  -- by formula method, finite element method and actual measurement method.

Wind pressure resistance is one of the most important physical properties of doors, windows and curtain walls, and the deflection value of the main stressed components (including rods, panels, etc.) under the action of wind load is used as the quantitative judgment index.

The formula method, the finite element method and the actual measurement method are three evaluation methods for the deflection change of insulating glass. This article compares and analyzes the deflection change of insulating glass under the three methods through typical cases, and gives calculation and detection suggestions.

#### 1. The analysis case

Generally, there are three methods can be used to measure the deflection value of insulating glass panels, namely the formula method, the finite element method and the actual measurement method. What is the difference between the results?

Taking a semi-hidden frame glass curtain wall project as an example, 8+12A+8 mm thick double tempered insulating glass is used, and the division is shown in Figure 1.

Figure 1 The glass curtain wall specimen grid

Take the largest plate A for analysis, the bottom side is 4500 mm long and the height is 2350 mm. One vertical side adopts the hidden frame method, and the remaining three sides are fixed by the exposed frame method; the standard value Wk of the wind load of the curtain wall project is taken as 1500 Pa.

In the following, the formula method, the finite element method and the actual measurement method are used to calculate the deflection change of the glass plate one by one, and the results are discussed.

#### 2. The formula method

"Technical Specifications for Glass Curtain Wall Engineering"  The formula for calculating mid-span deflection of insulating glass in glass curtain wall supported by middle frame is:

In the formula:

df is the maximum value of deflection under the standard value of wind load, mm;

wk is the standard value of wind load perpendicular to the plane of glass curtain wall, N/mm2

μ is the deflection coefficient, adopted according to Table 6.1.3 of "Testing Method for Air Tightness, Water Tightness and Wind Pressure Resistance of Building Curtain Wall";

η is the reduction factor, adopted according to Table 6.1.2-2 of "Testing Method for Air Tightness, Water Tightness and Wind Pressure Resistance of Building Curtain Wall";

D is the equivalent thickness of insulating glass, mm.

For the glass curtain wall project with the type and specification of insulating glass and the standard value of wind load determined, the formula is a single-variable linear function. The maximum deflection calculated under various wind loads is shown in Table 1, and the curve is shown in Figure 2.

Table 1 Calculate the deflection values under various wind pressures according to the code formula

 Wind pressure differential/PaCorresponding to deflection/mm 1508.00 30015.36 45022.30 60028.75 75034.70 Wind pressure differential/PaCorresponding to deflection/mm -150-8.00 -300-15.36 -450-22.30 -600-28.75 -750-34.70 Wind pressure differential/PaCorresponding to deflection/mm 90040.41 105045.85 120050.94 135055.91 150060.58 Wind pressure differential/PaCorresponding to deflection/mm -900-40.41 -1050-45.85 -1200-50.94 -1350-55.91 -1500-60.58

#### 3. The finite element method

The mid-span deflection of insulating glass panel A is calculated by geometric nonlinear finite element method, the results are shown in Table 2, and the curve is shown in Figure 2.

Table 2 The deflection values under various wind pressures calculated by the geometric nonlinear finite element method

 Wind pressure differential/PaCorresponding to deflection/mm 1507.73 30014.06 45019.11 60023.32 75026.94 Wind pressure differential/PaCorresponding to deflection/mm -150-7.73 -300-14.06 -450-19.11 -600-23.32 -750-26.94 Wind pressure differential/PaCorresponding to deflection/mm 90030.15 105033.02 120035.66 135038.09 150040.36 Wind pressure differential/PaCorresponding to deflection/mm -900-30.15 -1050-33.02 -1200-35.66 -1350-38.09 -1500-40.36

The comparison shows that the results obtained by the two calculation methods are quite different. The result curve obtained by the formula method approximates a linear function, and the result curve obtained by the finite element method approximates a power function.

In order to judge which method is closer to the real situation, the wind pressure resistance performance test is carried out, and the results of the formula method and the finite element method are compared with the measured data.

#### 4. The actual measurement method

According to "Testing Method for Air Tightness, Water Tightness and Wind Pressure Resistance of Building Curtain Wall", the standard value of 40% wind load (600 Pa) is P1, and the standard value of wind load (1500 Pa) is P3, and the wind pressure resistance is carried out. The performance test obtained the deflection value of the insulating glass panel A under the wind pressure difference at all levels, as shown in Table 3 and Figure 2.

Table 3 The measured values of glass deflection under various wind pressures in the wind pressure resistance performance test

 Wind pressure differential/PaCorresponding to deflection/mm 152.99.36 301.915.51 456.819.6 601.522.41 1503.133.18 Wind pressure differential/PaCorresponding to deflection/mm -153.5-5.12 -298.8-8.27 -450.8-10.95 -601.8-13.12 -1501.1-21.88

picture In Fig. 2, curve 1 is the result obtained by the formula method, curve 2 is the result obtained by the finite element method, and curve 3 is the actual measurement result.

