幕墻荷載計算-中英對照
三、荷載計算
Ⅲ. Load Calculation
1、 作用在幕墻上的風荷載標準值按下列規(guī)則：
1. The wind load standard value working on the curtain wall is used following the rules bellow:
按照《風洞試驗報告》中峰值1秒的幕墻凈風壓與幕墻壓差，
并參照《建筑結構荷載規(guī)范》GB50009-2001中公式：
Wk＝βZ•μS•μZ•WO
In accordance with the net wind pressure and the pressure difference of the curtain walls when the peak value duration is 1 second in the “Report of the wind hole test”,
And referring to the formula in the “GB50009-2001 Standard Load Code for the Design of Building Structures” following as:
Wk＝βZ•μS•μZ•WO
式中：
Wk－作用在幕墻上的風荷載標準值（KN／m2）；
βZ－考慮瞬時風壓的陣風系數(shù)，按《建筑結構荷載規(guī)范》GB50009-2001取值；
μS－風荷載體型系數(shù)，按《建筑結構荷載規(guī)范》GB50009-2001取值；
μZ－風壓高度變化系數(shù)，按《建筑結構荷載規(guī)范》GB50009-2001取值；
WO－基本風壓，取0.55KN／m2。按《建筑結構荷載規(guī)范》GB50009-2001取值（五十年一遇考慮）；
地區(qū)粗糙度取為C類。
Of this formula:
Wk－Standard value of the wind load working on the curtain wall (KN/m2);
βZ－Gust factor of the instantaneous wind pressure when the pressure is taken into consideration, valued according to the “GB50009-2001 Standard Load Code for the Design of Building Structures”;
μS－Wind load shape factor, valued according to the “GB50009-2001 Standard Load Code for the Design of Building Structures”;
μZ－Height variation factor of wind pressure, valued according to the “GB50009-2001 Standard Load Code for the Design of Building Structures”;
WO－Basic wind pressure, valued as 0.55KN/m2. It is valued according to the “GB50009-2001 Standard Load Code for the Design of Building Structures” (one time per 50 years, considerable);
The roughness of the area is supposed as Class-C.
2、地震作用標準值按下式計算
qEK＝βE•αmax•Gk
式中：
qEk——作用于幕墻平面外水平地震作用（KN）；
Gk ——幕墻構件的重量（KN）；
αmax——水平地震影響系數(shù)最大值，7度抗震設計取0.08；
βE——動力放大系數(shù)，取5.0；
2. The standard value of the earthquake action is calculated according to the following formula:
qEK＝βE•αmax•Gk
Of this formula:
qEk— Level earthquake action working beyond the surface of the curtain wall (KN);
Gk —Weight of the components of the curtain wall (KN);
αmax—Maximum value of the level earthquake impact factor, and it is valued as 0.08 for 7°anti-earthquake design;
βE—Dynamic magnification factor, valued as 5.0.
3、荷載和作用效應組合的分項系數(shù)，應按下列規(guī)定采用
3. Subentry factors of the combinations of loads and action effects shall be used according to the following provisions:
①進行幕墻構件、連接件和預埋件承載力計算時：
重力荷載，γG取1.2
風荷載 ，γw取1.4
地震作用，γE取1.3
① When the load capacities of the components, connecting pieces and pre-embedded pieces are calculated,
Weight load γG is valued as 1.2
Wind load γw is valued as 1.4
Earthquake action γE is valued as 1.3
②進行位移和撓度計算時
重力荷載，γG取1.0
風荷載 ，γw取1.0
地震作用，γE取1.0
② When the displacement and deflection are calculated,
Weight load γG is valued as 1.0
Wind load γw is valued as 1.0
Earthquake action γE is valued as 1.0
③當兩個及以上的可變荷載或作用（風荷載、地震作用和溫度作用）效應參加組合時，第一個可變荷載或作用效應的組合系數(shù)可按1.0采用；第二個可變荷載或作用效應的組合系數(shù)可按0.5（玻璃幕墻）或0.6（石材及金屬幕墻）采用；第三個可變荷載或作用效應的組合系數(shù)可按0.2采用。
③ If the combination consists of two and above two variable loads or action (wind load, earthquake action and temperature action) effects, the combination factor of the first variable load or action effect can use 1.0; the combination factor of the second variable load or action effect can use 0.5 (glass curtain wall) or 0.6 (stone and metal curtain walls); and the combination factor of the third variable load or action effect can use 0.2.
④荷載和作用效應可按下式進行組合：
S＝γGSG＋ψwγwSw＋ψEγESE＋ψTγTST
式中：S——荷載和作用效應組合后的設計值；
SG——重力荷載作為永久荷載產(chǎn)生的效應；
Sw,SE,ST——分別為風荷載，地震作用和溫度作用作為可變荷載和作用產(chǎn)生的效應；按不同的組合情況，三者可分別作為第一個、第二個和第三個可變荷載和作用產(chǎn)生的效應；
γG,γw,γE,γT——各效應的分項系數(shù)，可按第（3）項中①②規(guī)定采用；
ψw,ψE,ψT——分別為風荷載，地震作用和溫度作用效應的組合系數(shù)。取決于各效應分別作為第一個、第二個和第三個可變荷載和作用的效應，可按第（3）項中③規(guī)定取值。
④ Loads and action effects can be combined according to the formula below:
S＝γGSG＋ψwγwSw＋ψEγESE＋ψTγTST
Of this formula:
S—Designed value of the combination of load and action effect;
SG—Effect generated by the weight load as permanent load;
Sw,SE,ST—Separately the effects generated by wind load, earthquake action and temperature action as variable load and action; and according to the situation of different combinations, they can be separately used as the effects generated by the first, second or third load and action;
G,γw,γE,γT—Subentry factors of various effects, can be used according to Provision ① and ② in Item (3);
ψw,ψE,ψT—Separately the combination factors of wind load, earthquake action and temperature action. Depending on various effects, they can be separately used as the effects generated by the first, second or third load and action, and can be valued according to Provision ③ in Item (3).
