JP7605699B2 - Steel temperature calculation method and steel temperature calculation program - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Act Shimizu Corporation Research Report No. 98 Publication date December 21, 2020

The present invention relates to a steel temperature calculation method and a steel temperature calculation program for calculating the steel temperature of steel members covered with fire-resistant coating material.

Conventionally, in the framework of a steel building structure, steel members covered with fire-resistant covering materials such as calcium silicate boards, wrapped fire-resistant covering materials, and sprayed rock wool (hereafter referred to as general fire-resistant covering materials) may be joined to steel members covered with wood materials as fire-resistant covering materials (hereafter referred to as wood fire-resistant covering materials). As an example, Figure 5 (1) shows a beam plan, (2) and (3) show cross-sectional views of beam 1, and (4) shows a cross-sectional view of beam 2. Reference number 3 in the figure indicates floor members that are placed on the top surfaces of beams 1 and 2.

Beam 1 is a beam in which a steel beam 4 (steel member) made of H-shaped steel as shown in Figure 5 (2) or (3) is covered with a general fire-resistant coating material 5 (see, for example, Patent Document 1). Figure 5 (2) is an example in which the general fire-resistant coating material 5 is box-clad and coated at intervals on both sides of the web of the steel beam 4, and (3) is an example in which the general fire-resistant coating material 5 is directly coated on the surface of the steel beam 4. When the steel beam 4 is heated for the required fire resistance time, the maximum steel temperature reaches about 350 to 500°C.

In contrast, the beam 2 is a beam in which a steel beam 6 (steel member) made of H-shaped steel is covered with a wood fire-resistant coating material 7. The overall cross-sectional shape of this beam is rectangular. When the steel beam 6 is heated for the required fire resistance time, if the wood fire-resistant coating material 7 does not stop burning before it reaches the steel, the maximum steel temperature may exceed 500°C due to the burning of the wood fire-resistant coating material 7. Therefore, the maximum steel temperature of the steel beam 6 covered with the wood fire-resistant coating material 7 must not exceed 260°C, which is the ignition temperature of wood. However, since there is a high possibility that the burning will not stop if the maximum steel temperature exceeds 150°C, it is preferable to aim for a maximum steel temperature of about 150°C in the steel beam 6 covered with the wood fire-resistant coating material 7.

JP 2016-217071 A

As shown in Figure 5 (1), when considering a frame composed of a steel member (beam 1) covered with a general fire-resistant coating material and a steel member (beam 2) covered with a wood-based fire-resistant coating material, if one were to ensure the required fire resistance time performance for each member individually, the maximum steel temperature of the steel member (beam 1) covered with a general fire-resistant coating material would be higher than that of the steel member (beam 2) covered with a wood-based fire-resistant coating material. As a result, thermal energy would transfer from the former to the latter through the joints between the two members, and there is a possibility that the maximum steel temperature of the steel member covered with the wood-based fire-resistant coating material would exceed the allowable temperature.

If the wood fire-resistant coating material does not stop burning, the maximum temperature of the steel in the steel frame members will exceed 500°C. Furthermore, if this happens, the steel frame members covered with the wood fire-resistant coating material will be unable to support the load and will be destroyed, which may ultimately lead to the collapse of the structure.

To avoid such a situation, it is necessary to properly design the type and coverage of fire-resistant coating material so that the steel temperature of steel members coated with wood-based fire-resistant coating material does not exceed the allowable temperature (150°C). To design efficiently, there was a need to be able to easily calculate the steel temperature taking into account the transfer of thermal energy through the joints between the two members.

The present invention has been made in consideration of the above, and aims to provide a steel temperature calculation method and a steel temperature calculation program that can easily calculate the steel temperature, taking into account the transfer of thermal energy through the joints between steel members covered with general fire-resistant coating material and steel members covered with wood-based fire-resistant coating material, in a structure composed of these members.

