨯== 取-500x12x900,则:2222262/175/7.72500122908005.15.1/300/4950012101.2955mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 靴梁与柱底板采用双面角焊缝:mmh mm t h mmt h f f f 125.7255.15.14.14122.12.1max min min max ===≥=⨯=≤取施焊时不采用引弧板,则焊缝计算长度为:l W =200-10=190mm22/200/1.911902127.02908007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 靴梁与柱翼缘板采用h f =12mm 的单面角焊缝,其焊缝计算长度为:l W =500-10=490mm22/200/71490127.02908007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 柱底板加劲肋计算:柱底板加劲肋所承担的均布线荷载为:q=7.38x100=738N/mm 2 则:N ql V mm N ql M 922502507382121/1077.525073881812622=⨯⨯==⨯=⨯⨯== 取-250x10x500则:2222262/175/2850010922505.15.1/300/54.11500101077.555mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 底板加劲肋与底板连接时采用h f =8mm 的单面角焊缝,其计算长度为: l W =250-10=240mm22/200/6924087.0922507.0mm N f mm N l h V w f w f =<=⨯⨯==τ 底板加劲肋与靴梁连接时采用h f =6mm 的单面角焊缝,其计算长度为: l W =500-10=490mm22/200/4549067.0922507.0mm N f mm N l h V w f w f =<=⨯⨯==τ 锚栓计算:受压区计算长度:mm x 4706.838.938.9900=+⨯=底板形心到受压区合力线的距离为:mm a 29334702900=-= 锚栓轴线到受压区合力线的距离为:mm y 6433470100900=--= 则锚栓所受的最大拉力为: KN y Na M N t 5356432931053.1091032.37636=⨯⨯-⨯=-= 采用2M56-Q235钢锚栓,查得其单个锚栓所能承担的最大拉力为:[N t ]=284.2KN>N t =535/2=267.5KN锚栓支承加劲肋计算:每个锚栓支承加劲肋所承受的剪力为:V=535/4=134KN取-195x10x400 则:22/175/3.50400101340005.15.1mm N f mm N th V V =<=⨯⨯==τ 锚栓支承加劲肋与靴梁采用h f =6mm 的双面角焊缝连接,其计算长度为: l W =400-10=390mm 则:22222223222/200/6541)22.161(/41239067.0101347.0/61239067.05.9713400067.06mm N f mm N mm N l h V mm N l h Ve w f f f f w f f w f f =<=+=+⎪⎪⎭⎫ ⎝⎛=⨯⨯⨯⨯===⨯⨯⨯⨯⨯==τβστσ 锚栓支承加劲肋与顶板的连接采用h f =8mm 双面角焊缝,其计算长度为: l W =195-10=185mm 则:22/200/22.86218587.01340007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 锚栓支承垫板的计算:mm N Qa M ∙⨯=+⨯⨯==4105.224)562(22684141 采用-160x25x160则:22432/300/176106252.1105.224;1062525)58160(61mm N f mm N W M mm W n n =<==⨯⨯===⨯-⨯=γσ经计算,柱脚安全三、GZ2柱脚计算:查得节点处的最不利内力组为:M=340.63KN ·MN=594.54KN柱脚计算简图如附图四所示假定砼柱的强度等级为C20,则 fc=10N/mm 2按构造要求,底板尺寸取为:B ×L=360x1050则底板所受的最反力为:2272.658.32632max min/10/15.557.110503601063.34061050360105.5946mm N f mm N BL M BL N c =<=±=⨯⨯⨯±⨯⨯=+=-σ经计算,砼柱抗压强度满足!如图所示,经计算,底板各区格所受的反力为:2221/76.4,/74.5mm N mm N ==σσ底板所受的最大弯矩为:1.对三边简支板:b 1=100,a 1=300b 1/a 1=0.330查得β2=0.03552221max 23/4.2147030072.60355.0mm N a M =⨯⨯==σβ2.对四边支承板b 1=300,a 1=100b 1/a 1=3.0查得α=0.1189222114/682510074.51189.0mm N a M =⨯⨯==ασ3.