⑤玻璃幕墻應按各效應組合中的最不利組合進行設計。
⑤ The glass curtain walls shall be designed following the most disbeneficial combination among the combinations of various effects.
4、關于本次計算中所需查表的數(shù)值，力學方面均來自《建筑結構靜力計算手冊》（第二版）；熱工方面均來自《民用建筑熱工設計規(guī)范》GB50176-93。
4. As for those values in the calculation required to look up the table, the mechanical values are all from the “Static Calculation Handbook for Architecture Structures” (second edition), and the thermal engineering values are all from the “GB50176-93 Thermal Design Criterion for Civil Architecture”.
四、玻璃、鋁板幕墻所用材料的力學性能
Ⅳ. Mechanical Properties of Sections used by Glass and Aluminum-sheet Curtain Walls
1、玻璃的強度設計值fg(N/mm2)
類型 厚度（mm） 強度設計值fg
大面上的強度 側面強度
普通玻璃 5 28.0 19.5
浮法玻璃 5～12 28.0 19.5
15～19 24.0 17.0
≥20 20.0 14.0
鋼化玻璃 5～12 84.0 58.8
15～19 72.0 50.4
≥20 59.0 41.3
注：招標文件要求，玻璃厚度設計滿足風壓要求。玻璃的撓曲位移量不得超過其跨度的1/60及25mm中小值。
1. Designed glass strength value, fg (N/mm2)
Type Thickness (mm) Designed strength value fg
Strength on the big surface Strength on the profile
Universal glass 5 28.0 19.5
Float glass 5～12 28.0 19.5
15～19 24.0 17.0
≥20 20.0 14.0
Toughened glass 5～12 84.0 58.8
15～19 72.0 50.4
≥20 59.0 41.3
Note: According to the requirements of the bid documents, the glass thickness design shall meet the demand of wind pressure, and the deflecting displacement of the glass shall not exceed 1/60 of the span and the middle small value of 25mm.
2、單層鋁合金板強度設計值fa1(N/mm2)
牌號 試樣狀態(tài) 厚度（mm） 抗拉強度fa1t 抗剪強度fa1t
2A11 T42 0.5～2.9 129.5 75.1
＞2.9～10.0 136.5 79.2
2A12 T42 0.5～2.9 171.5 99.5
＞2.9～10.0 185.5 107.6
7A04 T62 0.5～2.9 273.0 158.4
＞2.9～10.0 287.0 166.5
7A09 T62 0.5～2.9 273 158.4
＞2.9～10.0 287 166.5
注：招標文件要求，鋁板設計滿足風壓要求。鋁單板的撓曲位移量不得超過其跨度的1/120及6mm中小值。
2. Designed strength value of single-layer aluminum alloy sheets, fa1 (N/mm2)
Sheet No. Sample state Thickness（mm） Tensile strength fa1t Shearing strength fa1t
2A11 T42 0.5～2.9 129.5 75.1
＞2.9～10.0 136.5 79.2
2A12 T42 0.5～2.9 171.5 99.5
＞2.9～10.0 185.5 107.6
7A04 T62 0.5～2.9 273.0 158.4
＞2.9～10.0 287.0 166.5
7A09 T62 0.5～2.9 273 158.4
＞2.9～10.0 287 166.5
Note: According to the requirements of the bid documents, the aluminum sheet design shall meet the demand of wind pressure, and the deflecting displacement of the aluminum sheet shall not exceed 1/120 of the span and the middle small value of 6mm.
3、鋁合金型材的強度設計值fa(N/mm2)
鋁合金牌號 狀態(tài) 強度設計值fa
受拉、受壓 受剪
6061 T4 85.5 49.6
T6 190.5 110.5
6063 T5 85.5 49.6
T6 140.0 81.2
注：在風荷載標準值和地震作用標準值作用下，鋁合金型材其相對撓度不應大于L/250(L指跨度)，絕對撓度不應大于20mm；作為橫料的鋁合金型材其相對撓度不應大于L/500(L指跨度)，絕對撓度不應大于3mm（招標文件要求）
3. Designed strength value of aluminum alloy sections, fa (N/mm2)
Al. alloy No. State Designed strength value fa
Tensing and pressing Shearing
6061 T4 85.5 49.6
T6 190.5 110.5
6063 T5 85.5 49.6
T6 140.0 81.2
Note: Under the action of the standard wind load value and the standard earthquake action value, the relative deflection of aluminum alloy sections shall not be more than L/250 (L--span), and the absolute deflection shall not be more than 20mm. As for the aluminum alloy sections as beam, the relative deflection shall not be more than L/500 (L--span), and the absolute deflection shall not be more than 3mm.
4、結構硅酮密封膠的強度(f1、f2)
結構硅酮密封膠短期強度允許值f1 0.2 N/mm2
結構硅酮密封膠長期強度允許值f2 0.01 N/mm2
4. Strength of the structural silicone sealant (f1 and f2)
Short-term strength allowable value of the structural silicone sealant, f1 0.2 N/mm2
Long-term strength allowable value of the structural silicone sealant, f2 0.01 N/mm2
5、鋼材的強度設計值fS(N/mm2)
鋼材牌號 厚度或直徑（mm） 抗拉、抗彎、抗壓 抗剪 端面承壓
Q235 d≤16 215 125 325
16＜d≤40 205 120
40＜d≤60 200 115
Q345 d≤16 310 180 400
16＜d≤35 295 170
35＜d≤50 265 155
注：在風荷載標準值和地震作用標準值作用下，鋼型材其相對撓度不應大于L/250， 絕對撓度不應大于15mm（招標文件要求）。
5. Designed strength value of steels fS (N/mm2)
Steel No. Thickness or diameter (mm) Tensile, bendable and pressable Shearing End pressure
Q235 d≤16 215 125 325
16＜d≤40 205 120
40＜d≤60 200 115
Q345 d≤16 310 180 400
16＜d≤35 295 170
35＜d≤50 265 155
Note: Under the action of the standard wind load value and the standard earthquake action value, the relative deflection of steels shall not be more than L/250, and the absolute deflection shall not be more than 50mm (see the requirements of the bid documents).