In order to solve the above problems and achieve the objective, the steel temperature calculation method of the present invention is a method for calculating the steel temperature of a steel member by taking into account heat transfer through the joints between a steel member covered with a non-wood fire-resistant coating material and a steel member covered with a wood fire-resistant coating material, and is characterized by having the steps of: calculating the maximum steel temperature of each steel member when heated for a preset required fire resistance time; setting the relationship between the steel temperature and time from the start of the fire to the required fire resistance time elapsed based on the calculated maximum steel temperature, and calculating the change in thermal conductance over time based on the set relationship; and dividing each steel member near the joint into multiple elements in the material axis direction, and calculating the steel temperature of each steel member based on the heat transfer characteristics between adjacent elements and the calculated change in thermal conductance over time.

The steel temperature calculation program according to the present invention is characterized in that it causes a computer to execute the above-mentioned steel temperature calculation method.

The steel temperature calculation method according to the present invention is a method for calculating the steel temperature of a steel member by taking into account heat transfer through the joints between a steel member covered with a non-wood fire-resistant coating material and a steel member covered with a wood fire-resistant coating material, and includes the steps of: calculating the maximum steel temperature of each steel member when heated for a preset required fire resistance time; setting the relationship between the steel temperature and time from the start of the fire to the required fire resistance time based on the calculated maximum steel temperature, and calculating the change in thermal conductance over time based on the set relationship; and dividing each steel member near the joint into multiple elements in the material axis direction, and calculating the steel temperature of each steel member based on the heat transfer characteristics between adjacent elements and the change in calculated thermal conductance over time. This has the effect of making it possible to easily calculate the steel temperature by taking into account the transfer of thermal energy through the joints.

FIG. 1 is a beam plan to which an embodiment of a steel material temperature calculation method and a steel material temperature calculation program according to the present invention is applied. Figure 2 shows an example of a calculation, where (1) is a beam plan, (2) is a division diagram of the steel beam within the calculation range into sub-components, and (3) is a list of the fire-resistant coating conditions in the calculation example. FIG. 3 is a diagram showing the calculation results of calculation example 1. In FIG. FIG. 4 is a diagram showing the calculation results of the calculation example 2. In FIG. FIG. 5 (1) is a conventional beam plan, (2) and (3) are cross-sectional views of beam 1, (4) is a cross-sectional view of beam 2, and (5) is a parameter table described in Reference Material 1.

Below, an embodiment of the steel temperature calculation method and steel temperature calculation program according to the present invention will be described in detail with reference to the drawings. Note that the present invention is not limited to this embodiment.

First, an example of a frame to which a steel temperature calculation method according to an embodiment of the present invention is applied is shown in FIG.
FIG. 1 ( 1 ) shows an example in which the end portion near the joint of a steel frame member 12 covered with a wood fire-resistant covering material 16 is covered with a general fire-resistant covering material 14 that is thicker than the steel frame member 10 .
FIG. 1 (2) shows an example in which at a joint between a steel member 10 covered with a general fire-resistant coating material 14 and a steel member 12 covered with a wood-based fire-resistant coating material 16, the thickness of the general fire-resistant coating material 14 near the joint of the steel member 10 is made thicker than the thickness in the area away from the joint.
5. The steel frame member 10 corresponds to the beam 1 in FIG. 5, and the steel frame member 12 corresponds to the beam 2 in FIG.

The steel temperature calculation method in this embodiment includes step 1 of calculating the maximum steel temperature of each steel member 10, 12 alone when heated for a predetermined required fire resistance time; step 2 of setting a relationship between the steel temperature and time from the start of the fire to the elapse of the required fire resistance time based on the calculated maximum steel temperature, and calculating the change in thermal conductance over time based on the set relationship; and step 3 of dividing each steel member 10, 12 in the vicinity of the joint into a number of small elements in the material axis direction, and calculating the steel temperature of each steel member based on the heat transfer characteristics between adjacent small elements and the calculated change in thermal conductance over time.
Next, the specific processing contents of steps 1 to 3 will be described.