对四边支承板b 1=650,a 1=150b 1/a 1=4.3查得β2=0.12502221223/1338815076.41250.0mm N a M =⨯⨯==σβ则:mm t mm f M t 25,213004.2147066max min ==⨯==取 靴梁计算:靴梁所承担的均布线荷载为:q=180×6.72=1210N/mm 2,则:Nql V mm N ql M 2420002001210/102.24200121021212622=⨯==⨯=⨯⨯== 取-500x12x1050,则:2222262/175/61500122420005.15.1/300/4050012102.2455mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 靴梁与柱底板采用双面角焊缝:mmh mm t h mmt h f f f 125.7255.15.14.14122.12.1max min min max ===≥=⨯=≤取施焊时不采用引弧板,则焊缝计算长度为:l W =200-10=190mm22/200/761902127.02420007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 靴梁与柱翼缘板采用h f =12mm 的单面角焊缝,其焊缝计算长度为:l W =500-10=490mm22/200/59490127.02420007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 柱底板加劲肋计算:柱底板加劲肋所承担的均布线荷载为:q=5.74x100=574N/mm 2 则:N ql V mm N ql M 861003005742121/1046.630057481812622=⨯⨯==⨯=⨯⨯== 取-300x10x500则:2222262/175/83.2550010861005.15.1/300/92.12500101046.655mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 底板加劲肋与底板连接时采用h f =8mm 的单面角焊缝,其计算长度为: l W =300-10=290mm22/200/5329087.0861007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 底板加劲肋与靴梁连接时采用h f =6mm 的单面角焊缝,其计算长度为: l W =500-10=490mm22/200/4249067.0861007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 锚栓计算:受压区计算长度:mm x 68558.372.672.61050=+⨯=底板形心到受压区合力线的距离为:mm a 297368521050=-= 锚栓轴线到受压区合力线的距离为:mm y 72236851001050=--= 则锚栓所受的最大拉力为: KN y Na M N t 2277222971054.5941063.34036=⨯⨯-⨯=-= 采用2M42-Q235钢锚栓,查得其单个锚栓所能承担的最大拉力为:[N t ]=156.9KN>N t =227/2=114KN锚栓支承加劲肋计算:每个锚栓支承加劲肋所承受的剪力为:V=227/4=57KN取-190x10x400 则:22/175/2140010570005.15.1mm N f mm N th V V =<=⨯⨯==τ 锚栓支承加劲肋与靴梁采用h f =6mm 的双面角焊缝连接,其计算长度为: l W =400-10=390mm 则:22222223222/200/2717)22.125(/17239067.010577.0/25239067.0955700067.06mm N f mm N mm N l h V mm N l h Ve w f f f f w f f w f f =<=+=+⎪⎪⎭⎫ ⎝⎛=⨯⨯⨯⨯===⨯⨯⨯⨯⨯==τβστσ 锚栓支承加劲肋与顶板的连接采用h f =6mm 双面角焊缝,其计算长度为: l W =190-10=180mm 则:22/200/38218067.0570007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 锚栓支承垫板的计算:mm N Qa M ∙⨯=+⨯⨯==41023.81)552(21144141 采用-100x25x160则:22432/300/11658332.11023.81;583325)44100(61mm N f mm N W M mm W n n =<==⨯⨯===⨯-⨯=γσ经计算,柱脚安全三、GZ3,3a,4,4a 柱脚计算:查得节点处的最不利内力组为:M=539.34KN ·MN=800.2KN柱脚计算简图如附图五所示假定砼柱的强度等级为C20,则 fc=10N/mm 2 按构造要求,底板尺寸取为:B ×L=380x1050则底板所受的最反力为:2273.971.52632max min/10/72.701.210503801034.53961050380102.8006mm N f mm N BL M BL N c =<=±=⨯⨯⨯±⨯⨯=+=-σ经计算,砼柱抗压强度满足!如图所示,经计算,底板各区格所受的反力为: 2221/79.6,/26.8mm N mm N ==σσ底板所受的最大弯矩为:1.对三边简支板:b 1=100,a 1=320b 1/a 1=0.32查得β2=0.03062221max 23/3048832073.90306.0mm N a M =⨯⨯==σβ2.对四边支承板b 1=320,a 1=100b 1/a 1=3.2查得α=0.1201222114/992010026.81201.0mm N a M =⨯⨯==ασ3.