6、不銹鋼螺栓強度設計值：（N/mm2）
類別 組別 性能等級 σb 抗拉 抗剪
A（奧氏體） A1、A2 50 500 230 175
A3、A4 70 700 320 245
A5 80 800 370 280
C（馬氏體） C1 50 500 230 175
70 700 320 245
100 1000 460 350
C3 80 800 370 280
C4 50 500 230 175
70 700 320 245
F（鐵素體） F1 45 450 210 160
60 600 275 210
6. Designed strength value of stainless steel bolts (N/mm2)
Type Group Property class σb Tensile Shearing
A (austenite) A1、A2 50 500 230 175
A3、A4 70 700 320 245
A5 80 800 370 280
C (martensite) C1 50 500 230 175
70 700 320 245
100 1000 460 350
C3 80 800 370 280
C4 50 500 230 175
70 700 320 245
F(ferrite) F1 45 450 210 160
60 600 275 210
五、EWS-01及EWS-02玻璃幕墻系統(tǒng)的計算
Ⅴ. Calculation of the Glass Curtain Wall System EWS-01 and EWS-02
按照招標文件及風洞實驗報告要求，1#、2#塔樓中EWS-01及 EWS-02玻璃幕墻系統(tǒng)的1秒峰值幕墻凈風壓：負風壓絕大部份在-3.50KN／m2至-2.00KN／m2之間，局部最大值為-4.41 KN／m2；正風壓絕大部份在2.80KN／m2至2.00KN／m2。選取最危險的情況負風壓為-3.50 KN／m2及-4.41 KN／m2分別進行計算，計算過程按正值代入。
In accordance with the requirements of the bid documents and the wind hole test report, when the peak value duration is 1 second, the net wind pressure of the curtain wall in the glass curtain wall system EWS-01 and EWS-02 in Tower 1# and 2# is as follow as: The passive wind pressure of the majority of parts is -3.50KN/m2 to -2.00KN/m2, and the local maximum is -4.41 KN/m2; and the positive wind pressure of the majority of parts is 2.80KN/m2 to 2.00KN/m2. Under the most dangerous situation, the passive pressure is selected as -3.50 KN/m2 and -4.41 KN／m2 to calculate separately, which are input by a positive value in the calculation process.
(一)采光區(qū)雙銀LOW-E中空玻璃的設計計算
(Ⅰ) Design and calculation of double-silver LOW-E hollow glass in the lighting area
1、 1#塔樓局部風壓為-4.41KN／m2處中空玻璃的計算(玻璃分格:高2.5m，寬1.5m)
此處幕墻需采用8mm雙銀LOW-E鋼化玻璃＋12A+10mm鋼化玻璃的中空玻璃。
1. Calculation of the hollow glass on the local part of Tower 1# with a wind pressure of -4.41KN/m2 (glass sash: 2.5m high and 1.5m wide)
The curtain wall here uses the 8mm double-silver LOW-E toughened glass and the 12A+10mm toughened hollow glass.
1.1、 玻璃強度計算
1.1 Calculation of glass strength
風荷載標準值為
The standard wind load is:
Wk＝4.41KN／m2
水平分布地震作用標準值為
The standard value of the level distributed earthquake action is:
qEk＝βe•αmax•γ玻•t•10-3
＝5×.08×25.6×18×10-3
＝.184KN／m2
中空玻璃把荷載分配到單片玻璃上分別計算：
For the hollow glass distributes the load on the single glass sheet, the load shall be calculated separately:
Wk1 = 1.1×Wk×t13/(t13+t23)=1.643KN／m2
Wk2 = Wk×t23/(t13+t23)=2.917KN／m2
qEk1 = βe•αmax•γ玻•t1•10-3=.082KN／m2
qEk2 = βe•αmax•γ玻•t2•10-3=.102KN／m2
① 風荷載作用下應力標準值按下式分別在兩個單片玻璃上計算
① The stress standard value under the action of wind load will be calculated separately on two single glass sheets:
σwk＝6•η•ψ1•Wk•a2/t2
式中:σwk—風荷載作用下的應力標準值，(N/mm2)；
a——矩形玻璃板材短邊邊長，(mm)；
t——玻璃的厚度，(mm)；
ψ1——彎曲系數(shù)，按a/b的值查表
η——折減系數(shù)，按θ查表
Of this formula:
σwk—Stress standard value under the action of wind load, (N/mm2);
a— Side length of the short sides of the rectangle glass board, (mm);
t—Thickness of the glass, (mm);
ψ1—Bend factor, looking up the table by the value of a/b;
η—Reduction faction, looking up the table by θ.
θ1＝(Wk1＋0.5•qEk1)•a4/(E•t14)
＝(1.643＋0.5×.082)×10-3×15004/(0.72×105×84)
＝28.91
查表取η1＝.8844
According to the result of looking up the table, η1＝.8844
θ2＝(Wk2＋0.5•qEk2)•a4/(E•t24)
＝(2.917＋0.5×.102)×10-3×15004/(0.72×105×104)
＝20.87
查表取η2＝.9165
According to the result of looking up the table, η2＝.9165
則σwk1＝6•η1•ψ1•Wk1•a2/t12
＝6×.8844×.0868×1.643×10-3×15002/82
＝26.6 N/mm2
σwk2＝6•η2•ψ1•Wk2•a2/t22
＝6×.9165×.0868×2.917×10-3×15002/102
＝31.33 N/mm2
Thus,
σwk1＝6•η1•ψ1•Wk1•a2/t12
＝6×.8844×.0868×1.643×10-3×15002/82
＝26.6 N/mm2
σwk2＝6•η2•ψ1•Wk2•a2/t22
＝6×.9165×.0868×2.917×10-3×15002/102
＝31.33 N/mm2
② 地震作用下應力標準值按下式分別在兩個單片玻璃上計算
② The stress standard value under the earthquake action will be calculated separately on two single glass sheets:
σEk＝6•η•ψ1•qEk•a2/t2
式中:σEk—地震作用下的應力標準值，(N/mm2)；
η——取風荷載作用下應力計算時的值
Of this formula:
σEk—Stress standard value under the earthquake action, (N/mm2);
η—Stress value calculated under the action of wind load.