Figure 2 Deflection values calculated by formula method and finite element method (curves 1 and 2) and measured deflection value (curve 3)

#### 5. The result analysis

5.1 Analysis of calculation results

It can be seen from Figure 2 that curve 1 approximates a linear function. Although the "Technical Specifications for Glass Curtain Wall Engineering" has used the reduction factor η to correct the calculation of large deflection glass panels, the value of η is relatively safe, resulting in the calculated value of glass deflection being much larger than the measured value under the action of wind load.

The changing trends of curves 2 and 3 are relatively close, indicating that the results obtained according to the geometric nonlinear finite element method are closer to the actual situation: under the action of wind load, the deflection of large-deflection insulating glass changes in a non-linear function.

It can be seen from this example that the actual deflection value is 33.18 mm under the wind load of +1500 Pa, which is far from the calculation result of the code formula of 60.58 mm (the calculated value is 82.6% larger), and it is different from the calculation result of the geometric nonlinear finite element method. 40.36 mm is relatively close (the calculated value is 21.6% larger).

5.2 Analysis of test results

The principles for evaluating the deformation of curtain wall glass panels in "Testing methods for air tightness, water tightness and wind pressure resistance of building curtain walls" are as follows:

During deformation detection, under the action of 40% wind load standard value (Wk), the deflection of the normal line of the opposite surface should be less than or equal to f0/2.5; during safety detection, the corresponding normal line of the opposite surface under the action of the standard value of wind load (Wk) The deflection should be less than or equal to the allowable deflection f0

The premise of this assessment principle is that the component deflection change conforms to a linear function change law, which is applicable to all kinds of components including insulating glass, but the test shows that it is more difficult to judge the insulating glass. It can be seen from this evaluation principle that the deflection (limit value) of insulating glass panel A corresponding to f/2.5 and f0 is shown in Table 4.

Table 4 The deflection (limit value) of insulating glass panel A corresponding to f0/2.5 and f0

 The short side length of glass/mm 2350 f0 1/60 Test wind pressure difference/Paf0/2.5 corresponds to deflectionf0 corresponds to deflection ±60015.67- ±1500-39.17

The deflection measured value and the deflection limit data specified in the standard in Table 4 are plotted into a curve, as shown in Figure 3.

Figure 3 Comparison of the measured deflection with the deflection limit specified in the standard

It can be seen that under the wind pressure difference of 600 Pa (P1), the actual maximum deflection of the insulating glass is 22.41 mm, which is greater than f/2.5 and corresponds to a deflection of 15.67 mm, which does not meet the requirements of the testing standard.

However, under the wind pressure difference of 1500 Pa (P3), the actual maximum deflection of the insulating glass is 33.18 mm, which is less than f0 and corresponds to a deflection of 39.17 mm, which meets the requirements of the testing standard.

So, can it be judged unqualified only by the deflection corresponding to f0/2.5, and ignore the deflection corresponding to f0

The international industry standard "Testing Methods for Air Tightness, Water Tightness, and Wind Pressure Resistance of Building Curtain Walls" requires the deflection limit value of the stressed members of the curtain wall under wind load, which is actually for f0/2.5(±P1) and f0(±P3) The following double requirements, but the final judgment should fall on "f0(±P3) corresponding to Wk".

In this example, it should not be judged as unqualified just based on the deflection of the insulating glass corresponding to f/2.5, but should be judged by comparing the measured value of the deflection under ±P3 with f0

In particular, the international industry standard "Testing Methods for Air Tightness, Water Tightness, and Wind Pressure Resistance of Building Curtain Walls" has required testing the deflection value under the standard value of wind load (Wk, corresponding to P3) and the safety performance under the design value of wind load.

#### 6. The Analysis Conclusion

The formula method, the finite element method and the actual measurement method are three evaluation methods for the deflection change of insulating glass. This article compares and analyzes the deflection change of insulating glass under the three methods through typical cases, and gives calculation and detection suggestions.

The result curve calculated by the formula method approximates a linear function. Although the correction of the reduction coefficient has been considered, the calculated value of the glass deflection is much larger than the measured value under the action of a large wind load; while the result obtained by the geometric nonlinear finite element method is closer to the actual Condition.

When evaluating the deformation of glass panels according to the "Testing Method for Air Tightness, Water Tightness, and Wind Pressure Resistance of Building Curtain Walls", the deflection of the insulating glass under the action of 40% of the standard value of wind load (Wk) will be unqualified, and the deflection of the insulating glass under ±P3(Wk) will be unqualified.

Insulating glass deflection is qualified. "Testing methods for air tightness, water tightness, and wind pressure resistance of building curtain walls" have added the requirements for testing the deflection value under the standard value of wind load (Wk, corresponding to P3) and the safety performance under the design value of wind load.