(Step 1: Calculate the maximum temperature of the steel of a single beam)
First, the maximum temperature of the steel material of each component when heated for the required fire resistance time is calculated using the following formulas (1) to (3) shown in the fire resistance performance verification method described in Reference 1 below.

[Reference 1] Ministry of Land, Infrastructure, Transport and Tourism, Housing Bureau, Building Guidance Division, et al., "Explanation of the 2001 Edition Fire Resistance Verification Method and Calculation Examples and Explanations," March 2001.

Here,
_Ts : Maximum steel temperature (℃), _T0 : Initial steel temperature α: Fire temperature rise coefficient (℃min ^1/6 )
t: Fire duration (min)
h: component temperature rise coefficient (min ^-1 )
_tw : Temperature rise delay time (min)
φ: H _i /H _s (perimeter ratio of the coating material to the steel material in the heated portion)
C: _{ρici / ρscs} (heat capacity _ratio of coating material and steel material), _ρs : density of steel material 7860 (kg/ ^m3 ), _cs : specific heat of steel material 442 (J/(kg·K)), density of coating material (kg/ ^m3 ), specific heat of coating material (J/(kg·K))
R: _ht / _λi (thermal resistance coefficient (m ^-1 )), _ht : overall heat transfer coefficient between the steel surface and the fire space (W/ ^m2K ), _λi : thermal conductivity of the coating material (W/(m·K)).
K ₀ : Base temperature rise rate (m/min)
α _w : Temperature rise delay time coefficient (min/m ² )
H: perimeter of the part subjected to heat (m), subscript s: steel material, subscript i: coating material A: cross-sectional area ( ^m2 ), subscript s: steel material, subscript i: coating material Note that for the above C, R, _K0 , and _αw , the values given in Figure 5 (5) are used.

(Step 2: Calculating thermal conductance)
Next, the steel temperature at 0 minutes before the start of the fire is set to 20°C, and the steel temperature at the end of the required fire resistance time is set to the maximum steel temperature obtained in step 1 above.Assume that the steel temperature-time relationship is a linear relationship in which a straight line connects the coordinates (0 minutes, 20°C) and (maximum steel temperature at the end of the required fire resistance time).

From the above steel temperature-time relationship, the change in thermal conductance over time is calculated, which is the sum of the heat transfer coefficient of the steel surface and the thermal conductivity of the coating material. Specifically, the thermal conductance-time relationship is calculated by sequentially calculating the following formula (4).

U _i+1 = {(c _s ×ρ _s ×V _s )×(T _s,i+1 −T _s,i )}/{H _s ×(T _f,i+1 −T _s,i )× (t _i+1 −t _i )×60} ...(4)

Here,
U: Thermal conductance (W/( ^m2 ·K))
c _s : Specific heat of steel (= 442 J/(kg・K))
ρ _s : Density of steel material (=7860kg/m ³ )
_Vs : Volume per unit length of steel member ( ^m3 )
_Ts : Steel temperature (℃)
_Hs : Heated area per unit length of steel member ( ^m2 )
_Tf : Heating temperature (℃)
t: time (minutes)
i, i+1: time step

(Step 3: Calculate the steel temperature of the members in the partial structure)
Next, the longitudinal direction of the steel members constituting the partial frame is divided into elements, and the thermal conductance obtained in step 2 above is used to calculate the steel temperature of the steel members in the partial frame by sequential calculation of the following equation (5).

