1.计ç®è·è½½ï¼æè·è½½ï¼æ´»è·è½½ï¼ 2.åææ¿çç±»åï¼ååæ¿è¿æ¯ååæ¿ï¼ 3.éæ©æ¿å 4.导ç®è·è½½è®¡ç®åºå¼¯ç© 5.æ ¹æ®å¼¯ç©è®¡ç®é
ç 6.éªç®è£ç¼ãæ 度åæå°é
çç 7.è°æ´é¢çåæ¿å满足è¦æ±ã å
·ä½æä¹è®¡ç® æç»ä½ 个计ç®è¿ç¨ ä¸è¿å»ºè®®ä½ çæç§ä¹¦ã
ä¸ãæ件ç¼å·: LB-1
äºãä¾æ®è§è
ã建çç»æè·è½½è§èã GB50009-2001
ãæ··ååç»æ设计è§èã GB50010-2002
ä¸ã计ç®ä¿¡æ¯
1.å ä½åæ°
计ç®è·¨åº¦: Lx = 4000 mm; Ly = 3000 mm
æ¿å: h = 100 mm
2.ææä¿¡æ¯
æ··ååç级: C25 fc=11.9N/mm2 ft=1.27N/mm2 ftk=1.78N/mm2 Ec=2.80Ã104N/mm2
é¢çç§ç±»: HRB335 fy = 300 N/mm2 Es = 2.0Ã105 N/mm2
æå°é
çç: Ï= 0.200%
纵ååæé¢çååç¹è³è¿è¾¹è·ç¦»: as = 20mm
ä¿æ¤å±å度: c = 10mm
3.è·è½½ä¿¡æ¯(åå¸è·è½½)
æ°¸ä¹
è·è½½å项系æ°: γG = 1.200
å¯åè·è½½å项系æ°: γQ = 1.400
åæ°¸ä¹
å¼ç³»æ°: Ïq = 1.000
æ°¸ä¹
è·è½½æ åå¼: qgk = 5.000kN/m2
å¯åè·è½½æ åå¼: qqk = 3.000kN/m2
4.计ç®æ¹æ³:å¼¹æ§æ¿
5.è¾¹çæ¡ä»¶(ä¸ç«¯/ä¸ç«¯/左端/å³ç«¯):ç®æ¯/ç®æ¯/ç®æ¯/ç®æ¯
6.设计åæ°
ç»æéè¦æ§ç³»æ°: γo = 1.00
æ³æ¾æ¯:μ = 0.200
äºã计ç®åæ°:
1.计ç®æ¿ç跨度: Lo = 3000 mm
2.计ç®æ¿çææé«åº¦: ho = h-as=100-20=80 mm
å
ãé
ç计ç®(lx/ly=4000/3000=1.333<2.000 æ以æååæ¿è®¡ç®):
1.Xååºæ¿é¢ç
1) ç¡®å®Xåæ¿åºå¼¯ç©
Mx = 表ä¸ç³»æ°(γG*qgk+γQ*qqk)*Lo2
= (0.0317+0.0620*0.200)*(1.200*5.000+1.400*3.000)*32
= 4.048 kN*m
2) ç¡®å®è®¡ç®ç³»æ°
αs = γo*Mx/(α1*fc*b*ho*ho)
= 1.00*4.048Ã106/(1.00*11.9*1000*80*80)
= 0.053
3) 计ç®ç¸å¯¹åååºé«åº¦
ξ = 1-sqrt(1-2*αs) = 1-sqrt(1-2*0.053) = 0.055
4) 计ç®åæé¢çé¢ç§¯
As = α1*fc*b*ho*ξ/fy = 1.000*11.9*1000*80*0.055/300
= 173mm2
5) éªç®æå°é
çç
Ï = As/(b*h) = 173/(1000*100) = 0.173%
Ï<Ïmin = 0.200% ä¸æ»¡è¶³æå°é
çè¦æ±
æ以åé¢ç§¯ä¸ºAs = Ïmin*b*h = 0.200%*1000*100 = 200 mm2
éåæ¹æ¡d8@200, å®é
é¢ç§¯251 mm2
2.Yååºæ¿é¢ç
1) ç¡®å®Yåæ¿åºå¼¯ç©
My = 表ä¸ç³»æ°(γG*qgk+γQ*qqk)*Lo2
= (0.0620+0.0317*0.200)*(1.200*5.000+1.400*3.000)*32
= 6.274 kN*m
2) ç¡®å®è®¡ç®ç³»æ°
αs = γo*Mx/(α1*fc*b*ho*ho)