則σEk1＝6•η1•ψ1•qEk1•a2/t12
＝6×.8844×.0868×.082×10-3×15002/82
＝1.33 N/mm2
σEk2＝6•η2•ψ1•qEk2•a2/t22
＝6×.9165×.0868×.102×10-3×15002/102
＝1.1 N/mm2
Thus,
σEk1＝6•η1•ψ1•qEk1•a2/t12
＝6×.8844×.0868×.082×10-3×15002/82
＝1.33 N/mm2
σEk2＝6•η2•ψ1•qEk2•a2/t22
＝6×.9165×.0868×.102×10-3×15002/102
＝1.1 N/mm2
③ 玻璃的應力組合設計值按下式分別在兩個單片玻璃上計算
③ The designed value of the glass stress combination will be calculated separately on two single glass sheets:
σ＝ψw•γw•σwk＋ψe•γe•σEk
則σ1＝ψw•γw•σwk1＋ψe•γe•σEk1
＝1.0×1.4×26.6＋0.5×1.3×1.33
＝38.1N/mm2<fa＝84N/mm2
σ2＝ψw•γw•σwk2＋ψe•γe•σEk2
＝1.0×1.4×31.33＋0.5×1.3×1.1
＝44.58N/mm2<fa＝84N/mm2
所以玻璃強度滿足要求。
Thus,
σ1＝ψw•γw•σwk1＋ψe•γe•σEk1
＝1.0×1.4×26.6＋0.5×1.3×1.33
＝38.1N/mm2<fa＝84N/mm2
σ2＝ψw•γw•σwk2＋ψe•γe•σEk2
＝1.0×1.4×31.33＋0.5×1.3×1.1
＝44.58N/mm2<fa＝84N/mm2
Therefore, the glass strength meets the requirements.
1.2、 玻璃撓度計算
1.2 Calculation of glass deflection
風荷載標準值為
The standard wind load is:
Wk＝4.41 KN/m2
玻璃跨中最大撓度為
The maximum deflection in the glass span is:
μ＝η•ψ2•Wk•a4／Ｄ
式中：μ－玻璃跨中最大撓度 mm
ψ2－跨中最大撓度系數(shù)，由a/b查表
a－玻璃短邊長 (mm)
b－玻璃長邊長 (mm)
Of this formula:
μ－Maximum deflection in the glass span, mm
ψ2－Maximum deflection factor in the span, looking up the table by the value of a/b
a－Side length of the short sides of the glass (mm)
b－Side length of the long sides of the glass (mm)
玻璃板的彎曲剛度
The bend stiffness of the glass sheet is:
Ｄ＝Ｅt3／(12(1-ν2))
＝0.72×105×10.93／(12(1－0.22))
＝8093931.3 Ｎ•mm
式中：ν－泊松比，取ν＝0.2
Ｅ－玻璃彈性模量，取0.72×105 Ｎ／mm2
t －玻璃等效厚度 (mm)
Of this formula:
ν－Poisson’s ratio, that is, ν＝0.2
Ｅ－Glass elastic modulus, valued as 0.72×105 Ｎ/mm2
t －Glass equivalent thickness (mm)
t=0.95×(t13+t23)1/3
θ ＝ Wk•a4 / Et4
＝4.41×10-3×15004／(0.72×105×10.94)
＝22
查表取η = .912
則玻璃的撓度
According to the result of looking up the table, η = .912
Thus, the glass deflection is:
μ＝η•ψ2•Wk•a4／Ｄ
＝.912×.0087×4.41×10-3×15004／8093931.3
＝21.9 mm<25 mm
μ/a＝1/68<1/60
所以玻璃撓度滿足要求。
Therefore, the glass deflection meets the requirements.
(三)單元橫框的設計計算
(Ⅲ) Design and calculation of the unit transverse frame
1、 1#塔樓局部風壓為-4.41KN／m2處單元下橫框的計算
1. Calculation of the unit transverse frame on the local part of Tower 1# with a wind pressure of -4.41KN/m2 (glass sash: 2.5m high and 1.5m wide)
橫框受兩個方向力的作用，一個是重力作用，另一個是垂直于玻璃表面的風荷載和地震作用。橫框長B=1.5米，承擔重力方向分格高H1=2.5米，下分格高H2=0米。上下分格平均高H=1.25米。
The transverse frame has the force action from two directions, one is gravity action and other is the wind load and earthquake action which are upright to the glass surface. The length (B) of the transverse frame is 1.5m, the height (H1) of the sash bearing the gravity is 2.5m, and the height (H2) of the lower sash is 0m. The mean height (H) of the upper and lower sashes is 1.25m.