对四边支承板b 1=650,a 1=160b 1/a 1=4.1查得β2=0.12502221223/2172816079.61250.0mm N a M =⨯⨯==σβ 则:mm t mm f M t 32,1.252903048866max min ==⨯==取 靴梁计算:靴梁所承担的均布线荷载为:q=190×9.73=1849N/mm 2,则:Nql V mm N ql M 3698002001849/1037200184921212622=⨯==⨯=⨯⨯== 取-500x12x1050,则:2222262/175/5.92500123698005.15.1/300/6250012103755mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 靴梁与柱底板采用双面角焊缝:mmh mm t h mmt h f f f 125.7255.15.14.14122.12.1max min min max ===≥=⨯=≤取施焊时不采用引弧板,则焊缝计算长度为:l W =200-10=190mm22/200/1161902127.03698007.0mm N f mm N l h V w f w f =<=⨯⨯⨯==τ 靴梁与柱翼缘板采用h f =12mm 的单面角焊缝,其焊缝计算长度为:l W =500-10=490mm22/200/90490127.03698007.0mm N f mm N l h V w f w f =<=⨯⨯==τ 柱底板加劲肋计算:柱底板加劲肋所承担的均布线荷载为:q=8.26x100=826N/mm 2 则:N ql V mm N ql M 1321603208262121/106.1032082681812622=⨯⨯==⨯=⨯⨯== 取-320x10x500则:2222262/175/40500101321605.15.1/300/2.2150010106.1055mm N f mm N th V mm N f mm N th M V =<=⨯⨯===<=⨯⨯⨯==τσ 底板加劲肋与底板连接时采用h f =8mm 的单面角焊缝,其计算长度为:l W =320-10=310mm22/200/7631087.01321607.0mm N f mm N l h V w f w f =<=⨯⨯==τ底板加劲肋与靴梁连接时采用h f =6mm 的单面角焊缝,其计算长度为: l W =500-10=490mm22/200/2.6449067.07.0mm N f mm N l h w f w f =<=⨯⨯==τ锚栓计算: 受压区计算长度:mm x 66271.573.973.91050=+⨯=底板形心到受压区合力线的距离为:mm a 304366221050=-= 锚栓轴线到受压区合力线的距离为:mm y 72936621001050=--= 则锚栓所受的最大拉力为:KN y Na M N t 406729304102.8001034.53936=⨯⨯-⨯=-= 采用2M52-Q235钢锚栓,查得其单个锚栓所能承担的最大拉力为:[N t ]=246.1KN>N t =406/2=203KN锚栓支承加劲肋计算:每个锚栓支承加劲肋所承受的剪力为:V=406/4=102KN取-188x10x400 则:22/175/38400101020005.15.1mm N f mm N th V V =<=⨯⨯==τ 锚栓支承加劲肋与靴梁采用h f =6mm 的双面角焊缝连接,其计算长度为: l W =400-10=390mm 则:22222223222/200/4831)22.145(/31239067.0101027.0/45239067.0941*******.06mm N f mm N mm N l h V mm N l h Ve w f f f f w f f w f f =<=+=+⎪⎪⎭⎫ ⎝⎛=⨯⨯⨯⨯===⨯⨯⨯⨯⨯==τβστσ锚栓支承加劲肋与顶板的连接采用h f =6mm 双面角焊缝,其计算长度为:l W =190-10=180mm 则:22/200/68217867.07.0mm N f mm N l h w f w f =<=⨯⨯⨯==τ锚栓支承垫板的计算:mm N Qa M ∙⨯=+⨯⨯==41033.157)557(22034141采用-100x32x160则:22432/295/16778512.11033.157;785132)54100(61mm N f mm N W M mm W n n =<==⨯⨯===⨯-⨯=γσ经计算,柱脚安全。
钢牛腿设计一、计算资料牛腿尺寸(单位:mm)荷载竖向压力设计值F=80kN柱边与竖向压力距离e=0.5m 材料钢材为Q345-B焊条为E50焊接形式手工焊焊缝质量三级角焊缝焊角尺寸hf(mm)=6牛腿翼缘和柱的连接采用对接焊缝(坡口焊)连接,腹板和柱的连接采用角焊缝连接。
二、牛腿强度的计算作用于牛腿根部的弯炬M和剪力VM=F*e=40.00kN.mV=F=80kN牛腿根部的净截面积AnAn=bf1*t1+bf2*t2+tw*hw=6208mm2上翼缘板中心至截面形心轴处的距离yy=(tw*hw*0.5*(hw+t1)+bf2*tf2*(hw+0.5*t1+0.5*t2))/An=143.00mm 形心轴以上面积对形心轴的面积矩SS=(y-0.5*t1)*tw*0.5*(y-0.5*t1)+t1*bf1*y=362176mm3净截面的惯性矩In腹板中心距与y的距离a=(0.5*hw+0.5*t1-y)=0mmIn=(bf1*t1^3)/12+t1*bf1*y^2+(bf2*t2^3)/12+t2*bf2*(hw+0.5*t1+0.5*t2)^2+(tw*hw^3)/12+tw*hw*a^2=95845717.33mm4净截面的上、下抵抗矩Wn1、Wn2Wn1=In/(y+0.5*t1)=647606.1982mm3Wn2=In/(hw+0.5*t1-y+t2)=647606.1982mm3上翼缘外边的正应力σσ=M/ Wn1=61.77N/mm2<310N/mm2,满足要求下翼缘外边的正应力σσ=M/ Wn2=61.77N/mm2<310N/mm2,满足要求截面形心轴处的剪应力ττ=V*S/(I*tw)=37.79N/mm2<310N/mm2,满足要求截面腹板下端抵抗矩W’n2W'n2=In/(hw+0.5*t1-y)=694534.1836mm3下翼缘对形心轴的面积矩S1S1=t2*bf2*(hw+0.5*t1+0.5*t2-y)=286000mm3腹板下端的正应力σ1σ1= M/W'n2=57.59 N/mm2腹板下端的剪应力τ1τ=V*S1/(I*t w)=29.84 N/mm2腹板下端的折算应力√(σ12+3τ12)=77.38N/mm2<1.1*310 N/mm2,满足要求腿与柱的连接焊缝计算:由于牛腿翼缘竖向刚度较差,一般不考虑承担剪力。