= 1.00*6.274Ã106/(1.00*11.9*1000*80*80)
= 0.082
3) 计ç®ç¸å¯¹åååºé«åº¦
ξ = 1-sqrt(1-2*αs) = 1-sqrt(1-2*0.082) = 0.086
4) 计ç®åæé¢çé¢ç§¯
As = α1*fc*b*ho*ξ/fy = 1.000*11.9*1000*80*0.086/300
= 273mm2
5) éªç®æå°é
çç
Ï = As/(b*h) = 273/(1000*100) = 0.273%
Ïâ¥Ïmin = 0.200% 满足æå°é
çè¦æ±
éåæ¹æ¡d8@180, å®é
é¢ç§¯279 mm2
ä¸ãè·¨ä¸æ 度计ç®ï¼
Mk -------- æè·è½½æåºçæ åç»å计ç®ç弯ç©å¼
Mq -------- æè·è½½æåºçåæ°¸ä¹
ç»å计ç®ç弯ç©å¼
1.计ç®è·è½½æåº
Mk = Mgk + Mqk
= (0.0620+0.0317*0.200)*(5.000+3.000)*32 = 4.920 kN*m
Mq = Mgk+Ïq*Mqk
= (0.0620+0.0317*0.200)*(5.000+1.000*3.000)*32 = 4.920 kN*m
2.计ç®å弯æ件ççæå度 Bs
1) 计ç®æè·è½½è·è½½æåºçæ åç»åä½ç¨ä¸ï¼æ件纵ååæé¢çåºå
Ïsk = Mk/(0.87*ho*As) (æ··ååè§èå¼ 8.1.3ï¼3)
= 4.920Ã106/(0.87*80*279) = 253.393 N/mm
2) 计ç®æææåææ··ååæªé¢é¢ç§¯è®¡ç®ç纵ååæé¢çé
çç
ç©å½¢æªé¢ç§¯: Ate = 0.5*b*h = 0.5*1000*100= 50000mm2
Ïte = As/Ate (æ··ååè§èå¼ 8.1.2ï¼4)
= 279/50000 = 0.558%
3) 计ç®è£ç¼é´çºµååæé¢çåºåä¸ååç³»æ°Ï
Ï = 1.1-0.65*ftk/(Ïte*Ïsk) (æ··ååè§èå¼ 8.1.2ï¼2)
= 1.1-0.65*1.78/(0.558%*253.393) = 0.282
4) 计ç®é¢çå¼¹æ§æ¨¡éä¸æ··åå模éçæ¯å¼ αE
αE = Es/Ec = 2.0Ã105/2.80Ã104 = 7.143
5) 计ç®åå翼ç¼é¢ç§¯ä¸è
¹æ¿ææé¢ç§¯çæ¯å¼ γf
ç©å½¢æªé¢ï¼Î³f=0
6) 计ç®çºµååæé¢çé
ççÏ
Ï = As/(b*ho)= 279/(1000*80) = 0.349%
7) 计ç®å弯æ件ççæå度 Bs
Bs = Es*As*ho2/[1.15Ï+0.2+6*αE*Ï/(1+ 3.5γf')](æ··ååè§èå¼8.2.3--1)
= 2.0Ã105*279*802/[1.15*0.282+0.2+6*7.143*0.349%/(1+3.5*0.0)]
= 5.303Ã102 kN*m2
3.计ç®å弯æ件çé¿æå度B
1) ç¡®å®èèè·è½½é¿ææåºç»å对æ 度影åå¢å¤§å½±åç³»æ°Î¸
å½Ï'=0æ¶ï¼Î¸=2.0 (æ··ååè§è第 8.2.5 æ¡)
2) 计ç®å弯æ件çé¿æå度 B
B = Mk/(Mq*(θ-1)+Mk)*Bs (æ··ååè§èå¼ 8.2.2)
= 4.920/(4.920*(2.0-1)+4.920)*5.303Ã102
= 2.651Ã102 kN*m2
4.计ç®å弯æ件æ 度
fmax = f*(qgk+qqk)*Lo4/B
= 0.00663*(5.000+3.000)*34/2.651Ã102
= 16.203mm
5.éªç®æ 度
æ 度éå¼fo=Lo/200=3000/200=15.000mm
fmax=16.203mm>fo=15.000mmï¼ä¸æ»¡è¶³è§èè¦æ±!