所選用橫框型材的截面特性如下：
The section properties of the selected transverse frame sections are as follows:
Ix——對x軸方向的慣性矩=866.44cm4
Iy——對y軸方向的慣性矩=36.36cm4
Wx——對x軸方向的抵抗矩=67.94cm3
Wy——對y軸方向的抵抗矩=12.3cm3
Sx——對x軸方向的面積距=54.13cm3
Sy——對y軸方向的面積距=11.72cm3
Ix—Moment of inertia on the direction of x axis, 866.44cm4
Iy—Moment of inertia on the direction of y axis, 36.36cm4
Wx—Moment of resistance on the direction of x axis, 67.94cm3
Wy—Moment of resistance on the direction of y axis, 12.3cm3
1.1、荷載計算
1.1 Load calculation
a,橫框受重力作用時
橫框所承受的重力線荷載標準值為：
a. When the transverse frame bears the gravity action,
The standard load value of the transverse frame bearing along the gravity line is:
qxk＝γ玻•t•H1×1.2
＝25.6×18×2.5×1.2/1000
＝1.382 KN／m
式中： γ玻——玻璃的密度，取25.6 KN／m3
t ——玻璃的總厚度 m；
H1 ——自重方向分格高度 m；
Of this formula:
γ玻—Glass density, valued as 25.6 KN/m3
t —Total thickness of the glass, m
H1 —Sash height along the self-gravity direction, m
橫框所承受的重力線荷載設計值為：
The designed load value of the transverse frame bearing along the gravity line is:
qx＝1.2×qxk＝1.658 KN／m
b,橫框受風荷載和地震作用時：
b. When the transverse frame bears the wind load and earthquake action,
Wk＝4.41KN／m2
qEy＝βe•αmax•G／A
＝5×.08×1.037／1.875
＝.221KN／m2
式中：qEy——作用于幕墻平面外水平分布地震作用(KN／m2)；
G ——幕墻分格構件的重量(KN)；
A ——幕墻分格面積(m2)；
αmax——水平地震影響系數(shù)最大值，取.08；
βe——動力放大系數(shù)，取5 。
Of this formula:
qEy—Level distributed earthquake action working beyond the plane of the curtain wall (KN／m2);
G —Weight of the sash components of the curtain wall (KN);
A —Area of the sashes of the curtain wall (m2);
αmax—Maximum of the level earthquake impact factor, values as 0.08
其中 G＝H×B×t×γ玻×1.2
＝1.25×1.5×18×25.6× 1.2/1000
＝1.037ＫＮ
A＝H×B＝1.25×1.5
＝1.875m2
Among,
G＝H×B×t×γ玻×1.2
＝1.25×1.5×18×25.6× 1.2/1000
＝1.037ＫＮ
A＝H×B＝1.25×1.5
＝1.875m2
荷載組合值為
上、下分格Y方向風荷載標準值：
The load combination value is:
The standard wind load value of the upper and lower sashes on the Y direction is:
qyk1＝Wk×(H2/ 2)
＝4.41×(0/2)
＝0KN／m
qyk2＝Wk×(B / 2)
＝4.41×.221×(1.5/2)
＝3.308KN／m
上、下分格Y方向荷載組合設計值：
The designed load combination value of the upper and lower sashes on the Y direction is:
qy1＝(1.0×1.4×Wk＋0.5×1.3×qEy)×(H2/2)
＝(1×1.4×4.41＋0.5×1.3×.221)×(0/2)
＝0KN／m
qy2＝(1.0×1.4×Wk＋0.5×1.3×qEy)×(B/2)
＝(1×1.4×4.41＋0.5×1.3×.221)×(1.5/2)
＝4.738KN／m
1.2.剛度計算
1.2 Stiffness calculation
招標文件要求，承受風荷載時橫框的許用撓度［f］風為B／250及20mm中小值；
承受重力荷載時橫框的許用撓度［f］重為B／500及3mm中小值。
本系統(tǒng)中［f］風＝1500／250＝6mm；［f］重＝1500／500＝3mm
則按簡支梁計算，橫框所需的最小慣性矩為
According to the requirements of the bid documents, the allowable deflection (［f］風) of the transverse frame when bearing the wind load is B/250 and 20mm as the middle small value; while the allowable deflection (［f］重) of the transverse frame when bearing the gravity load is B/500 and 3mm as the middle small value;.
In this system, ［f］風＝1500/250＝6mm; and［f］重＝1500/500＝3mm.
Thus, calculated by the simple beam, the minimum moment of inertia required by the transverse frame is:
Iymin＝Fxk×a×B2×(3-4×(a2/B2))/24×E×［f］重
＝1.037×0.25×1.52×(3-4×(0.252/1.52))×108/(24×70000×3)
＝33.435 cm4≤Iy＝36.36cm4
Ixmin＝[(25-10×H22/B2＋H24/B4)×qyk1×B4／1920E•［f］風]+[qyk2×B4／120E•［f］風]
＝[(25-10×02/1.52＋04/1.54)×0×1.54×108／(1920×70000×6)]+[3.308×1.54×108／(120×70000×6)]
＝33.228 cm4≤Ix＝866.44cm4
式中：B──玻璃分格寬度 m；
E——彈性模量 N/mm2
Fxk——重力作用下的集中力標準值 KN
a——受力點到橫框端距離 m
Of this formula:
B ─Width of the glass sash, m
E —Elastic modulus, N/mm2
Fxk—Standard value of the resultantforce under the gravity action, KN
a—Distance from the fixed point to the end of the transverse frame, m
1.3. Strength calculation
The maximum bending moment of transverse frame is calculated by the following equation:
My＝Fx×a
＝1.244×0.25
＝.311 KN•m
Mx＝[qy1×(3×B2-H22)／24]+[qy2×B2／12]
＝[0×(3×1.52-02)／24] + [ 4.738×1.52／12]
＝.888 KN•m
The resist bending bearing capacity of the transverse frame shall meet requirements of the following equation:
Mx／γWx＋My／γWy≤fa
Then Mx／γWx＋My／γWy
＝103×.888／(1.05×67.94)＋103×.311／(1.05×12.3)
＝36.528N／mm2≤fa＝140N／mm2
The resist shear bearing capacity of the transverse frame shall meet requirements of the following equation:
Vy×Sx／(Ix×tx)≤fv
Vx×Sy／(Iy×ty)≤fv
In this equation: Vx、Vy——shear design value (N) of the crossbeam in the horizontal and vertical direction;
Sx、Sy——area moment (cm3) of the crossbeam section rounding axis X and Y;
tx、ty——total web section width (mm) of the crossbeam section vertical to axis Y and X;
fv ——shear resisting strength design value (N/mm2) of the profile;
Vx＝1000×qx×B/2＝1243.5 N
Vy＝[1000×qy1×B×(1－H2/2B)/2]+[1000×qy2×B/4]＝1776.75 N
Then, Vy×Sx／(10×Ix×tx)
＝1776.75×54.13／(10×866.44×6)
＝1.85≤fv＝81.2N/mm2
Then, Vx×Sy／(10×Iy×ty)
＝1243.5×11.72／(10×36.36×6)
＝6.68≤fv＝81.2N/mm2
So the stiffness and strength meet requirements.
