简支钢梁验算
（钢结构设计规范GB50017?2003）（建筑抗震设计规范GB50011?2001）
一、钢梁尺寸
弹性模量
a处截面b1:=450
tw1:=16
tf1:=24
h1:=1550
h01:=h1?2?tf1
4
3
2015-12-9
E:=206?10
N /mm2
fv:=170N /mm2
fce:=400
N /mm2
3
Q345钢fy:=345f:=295N /mm2
h01=1.502×10
A1:=b1?h1?(b1?tw1)?h01I1:=112???b1?h1?(b1?tw1)?h0133?A1=4.563×10mm2mm4
?I1=1.709×10
10
c处左截面b2:=450
tw2:=16
tf2:=24
h2:=1730
h02:=h2?2?tf2
4
h02=1.682×10
3
A2:=b2?h2?(b2?tw2)?h02I2:=112???b2?h2?(b2?tw2)?h0233?A2=4.851×10mm2mm4
?I2=2.206×10
10
c处右截面b3:=500
tw3:=18
tf3:=30
h3:=1730
h03:=h3?2?tf3
4
h03=1.67×10
3
A3:=b3?h3?(b3?tw3)?h03I3:=112???b3?h3?(b3?tw3)?h0333?A3=6.006×10mm2mm4
?I3=2.866×10
10
f处截面b4:=500
tw4:=18
tf4:=30
h4:=2000
h04:=h4?2?tf4
4
h04=1.94×10
3
A4:=b4?h4?(b4?tw4)?h04I4:=112???b4?h4?(b4?tw4)?h0433?A4=6.492×10mm2mm4
?I4=4.006×10
10
二、受力计算 荷载标准值
恒
qD0:=4.9?9.5?3twb:=12
tfb:=12
hb:=420
qD0=139.65hb0:=hb?2?tfb
3
KNhb0=396
次梁bb:=200
Ab:=bb?hb?(bb?twb)?hb0Ab=9.552×10mm2
9~1
2015-12-9
钢梁自重qD1:=(A4?3+Ab?9.5)?10
活
荷载设计值
qL0:=1.6?9.5?3
?6
?78.5qD1=22.412qL0=45.6P1=258.314P2=263.472P0=263.472
KNKNKNKNKNKN
P1:=1.2?(qD0+qD1)+1.4?qL0P2:=1.35?(qD0+qD1)+1.4?0.7?qL0P0:=max(P1,P2)
取
P:=270
三、端部支承加劲肋尺寸选择 1加劲肋尺寸选择外伸宽度h0430+40=104.667≤bs:=130厚度bs15=8.667≤ts:=162.加劲肋验算端部支承加劲肋采用钢板成对布置于腹板两侧。每侧宽取bs
(与中间肋一样),下端支承处刨平后与下翼顶紧。1）稳定性验算
支座反力
R:=P?102235fy3R=1.35×10
3
KN
tw00:=15?tw1?tw00=198.078取tw0:=20047
mmmm2mm4
9~2
截面面积惯性矩
A0:=(2?tw0)?tw1+2?bs?tsIy0:=ts?(2?bs+tw1)12+2?tw0?tw1123A0=1.056×10Iy0=2.817×10
2015-12-9回转半径长细比iy0:=λy0:=Iy0A0h01iy0iy0=51.648λy0=29.081mmGB50017?2003第132页注1公式截面类别b类α1:=0.65α2:=0.965α3:=0.300λn:=φ:=λy0π?fyE2λn=0.379ifλn≤0.2151?α1?λn12?λn2?2???α2+α3?λn+λn?()(α2+α3?λn+λn)22??4?λn?ifλn>0.2152?稳定系数
R?103φ=0.917
N /mm2 φ?A0=139.4192）端面承压计算 承压面积 R?10Ace3Ace:=2?(bs?20)?ts mm2 =383.5233）支承加劲肋与腹板焊缝相接角焊缝强度ffw:=160hf0=2.075tmax=16 N /mm2mmmm 焊缝高度 hf0:=(R?103)4?0.7?