å
«ãè£ç¼å®½åº¦éªç®:
1.è·¨ä¸Xæ¹åè£ç¼
1) 计ç®è·è½½æåº
Mx = 表ä¸ç³»æ°(qgk+qqk)*Lo2
= (0.0317+0.0620*0.200)*(5.000+3.000)*32
= 3.175 kN*m
2) å
é¢é¢ç,æ以åå¼vi=0.7
3) 计ç®æè·è½½è·è½½æåºçæ åç»åä½ç¨ä¸ï¼æ件纵ååæé¢çåºå
Ïsk=Mk/(0.87*ho*As) (æ··ååè§èå¼ 8.1.3ï¼3)
=3.175Ã106/(0.87*80*251)
=181.756N/mm
4) 计ç®æææåææ··ååæªé¢é¢ç§¯è®¡ç®ç纵ååæé¢çé
çç
ç©å½¢æªé¢ç§¯ï¼Ate=0.5*b*h=0.5*1000*100=50000 mm2
Ïte=As/Ate (æ··ååè§èå¼ 8.1.2ï¼4)
=251/50000 = 0.0050
å 为Ïte=0.0050 < 0.01,æ以让Ïte=0.01
5) 计ç®è£ç¼é´çºµååæé¢çåºåä¸ååç³»æ°Ï
Ï=1.1-0.65*ftk/(Ïte*Ïsk) (æ··ååè§èå¼ 8.1.2ï¼2)
=1.1-0.65*1.780/(0.0100*181.756)
=0.463
6) 计ç®åä½é¢ç§¯é¢çæ ¹æ°n
n=1000/dist = 1000/200
=5
7) 计ç®åæåºçºµåé¢çççæç´å¾deq
deq= (âni*di2)/(âni*vi*di)
=5*8*8/(5*0.7*8)=11
8) 计ç®æ大è£ç¼å®½åº¦
Ïmax=αcr*Ï*Ïsk/Es*(1.9c+0.08*Deq/Ïte) (æ··ååè§èå¼ 8.1.2ï¼1)
=2.1*0.463*181.756/2.0Ã105*(1.9*20+0.08*11/0.0100)
=0.1145mm ⤠0.30, 满足è§èè¦æ±
2.è·¨ä¸Yæ¹åè£ç¼
1) 计ç®è·è½½æåº
My = 表ä¸ç³»æ°(qgk+qqk)*Lo2
= (0.0620+0.0317*0.200)*(5.000+3.000)*32
= 4.920 kN*m
2) å
é¢é¢ç,æ以åå¼vi=0.7
3) 计ç®æè·è½½è·è½½æåºçæ åç»åä½ç¨ä¸ï¼æ件纵ååæé¢çåºå
Ïsk=Mk/(0.87*ho*As) (æ··ååè§èå¼ 8.1.3ï¼3)
=4.920Ã106/(0.87*80*279)
=253.393N/mm
4) 计ç®æææåææ··ååæªé¢é¢ç§¯è®¡ç®ç纵ååæé¢çé
çç
ç©å½¢æªé¢ç§¯ï¼Ate=0.5*b*h=0.5*1000*100=50000 mm2
Ïte=As/Ate (æ··ååè§èå¼ 8.1.2ï¼4)
=279/50000 = 0.0056
å 为Ïte=0.0056 < 0.01,æ以让Ïte=0.01
5) 计ç®è£ç¼é´çºµååæé¢çåºåä¸ååç³»æ°Ï
Ï=1.1-0.65*ftk/(Ïte*Ïsk) (æ··ååè§èå¼ 8.1.2ï¼2)
=1.1-0.65*1.780/(0.0100*253.393)
=0.643
6) 计ç®åä½é¢ç§¯é¢çæ ¹æ°n
n=1000/dist = 1000/180
=5
7) 计ç®åæåºçºµåé¢çççæç´å¾deq
deq= (âni*di2)/(âni*vi*di)
=5*8*8/(5*0.7*8)=11
8) 计ç®æ大è£ç¼å®½åº¦
Ïmax=αcr*Ï*Ïsk/Es*(1.9c+0.08*Deq/Ïte) (æ··ååè§èå¼ 8.1.2ï¼1)
=2.1*0.643*253.393/2.0Ã105*(1.9*20+0.08*11/0.0100)
=0.2216mm ⤠0.30, 满足è§èè¦æ±
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