6. Calculation of transverse frame in the unit of installing fixed pin of window-cleaning machine
According to requirements in the bidding document, the fixed pin of window-cleaning machine can produce a concentrated force of 2.7KN, and the direction is considered as the most unfavorable one. Meanwhile, the combination of this load with the inward or outward constant distribution static load of 500 Pa shall be considered.
Thus, when considering the concentrated force produced by the window-cleaning machine fixed pin, this frame has three kinds of stress: one is the gravity, another one is the static load of 500 Pa (calculated as 1000Pa) vertical to the glass surface, and the other one is the concentrated force produced by the fixed pin of the window-cleaning machine. The most unfavorable case is that the concentrated force produced by the fixed pin is along the direction of the gravity.
Transverse frame length B=1.5m, box height in the direction of gravity bearing H1=1.35m, the bottom box height H2=0.625m, the average height of the top and bottom boxes H=.988m.
The properties of the selected transverse frame sections are as follows:
Ix——inertia moment against axis x=468.28cm4
Iy——inertial moment against the axis y =223.14cm4
Wx——moment of resistance against the direction of axis x =42.89cm3
Wy——moment of resistance against the axis y =36.1cm3
6.1. Load calculation
a. When the transverse frame is under gravity,
The standard gravity line load the transverse frame bears is:
qxk＝γglass•t•H1×1.2
＝25.6×16×1.35×1.2/1000
＝.664 KN／m
In this equation: γglass——density of the glass, take 5.6 KN／m3
t ——total thickness of the glass m；
H1 ——box width in the deadgravity direction m；
The gravity line load design valve the transverse frame bears is:
qx＝1.2×qxk＝.797 KN／m
b. When the transverse frame bears wind load:
Take Wk＝1 KN／m2 in the calculation
The combine load is
qyk＝Wk×H
＝1×.988
＝.988KN／m
qy＝1.0×1.4×Wk×H
＝1×1.4×1×.988
＝1.383KN／m
6.2. Stiffness calculation
In the bidding document, it is required that when bearing wind load, the allowable deflection ［f］wind of the transverse frame is B／250 and 20mm of medium and small value;
The allowable deflection ［f］gravity of the transverse frame when bearing gravity load is B/500 and 3mm of medium and small value.
In this system,［f］wind＝1500／250＝6mm；［f］gravity＝1500／500＝3mm
If calculated as single beam, the minimum inertia moment the transverse frame requires is
Iymin＝Fxk×a×B2×(3-4×(a2/B2))/24×E×［f］重+ FCG×a1×(3B2 -4×a12)/ 48×E×［f］重
＝.498×0.375×1.52×(3-4×(0.3752/1.52))×108/(24×70000×3)+ 2.7×0.2× (3×1.52-4×0.22)×108/(48×70000×3)
＝22.927 cm4+35.3.5 cm4
＝58.231 cm4+≤Iy＝223.14cm4
Ixmin＝(25-10×H2/B2＋H4/B4)×qyk×B4／1920E•［f］
＝(25-10×.9882/1.52＋.9884/1.54)×.988×1.54×108／(1920×70000×3)
＝25.864 cm4≤Ix＝468.28cm4
In this equation:── glass box width m；
E——elastic modulus N/mm2
Fxk——standard concentrated force under gravity KN
FCG——standard concentrated force at the stress point of the fixed pin of the window-cleaning machine KN
a——distance from the stress point to the transverse frame end m
a1——distance from the stress point of the fixed pin of the window-cleaning machine m
6.3. Strength calculation
The maximum bending moment of the transverse frame is calculated as the following equation
My＝Fx×a+ 1.2×FCG×a1×（B-a1）／B
＝.598×0.375+1.2×2.7×0.2×（1.5-0.2）／1.5
＝.786 KN•m
Mx＝qy×(3×B2-H2)／24
＝1.509×(3×1.52-.9882)／24
＝.363 KN•m
The bend resisting bearing capacity of the transverse frame shall meet following requirements:
Mx／γWx＋My／γWy≤fa
則 Mx／γWx＋My／γWy
＝103×.363／(1.05×42.89)＋103×.786／(1.05×36.1)
＝28.79N／mm2≤fa＝140N／mm2
Thus the stiffness and strength of the transverse frame meet requirements.
8. Width calculation of the contact point of dilatation joint
1. Width calculation of the contact point of dilatation joint at layer height of 4.475m
To meet the needs of fitting to the temperature distortion of curtain wall and construction regulation, the connecting place between the upper and the lower units has a clearance----dilatation joint (d), the value of d is calculated as per the following equation:
d≥σλ／ε＋a1＋a2
In this equation: d——size of dilatation joint mm;
σ——displacement caused by change of temperature, mm;
σ＝α•△ｔ•L ＝2.35×10-5×80×4475＝8.413mm
α—— the expansion coefficient of the mullion materials, take 2.35×10-5;
△ｔ—change of temperature (℃) take 80℃;
λ——actual dilatation regulation coefficient, take 0.85;
ε——consider the distortion capacity of the sealant, take 0.5;
a1——construction error, take 2mm;
a2——axial compression distortion of the main structure, take 3mm.
then σλ／ε＋a1＋a2＝8.413×0.85／0.5＋2＋3
＝19.3mm
The actual dilatation joint clearance d is taken as 20mm, thus the width of the contact point of the dilatation joint meets requirements.
9. Strength checking computation of the structural silicon sealant
1. Computation of the structural silicon sealant at the layer height of 4.475m, and with wind pressure of -4.41KN／m2
In this calculation, the actual sealant width = 24 mm, and the actual sealant thickness = 10 mm.