T _s,j,i+1 =T _s,j,i +ΔT _s,j,i+1 ...(5)
ΔT _s,j,i+1 = {(Q _f→s,j +ΣQ _s,j+n→s,j )×(t _i+1 −t _i )×60}/(c _s ×ρ _s ×V _s,j ×L _s,j )
Q _f→s,j ＝U _j,i+1 ×H _s,j ×L _s,j ×(T _f,i+1 −T _s,j,i )
Q _s,j+n→s,j =λ _s ×A _s,j-j+n ×(T _s,j+n,i −T _s,j,i )／{(L _s,j+n +L _s,j )／2}

Here,
ΔT _s,j,i+1 : Temperature rise of the steel of the sub-member j (from time step i to i+1) (℃)
Q _f→s,j : Amount of heat flowing into small component j per unit time due to fire (W)
Q _s,j+n→s,j : Amount of heat flowing from adjacent sub-component j+n to sub-component j per unit time (W)
L _s,j : Length of sub-member j when the steel member is divided in the longitudinal direction (m)
λ _s : Thermal conductivity of steel (40W/(m・K))
A _s,j-j+n : Cross-sectional area at the boundary between submember j and adjacent submember j+n (m ² )
j: Element number of the small member when the steel member is divided in the length direction
j+n: Element number of the sub-member adjacent to sub-member j when dividing the steel member in the longitudinal direction

According to this embodiment, it is possible to easily predict the coating specifications (type and coverage of fire-resistant coating material) for preventing the steel temperature of the steel member coated with wood-based fire-resistant coating material from exceeding the allowable temperature (e.g., 150°C) at the joint between a steel member coated with a general fire-resistant coating material and a steel member coated with wood-based fire-resistant coating material. By using this calculation method at the joint design stage, the type and coverage of fire-resistant coating material can be easily determined.

The steel temperature calculation method of the above embodiment can be executed in the form of a steel temperature calculation program configured to cause a computer to execute each of the above steps 1 to 3. This steel temperature calculation program may be recorded on a computer-readable recording medium so that it can be used as needed. It can also be easily executed on a spreadsheet in a spreadsheet software running on a computer.

(Example)
Figure 2 is a beam plan of a steel beam used as a calculation example. The convex shaded area in Figure 2(1) was the subject of calculation. As shown in Figure 2(2), the calculation range of the main girder was divided into 9 parts by sub-members with a length of 100 mm, and the calculation range of the sub-beam was also divided into 10 parts by sub-members with a length of 100 mm. The fireproof coating conditions for the main girder and sub-beam were set as shown in Figure 2(3). The main girder corresponds to the steel member 10 in Figure 1(1), and the sub-beam corresponds to the steel member 12 in Figure 1(1).

[Calculation Example 1]
This calculation example 1 is calculated under the conditions of heating for 1 hour and covering the girder with sprayed rock wool (t = 25 mm). The calculation results of the maximum steel temperature of a single beam are as follows.

Beam: 320℃
Small beam: 111℃

Regarding the results of the thermal conductance calculations, the assumed steel temperature-time relationship of the main and secondary beams is shown in Figure 3 (1), and the results of the thermal conductance calculations are shown in Figure 3 (2).

As a result of calculating the steel temperature of the members in the partial frame, the relationship between the steel temperature of the main girder and time is shown in Figure 3 (3), and its enlarged view is shown in Figure 3 (4). The relationship between the steel temperature of the sub-beam and time is shown in Figure 3 (5), and its enlarged view is shown in Figure 3 (6). The maximum steel temperature distribution in the axial direction of the beam is shown in Figure 3 (7). The temperature of sub-member G5 corresponds to the steel temperature of the main girder at the joint with the sub-beam. The temperature of sub-member B1 corresponds to the steel temperature of the sub-beam at the joint with the main girder.

The results of this calculation show that in order to keep the steel temperature of the minor beam below the allowable temperature of 150°C, the range of fire-resistant coating for the minor beam should be 200 mm, preferably 300 mm, from the joint with the main beam, covered with a "box covering made of two layers of 25 mm thick calcium silicate boards."