(h01?2?20?10)?ffwtmax:=max(tw1,ts)>1.5?tmax=6hf=8 取 hf:=8mmmmmm (满足构造要求) 加劲肋与腹板焊缝相接焊缝高度四、验算整体稳定 钢梁受压翼缘上密铺deck板,并有牢固相接,能阻止梁受压翼缘的侧向位移.,故可不计算整体稳定性五、验算局部稳定 1验算翼缘局部稳定性抗震第9.2.12条 (b4?tw4)2?tf4(b3?tw3)2?tf3(b2?tw2)2?tf2(b1?tw1)2?tf1=8.033=8.033=9.042=9.042<<<<11?11?11?11?235fy235fy235fy235fy=9.079=9.079=9.079=9.079跨中截面翼缘外伸肢翼缘外伸肢翼缘外伸肢端部截面翼缘外伸肢2加劲肋设计校核170?80?235fy=66.026 mm 9~3 235fy235fy=140.305受压翼缘扭转受约束=123.799受压翼缘扭转无约束按构造要求设横向加劲肋,间距在次梁处设横向加劲肋,间距 3验算腹板局部稳定性1）支座区格ab段 2015-12-9 剪力Vab:=1215KN Mb:=3645弯矩Ma:=0σab:=Mab?10I1Vab?1036平均弯矩Mab:=Ma+Mb2Mab=1.822×103KN?m?h012σab=80.069N/mm2τab:=h01?tw1τab=50.558λb1:=N/mm2h01tw1?177?fy235λb1=0.643因双轴对称截面梁的受压翼缘扭转受到约束σcrab:=fifλb1≤0.85?1?0.75?(λb1?0.85)????fif0.85<λb1≤1.251.1?ah01fλb1=1.997h0141?tw1?4+5.34???h0141?tw1?5.34+4???τcrab:=fvifλs1≤0.8?fy235ifah01≤12ifλb1>1.25σcrab=295N/mm2λs1:=??a?h01?2h01?2?fy235ifah01λs1=1.102>1??a?τcrab=139.754N/mm2?1?0.59?(λs1?0.8)????fvif0.8<λs1≤1.21.1?fvλs122ifλs1>1.2σcab:=0集中力均为次梁传来,且次梁处设加劲肋。?σab?+?τab?+(0)2=0.205?????σcrab??τcrab?2）中间II区格bc段 2≤1.0满足要求KN2Mbc=5.063×103剪力Vbc:=945 Mc:=6480平均弯矩Mbc:=弯矩Mb:=3645σbc:=Mbc?10I2Vbc?1036Mb+McKN?m?h022σbc=192.98N/mm2τbc:=h02?tw2τbc=35.114λb2:=N/mm2h02tw2?177?fy235λb2=0.72因双轴对称截面梁的受压翼缘扭转受到约束σcrbc:=fifλb2≤0.85?1?0.75?(λb2?0.85)????fif0.85<λb2≤1.251.1?ah02fλb2=1.7842ifλb2>1.25σcrbc=295N/mm29~4 2015-12-9λs2:=h0241?tw2?4+5.34???h02h02?41?tw2?5.34+4?????a?2??a??fy235ifah02>1λs2=1.21h02?2?fy235ifah02≤1τcrbc:=fvifλs2≤0.8?1?0.59?(λs2?0.8)????fvif0.8<λs2≤1.21.1?fvλs222τcrbc=127.826N/mm2ifλs2>1.2σcbc:=0集中力均为次梁传来,且次梁处设加劲肋。?σbc?+?τbc?+(0)2=0.503?????σcrbc??τcrbc?3）中间III区格cd段2≤1.0满足要求剪力Vcd:=675KNMd:=8505平均弯矩Mcd:=Mc+Md2Mcd=7.492×103弯矩Mc:=6480σcd:=Mcd?10I3Vcd?1036KN?m?h032σcd=218.265N/mm2τcd:=h03?tw3τcd=22.455λb3:=N/mm2h03tw3?177?fy235λb3=0.635因双轴对称截面梁的受压翼缘扭转受到约束σcrcd:=fifλb3≤0.85?1?0.75?(λb3?0.85)????fif0.85<λb3≤1.251.1?ah03fλb3=1.796h03h03?41?tw3?4+5.34?????a?h0341?tw3?5.34+4???τcrcd:=fvifλs3≤0.822ifλb3>1.25σcrcd=295N/mm2λs3:=?fy235ifah03≤1??a?τcrcd=143.029 N/mm2 h03?2?fy235ifah03λs3=1.069 >1?1?0.59?(λs3?0.8)????fvif0.8<λs3≤1.21.1?fvλs322ifλs3>1.2σccd:=0 集中力均为次梁传来,且次梁处设加劲肋。?σcd?+?τcd?+(0)2=0.572?????σcrcd??τcrcd?4）中间IV区格de段 2≤1.0满足要求 剪力Vde:=405KN 9~5
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