Under the wind load and horizontal earthquake:
Ｃs＝(W+0.5qe)•a／2000f1 mm
＝(1.4×4.41+0.5×.287)×1500／(2000×.2)
＝23.691 mm
In this equation: Ｃs——felt width of the structure silicon sealant mm;
a ——length of the short side of the glass mm;
f1——allowable value of the short-term strength of the sealant, take.2 N／mm2 ;
W——wind load design value KN／m2 ;
qe——design value of the earthquake at the calculation unit KN／m2 ;
Since gluing width between the wind load and the horizontal effect is 23.691mm≤actual gluing width24mm, thus it meets requirements.
The gluing thickness ts of the structure silicon sealant is calculated as per the following equation:
ts＞μs／(δ(2＋δ))0.5 (6≤ts≤12)
In this equation: ts——gluing thickness of the structure silicon sealant mm；
δ——displacement capacity of the structure silicon sealant, take the elongation rate when its pull is 0.14MPa (provided by the manufacturer);
μs——relative displacement of the curtain glass, mm
Under wind load and earthquake effect μs is calculated as per the following equation:
μs = L×Δ
＝2.5×1000/500
＝5 mm
In this equation: Δ——the layer displacement angle of the main structure
Considering that the unit curtain wall can absorb a part of relative displacement, which is about 2mm,
Then ts＞μs／(δ(2＋δ))0.5＝3／(.125(2＋.125))0.5
＝5.821mm
Since 5.821mm≤actual gluing thickness8 mm, thus the strength of the structure silicon sealant meets requirements.
10. Calculation of multi-point locks of operating windows
1. Calculation of multipoint locks at the glass box height of 2.5m and width of 1.5m（wind pressure-3.5KN／m2）
According to the actual tress of the window sash, under the normal wind pressure, the window frame bears the entire load, the ironware is not stressed. Only check the stress of the ironware under the negative pressure:
Under negative pressure, the standard wind load takes Wk=3.5 KN／m2, and one window sash bears the wind pressure of 2.5×1.5×3.5=13.125 KN
The maximum bearing capacity of the lock points and lock block is calculated as 200kg, then the lock points needed is
13.125×1000/200×9.8=6.7（points）
Since the jal-awning window is hanging type to keep balance, and the hanging side is equal to two lock points, thus six-point lock is needed.
Each lock point is fixed by two ST4.8 self tapping nails. The loading area of each nail is A0=16.76mm2, thus the shear stress of each nail is as follows:
τ=V/2A0=（13.125/8）×103/（2×16.76）=48.95N/mm2<245N/mm2
Thus the lock points meet requirements.
Ⅵ. Calculation of the glass curtain wall system EWS-03
In accordance with the requirements of the bid documents and the wind hole test report, when the peak value duration is 1 second, the net wind pressure of the curtain wall in the glass curtain wall system EWS-03 in Tower 1# and 2# is as follow as: The passive wind pressure of the majority of parts is -3.50KN/m2 to -2.00KN/m2, and the local maximum is -4.5 KN/m2; and the positive wind pressure of the majority of parts is 3.0KN/m2 to 2.00KN/m2. Under the most dangerous situation, the passive pressure is selected as -3.50 KN/m2 and -4.5 KN/m2 to calculate separately, which are input by a positive value in the calculation process.
For the structure of the glass curtain wall system EWS-03 is similar to glass curtain wall system EWS-01 and EWS-02, the calculation of the transverse frame and glass can completely refer to that of EWS-01 and EWS-02.
1. Design and calculation of the unit corner mullion
1. Calculation of the corner mullion within the part with a wind pressure of -4.5KN/m2 (the height among layers is 4.475m)
The self-gravity (Gk/A) of the curtain structure is valued as 552.96N/m2, and the sash width borne by each mullion is 0.75 m.
The section properties of the selected transverse frame sections are as follows:
Ix-Moment of inertia on the direction of x axis, 1338.89cm4
Iy-Moment of inertia on the direction of y axis, 1551.79cm4
Wx-Moment of resistance on the direction of x axis, 120.85cm3
Wy-Moment of resistance on the direction of y axis, 118.71cm3
Wy——moment of resistance against the direction of axis y =118.71cm3
1.1 Mechanical model
The mullion adopts the mechanical model of equal span articulated statically determinate beam. From the top
to the bottom, take out a longitudinal calculation unit, the mullion bears meanly distributed load, every layer of the curtain poles is connected with the main structure by a connection piece, every layer of poles has a cantilevered span at the joint, and the end of the previous layer of poles is connected and supported with an inserting core on this cantilevered end and form the equal span articulated statically determinate beam.
This calculation is calculated with the fifth span.