The area at least 200 mm, preferably at least 300 mm, away from the joint with the girder can be covered with a wood-based fire-resistant covering material. The wood-based fire-resistant covering material can be made of, for example, Japanese cypress, larch, or cedar, and the covering thickness can be set to, for example, about 50 to 80 mm.

[Calculation Example 2]
Calculation example 2 was performed under the conditions of heating for 2 hours and covering the main girder with calcium silicate plate (t = 35 mm). The calculation results of the maximum steel temperature of the single beam are as follows.

Beam: 359℃
Small beam: 121℃

Regarding the results of the thermal conductance calculations, the assumed steel temperature-time relationship of the main and secondary beams is shown in Figure 4 (1), and the results of the thermal conductance calculations are shown in Figure 4 (2).

As a result of calculating the steel temperature of the members in the partial frame, the relationship between the steel temperature of the main girder and time is shown in Figure 4 (3), and its enlarged view is shown in Figure 4 (4). The relationship between the steel temperature of the secondary beam and time is shown in Figure 4 (5), and its enlarged view is shown in Figure 4 (6). The maximum steel temperature distribution in the axial direction of the beam is shown in Figure 4 (7). The temperature of secondary beam G5 corresponds to the steel temperature of the main girder at the joint with the secondary beam. The temperature of secondary beam B1 corresponds to the steel temperature of the secondary beam at the joint with the main girder.

The results of this calculation show that in order to keep the steel temperature of the minor beam below the allowable temperature of 150°C, the range of fireproofing for the minor beam should be 350 mm, preferably 400 mm, from the joint with the main beam, covered with a "box covering of two layers of 35 mm thick calcium silicate boards."

The area 350 mm or more, preferably 400 mm or more away from the joint with the girder, can be covered with a wood-based fire-resistant covering material. The wood-based fire-resistant covering material can be made of, for example, Japanese cypress, larch, or cedar, and the covering thickness can be set to, for example, about 125 to 200 mm.

As described above, the steel temperature calculation method according to the present invention is a method for calculating the steel temperature of a steel member by taking into account heat transfer through the joints between a steel member covered with a non-wood fire-resistant coating material and a steel member covered with a wood fire-resistant coating material, and includes the steps of: calculating the maximum steel temperature of each steel member when heated for a preset required fire resistance time; setting the relationship between the steel temperature and time from the start of the fire to the required fire resistance time based on the calculated maximum steel temperature, and calculating the change in thermal conductance over time based on the set relationship; and dividing each steel member near the joint into multiple elements in the material axis direction, and calculating the steel temperature of each steel member based on the heat transfer characteristics between adjacent elements and the change in calculated thermal conductance over time. This makes it possible to easily calculate the steel temperature by taking into account the transfer of thermal energy through the joints.

As described above, the steel temperature calculation method and steel temperature calculation program of the present invention are useful for designing structures in which steel members covered with general fire-resistant coating material are joined to steel members covered with wood-based fire-resistant coating material, and are particularly suitable for easily calculating steel temperatures taking into account the transfer of thermal energy through the joints.

10, 12 Steel frame members 14 General fireproof covering material 16 Wooden fireproof covering material

Claims (2)

A method for calculating the temperature of steel members in a steel frame member by taking into consideration heat transfer through a joint between a steel member covered with a non-wood-based fire-resistant coating material and a steel member covered with a wood-based fire-resistant coating material, comprising:
A step of calculating a maximum steel temperature of each steel member when heated for a predetermined required fire resistance time;
A step of setting a relationship between the steel temperature and time from the start of the fire to the required fire resistance time based on the calculated maximum steel temperature, and calculating a change in thermal conductance over time based on the thermal conductivity using the set relationship;
A steel temperature calculation method comprising the steps of: dividing each steel member near a joint into a plurality of elements in the material axis direction; and calculating the steel temperature of each steel member based on the heat transfer characteristics between adjacent elements and the change over time in the calculated thermal conductance. A steel temperature calculation program that causes a computer to execute the steel temperature calculation method described in claim 1.

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