例题8-1
某钢筋混凝土雨篷过梁,250600b h mm mm ⨯=⨯,已知设计弯
矩M=257kN-m,设计剪力V=210kN ,设计扭矩T=20 kN-m ,混凝
土等级为30C ,纵筋采用Ⅱ级(HRB335)钢筋,箍筋采用Ⅰ级
(HPB235)钢筋,试设计此梁。
解: 已知b=250mm. 0h =565mm , c f =14.3N/2mm
t f =1.432/N mm ,yv f =210N/2mm ,y f =300N/2mm
1.
计算t W ,cor U 和cor A t W =26
b (3h-b )=731.6110mm ⨯
cor U =2(cor b +co r h )=2(200550)⨯+=1500mm cor A =co cor r b h =52200550 1.110mm ⨯=⨯
2. 验算适用条件
(1) 验算截面尺寸
3627
021******* 3.04/0.82505650.81.6110t V T N mm bh W ⨯⨯+=+=⨯⨯⨯<20.250.2514.31 3.58/f N mm c c β=⨯⨯=
截面尺寸满足要求
(2)验算构造配筋界限
3627
021******* 2.73/250565 1.6110t V T N mm bh W ⨯⨯+=+=⨯⨯20.70.7 1.43 1.00/t f N mm >=⨯=
需按承载力计算配筋
(3) 验算简化条件
V=210kN > 0.35 070.7t f bh kN =
200.175 4.03t t T kN f W kN m =>=⋅
不能简化计算,需按钢筋混凝土弯,剪,扭构件进行计算
3. 确定箍筋用量(按剪扭构件考虑)
按剪扭构件进行计算
(1)设ζ=1.2
(2) 计算t β 33601.5 1.5210101.161010.510.5250565
2010t t W V T bh β==⨯⨯++⨯⨯⨯ 0.938=
0.5<t β=0.938<1
(3) 计算抗扭所需箍筋
10.35st t t t yv cor
A T f W S f A β-=
67520100.350.9381.431.61101.22101.110
⨯-⨯⨯⨯⨯=⨯⨯ 20.398/mm mm =
(4)计算抗剪所需箍筋
100
0.7(1.5)1.25sv t t yv nA V f bh S f h β--=
3210100.7(1.50.938)1.432505651.25210565
⨯-⨯-⨯⨯⨯=⨯⨯20.712/mm mm =
n=2 ∴120.356/sv A mm mm S
= 总用量1120.754/sv sv st A A A mm mm S S S
=+= 配置10@100∅ (*
0.7850.754A sv S
=>) (5)验算最小配箍率
.min 0.28t sv yv
f f ρ= =0.19 % *20.785250
nA sv bs ⨯==0.63%> .min sv ρ 4. 确定纵筋用量(按弯扭构件考虑)
(1)
计算抗扭纵筋 21485f A yv st A U mm cor stl f S
y ζ== (2)
计算抗弯纵筋
0(1x h =
=126mm< 0b h ξ=307mm
121674c SM y
f bx A mm f α== (2) 验算最小纵筋配筋率
受弯 .min 0.2%s y
f f ρ=t 或45 受扭
.min tl y
f f ρ=t
1.430.6300
=
0.18%= (2T Vb
≤) 实际纵筋配筋率
04851674250600250565
stl SM A A bh bh +=+⨯⨯ 1.51%=
> .min .min s tl ρρ+ 选配纵筋
受拉区: 218363
A stl A mm SM += 选配
4Φ25 (
2219641836S A mm mm =>)。