幕墻立柱橫梁強度計算

幕墻立柱計算:(主立柱),

幕墻立柱按簡支梁力學模型進行設計計算：,

1.選料:,

(1)風荷載線分布最大荷載集度設計值(矩形分布),

qw:風荷載線分布最大荷載集度設計值(kN/m),

rw:風荷載作用效應的分項系數(shù)：1.4,1.4

Wk:風荷載標準值:0.548kN/㎡,0.548

B:幕墻分格寬:1.2m,1.2

qw=1.4×Wk×B,

=1.4×0.548×1.2,

=0.92064kN/m,0.92064

(2)立柱彎矩:,

Mw:風荷載作用下立柱彎矩(kN.m),

qw:風荷載線分布最大荷載集度設計值:0.921(kN/m),0.921

Hsjcg:立柱計算跨度:4.5m,4.5

Mw=qw×Hsjcg2/8,

=0.921×4.5×4.5/8,

=2.33kN·m,2.33

qEA:地震作用設計值(KN/M2):,

GAk:玻璃幕墻構(gòu)件(包括玻璃和框)的平均自重:135N/㎡,135

垂直于玻璃幕墻平面的分布水平地震作用:,

qEAk:垂直于玻璃幕墻平面的分布水平地震作用(kN/m2),

qEAk=5×αmax×GAk,

=5×0.160×135/1000,

=0.108kN/㎡,0.108

γE:幕墻地震作用分項系數(shù):1.3,

qEA=1.3×qEAk,

=1.3×0.108,

=0.14kN/㎡,0.14

qE：水平地震作用線分布最大荷載集度設計值(矩形分布),

qE=qEA×B,

=0.14×1.2,

=0.168kN/m,0.168

ME:地震作用下立柱彎矩(kN·m):,

ME=qE×Hsjcg2/8,

=0.168×4.5×4.5/8,

=0.425kN·m,0.425

M:幕墻立柱在風荷載和地震作用下產(chǎn)生彎矩(kN·m),

采用SW+0.5SE組合,

M=Mw+0.5×ME,

=2.33+0.5×0.425,

=2.543kN·m,2.543

(3)W:立柱抗彎矩預選值(cm3),

W=M×103/1.05/84.2,

=2.543×103/1.05/84.2,

=28.764cm3,28.764

"(4)I1,I2:立柱慣性矩預選值(cm4)",

qWk:風荷載線分布最大荷載集度標準值(kN/m),

qWk=Wk×B,

=0.548×1.2,

=0.658kN/m,0.658

qEk:水平地震作用線分布最大荷載集度標準值(kN/m),

qEk=qEAk×B,

=0.108×1.2,

=0.13kN/m,0.13

I1=900×(qWk+0.5×qEk)×Hsjcg3/384/0.7,

=900×(0.658+0.5×0.13)×4.5^3/384/0.7,

=220.592cm4,220.592

I2=5000×(qWk+0.5×qEk)×Hsjcg4/384/0.7/20,

=5000×(0.658+0.5×0.13)×4.5^4/384/0.7/20,

=275.74cm4,275.74

選定立柱慣性矩應大于:275.74cm4,275.74

2.選用立柱型材的截面特性:,

選用型材號:80×80×5×2.5鋁方管,

型材強度設計值:85.500N/mm2,

型材彈性模量:E=0.7×105N/mm2,

X軸慣性矩:Ix=166.96cm4,166.96

Y軸慣性矩:Iy=95.24cm4,95.24

X軸抵抗矩:Wx1=41.74cm3,41.74

X軸抵抗矩:Wx2=41.74cm3,41.74

型材截面積:A=11.5cm2,11.5

型材計算校核處壁厚:t=2.5mm,2.5

型材截面面積矩:Ss=18.06cm3,18.06

塑性發(fā)展系數(shù):γ=1.05,

,,

3.幕墻立柱的強度計算:,

校核依據(jù):N/A+M/γ/w≤ｆa=85.5N/mm2(拉彎構(gòu)件),

B:幕墻分格寬:1.2m,1.2

GAk:幕墻自重:135N/㎡,135

幕墻自重線荷載:,

Gk=135×Wfg/1000,

=135×1.2/1000,

=0.162kN/m,0.162

NK:立柱受力:,

Nk=Gk×Hsjcg,

=0.162×4.5,

=0.729kN,0.729

N:立柱受力設計值:,

rG:結(jié)構(gòu)自重分項系數(shù):1.2,

N=1.2×Nk,

=1.2×0.729,

=0.875kN,0.875

σ:立柱計算強度(N/mm2)(立柱為拉彎構(gòu)件),

N:立柱受力設計值:0.875kN,0.875

A:立柱型材截面積:11.5cm2,11.5

M:立柱彎矩:2.543kN·m,2.543

Wx2:立柱截面抗彎矩:41.74cm3,41.74

γ:塑性發(fā)展系數(shù):1.05,

σ=N×10/A+M×103/1.05/Wx2,

=0.875×10/11.5+2.543×1000/1.05/41.74,

=58.784N/mm2,58.784

58.784N/mm2＜ｆa=85.5N/mm2,

立柱強度可以滿足,

,,

4.幕墻立柱的剛度計算:,

校核依據(jù):Umax≤L/180,

Umax:立柱最大撓度,

Umax=5×(qWk+0.5×qEk)×Hsjcg4×1000/384/0.7/Ix,

=5×(0.658+0.5×0.13)×4.5^4×1000/384/0.7/166.96,

=33mm,33

立柱最大撓度Umax為:33mm＜20mm,

Du:立柱撓度與立柱計算跨度比值:,

Hsjcg:立柱計算跨度:4.5m,4.5

Du=U/Hsjcg/1000,

=33/4.5/1000,

=0.0073＜1/180=0.0055,0.0073

撓度可以滿足要求,

,,

5.立柱抗剪計算:,

校核依據(jù):τmax≤[τ]=49.6N/mm2,

(1)Qwk:風荷載作用下剪力標準值(kN),

Qwk=Wk×Hsjcg×B/2,

=0.548×4.5×1.2/2,

=1.48kN,1.48

(2)Qw:風荷載作用下剪力設計值(kN),

Qw=1.4×Qwk,

=1.4×1.48,

=2.072kN,2.072

(3)QEk:地震作用下剪力標準值(kN),

QEk=qEAk×Hsjcg×B/2,

=0.108×4.5×1.2/2,

=0.292kN,0.292

(4)QE:地震作用下剪力設計值(kN),

QE=1.3×QEk,

=1.3×0.292,

=0.38kN,0.38

(5)Q:立柱所受剪力:,

采用Qw+0.5QE組合,

Q=Qw+0.5×QE,

=2.072+0.5×0.38,

=2.262kN,2.262

(6)立柱剪應力:,

τ:立柱剪應力:,

Ss:立柱型材截面面積矩:18.06cm3,18.06

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