The mechanical model sketch is as follows:
Calculation sketch of equal span articulated statically determinate beam
1.2 Stress analysis and bending calculation
R1support= q×L1 / 2
R1support＝q×LI×[1-(aI/LI)2]/2-PI-1×(aI/LI)
P1＝R1support
PI＝- R1support +q×(LI+aI)+PI-1
M1mid= q×L12 / 8
MImid＝q×LI2/8×(1-(aI/LI)2)2-PI-1×aI×[1-(1＋aI/LI)2/2＋aI/LI]
MIsupport＝-PI-1×aI-q×aI2/2
U1mid＝5×q×L14/(384×E×I)
U1articulation＝{q×a2×L23[-1+4(a2/L2)2+3(a2/L2)3]}/(24×E×I)
＋[P1×a22×L2×(1＋a2/L2)]/(3×E×I)
U1total = U1mid + U1articulation / 2
UImid＝5×q×LI4/(384×E×I)-q×aI2×LI2/(32×E×I)-PI×aI×LI2
/(16×E×I)
UIarticulation＝{q×aI×LI3[-1＋4(aI/LI)2＋3(aI/LI)3]}/(3×E×I)
＋[PI×aI2×LI×(1＋aI/LI)]/(3×E×I)
UItotal= UImid + UIarticulation / 2
1.3 Load calculation and geometrical parameters of floors
The standard wind load on the curtain wall is
Wk＝4.5KN／m2
qEk＝βe•αmax•Gk／A
＝5×.08×552.96/1000
＝.221KN／m2
Qstrength＝Wk×B
＝4.5×.75
＝3.375KN／m
Qstrength＝(1.0×1.4×Wk＋0.5×1.3×qEk)×B
＝(1.0×1.4×4.5＋1.3×0.5×.221)×.75
＝4.833KN／m
Main inertial moment of the mullion cross section: I＝1338.89 cm4
Area of mullion cross section: A0＝2999.98 mm2
The minimum moment of resistance of the mullion cross section: W＝120.85cm3
Mullion material: 6063-T6
Layer height: 4.475m
Cantilever length A: .5m
1.4 Verification of strength and stiffness of the mullion
(1) Principle for strength verification
The maximum stress shall satisfy:
σmax＝N/A0＋M/(γ×W)≤f
In this equation: σmax——maximum normal stress (N/mm2) in the mullion ;
N——pull design value (N) in the mullion;
A0——section area (mm2) of the mullion;
M——bending moment design value (N.mm) of the mullion;
γ——plastic adaptation coefficient of materials, take 1.05;
W——minimum bend resisting modulus (mm3) of the mullion in the direction of bending moment
(2) Stiffness verification principle
u≤L/250
(3) Verification of strength and stiffness
mid-span mid-span bending moment mid-span stress strength verification midpoint bending stiffness verification
The first span 9.546 75.971 √ 10.848 √
The second span 6.882 54.977 √ 6.68 √
The third span 7.217 57.617 √ 7.205 √
The forth span 7.175 57.286 √ 7.139 √
The fifth span 7.18 57.326 √ 7.147 √
Support support bending moment shear at support stress at support strength verification
Nil support 0 9.606 .742 √
The first support 5.407 22.988 43.353 √
The second support 4.727 21.456 37.994 √
The third support 4.813 21.65 38.672 √
The forth support 4.801 21.625 38.578 √
From the table, we know that the strength and stiffness of selected mullion meet requirements.
(二) Design calculation of the steel mullion
The calculated layer height of the curtain wall is L=5.35m, the box width the mullion bears is B=3m. The material selected for the mullion is Q235 welded steel pipe, with outside cover of aluminum alloy sections, and in calculation, only the welded steel pipe is considered.
The section properties of the selected mullion profile are:
Ix——inertial moment against the direction of axis x=2723.09cm4
Iy——inertial moment against the direction of axis y=566.76cm4
Wx——moment of resistance against the direction of x axis=252.89cm3
Wy——moment of resistance against the direction of y axis=86.29cm3
A0——section area=4739.7mm2
Mechanical model sketch is as follows:
1. Load calculation
a. Calculation of standard wind load
Wk＝3.40KN／m2
b. The earthquake effect in the direction of axis y (vertical to the curtain wall face) is
qEy＝βe•αmax•G／A
In this equation, qEy——horizontal earthquake effect (KN／m2) acting outside the curtain wall plane;
G ——gravity (KN) of curtain components;
A ——area (m2) of curtain wall components;
αmax——maximum coefficient of horizontal earthquake effect, take .08;
βe——Dynamic Amplification Coefficients, take 5 .
thereinto, G＝L×B×t×γglass×1.2
＝5.35×3×24×25.6× 1.2/1000
＝11.833ＫＮ
In this equation: L——calculated layer height m；
B——box width m；
t——thickness of the glass mm；
γglass——density of the glass, take 25.6 KN／m3
A＝L×B＝5.35×3
＝16.05m2
Then qEy＝βe•αmax•G／A
＝5×.08×11.833／16.05
＝.295KN／m2
c. The earthquake effect of in the direction of x axis (in the curtain wall plane) is
qEx＝βe•αmax•G/L
＝5×.08×11.833／5.35
＝.885KN/m
2. Stiffness calculation
Under the rectangular load, the combined value of the line load and effect of the mullion is
Qstiffness＝Wk×B＝3.40×3
＝10.203KN／m
If calculated as single beam, the bending of the mullion is calculated according to the following equation:
f＝5qstiffness•L4／384EI
Take［f］＝L/250＝5350／250＝21.4mm
From the above equation, we know that the minimum inertial moment Ixmin required for mullion is:
Ixmin＝5qstiffness L4／384E•［f］
＝5×10.203×5.354×108／384×206000×21.4
＝2468.8847< Ix=2723.09 (cm4)
3. Strength calculation
The strength load combined as:
q＝1.4×1×Wk＋1.3×0.5×qEy
＝1.4×1×3.40＋1.3×0.5×.295
＝4.953KN／m2
The line load of the mullion is
Qstrength＝q×B＝4.953×3
＝14.859KN／m
Then calculated as single beam, the maximum bending moment of the mullion is
M＝qstrength•L2／8＝14.859×5.352／8
＝53.163KN•m
In this equation: M——maximum bending moment the mullion bears, KN•m；
L——calculated layer height m.
The axial pull of the mullion is N＝1.2×G＝14.2KN
The bearing capacity of the mullion shall meet requirements of the following equation (the mullion designed for this project doesn’t bear compression, and is a pull component only)
N／A0＋M／(γ•W)≤fa
In this equation: N——the pull design value (KN) of the mullion;
M——Bending moment design value (KN•m) of the mullion;
A0——Net section area (mm2) of the mullion;
W——net section moment of resistance (cm3) in the direction of bending moment
γ——plastic adaptation coefficient, take 1.05;
fa——Strength design valve of the mullion material, take 215N／mm2.
Then N／A0＋M／(γ•W)
＝103×14.2／4739.7＋103×53.163／(1.05×252.89)
＝203.207 N／mm2< fa＝215 N／mm2
Thus the stiffness and strength of the mullion meet requirements.
2012.10.21