Method for calculating bearing capacity of longitudinally cracked wood-bamboo beam under fire

Abstract

The invention discloses a method for calculating the bearing capacity of a longitudinally cracked wood-bamboo beam in a fire disaster, which comprises the following steps: S1, measuring the depth d and width w of a longitudinal crack of the wood-bamboo beam, and measuring the distances hT and hB from the crack to the upper edge and the lower edge; s2, determining the size of the remaining section and the size of the crack after the wood-bamboo beam with the three fire surfaces is burnt at the fire time t; and S3, the bending failure limit load of the wood-bamboo beam with the three faces subjected to fire at the fire time t, the crack critical index of changing bending failure into rift-grain shear failure and the residual bending failure limit load after rift-grain shear failure occur are calculated, and finally the bearing capacity of the wood-bamboo beam with the three faces subjected to fire considering the longitudinal cracking influence is determined. According to the method, the influence of cracking on the bearing capacity of the wood-bamboo beam in the fire disaster is considered, and compared with an existing method for determining the bearing capacity of a non-cracked wood-bamboo beam in the fire disaster, the calculation precision is higher.

Description

Technical Field

[0001] The invention relates to the field of construction, and in particular to a method for calculating the bearing capacity of a longitudinally cracked wood-bamboo beam under fire. Background Art

[0002] Wood-bamboo structure is one of the most important structural forms of traditional Chinese architecture. Compared with other structural forms, wood-bamboo structure has the advantages of simple construction, short construction period, energy saving, environmental protection, and good earthquake resistance. Since wood and bamboo are combustible materials, the fire resistance of wood-bamboo structure has always been a concern. After the fire, the bearing capacity of wood-bamboo components gradually deteriorates, causing partial damage to the structure or even the collapse of the entire structure. Therefore, accurately calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire is an important issue to ensure the fire safety of wood-bamboo structures.

[0003] Since wood and bamboo are biomass materials, during the processing, production and use of wood and bamboo materials, they are affected by external temperature and humidity, and the internal and external shrinkage of wood and bamboo fibers is inconsistent, and they separate from each other along the longitudinal direction to produce longitudinal shrinkage cracks. As time goes by, the mechanical properties of wood and bamboo materials decrease under the action of external loads, and the shrinkage cracks continue to deepen and widen, becoming a hidden danger affecting the safety performance of components and the entire structure. At present, there is no calculation method for the bearing capacity of wood and bamboo beams under fire that takes into account the influence of longitudinal cracking. Summary of the invention

[0004] In view of the above-mentioned defects of the prior art, the present invention aims to propose a scientific, accurate and effective method for calculating the bearing capacity of longitudinally cracked bamboo beams under fire. The calculation method can be applied to the calculation of the bearing capacity of longitudinally cracked bamboo beams under fire, providing theoretical support for the evaluation of the fire resistance performance of longitudinally cracked bamboo beams.

[0005] To achieve the above objectives, the present invention provides a method for calculating the bearing capacity of a longitudinally cracked wood-bamboo beam under fire, which comprises the following steps:

[0006] S1: Measure the depth d and width w of the longitudinal cracks in the wood-bamboo beam, and the distance h from the cracks to the upper and lower edges T and h B ;

[0007] S2: Determine the remaining cross-sectional dimensions and crack dimensions of the three-sided fire-exposed wood and bamboo beam after burning at time t;

[0008] S3: Calculate the ultimate bending failure load of the wood-bamboo beam exposed to fire on three sides at time t, the critical crack index for the change from bending failure to shear failure along the grain, and the ultimate bending failure load remaining after shear failure along the grain occurs, and finally determine the bearing capacity of the wood-bamboo beam exposed to fire on three sides considering the influence of longitudinal cracking.

[0009] A further improvement of the present invention is that step S2 specifically includes: the remaining cross-sectional width b(t)=b-2def , height h(t) = hd ef ; In the formula, d ef is the effective carbonization depth of wood and bamboo beams;

[0010] The crack depth after combustion is d(t)=d, and the expression of width w(t) is:

[0011]

[0012] Distance h from the crack to the upper edge T (t) = h T , distance from the lower edge h B (t) = h B -d ef .

[0013] A further improvement of the present invention is that in step S2: the effective carbonization depth d of the wood-bamboo beam is ef =1.2β n t 0.813 , where β n is the carbonization speed, which is determined according to the type of wood and bamboo; t is the fire exposure time

[0014] A further improvement of the present invention is that in step S3, the bending failure limit load F of the wood-bamboo beam exposed to fire on three sides at time t is m The calculation formula of (t) is:

[0015]

[0016] In the formula, I x (t) is the cross-sectional bending moment calculated based on the remaining cross-sectional dimensions of the three-sided fire-exposed wood-bamboo beam after burning at time t, y max is the larger value of the distance between the centroid of the remaining cross section after combustion and the upper edge and the lower edge, f m is the bending strength of wood and bamboo along the grain, and L1 is the distance between the loading point and the support.

[0017] A further improvement of the present invention is that the cross-section bending resistance moment I x (t) and the larger value y of the distance between the centroid of the remaining cross section after combustion and the upper edge and the lower edge max It is determined by using the face region characteristic query function in AutoCAD software.

[0018] A further improvement of the present invention is that in step S3, the expression of the critical crack index ψ(t) for the three-sided fire-exposed wood-bamboo beam to change from bending failure to shear failure along the grain at time t is:

[0019]

[0020] In the formula, fc 、f v They are the compressive strength and shear strength along the grain of wood and bamboo respectively; a is the distance from the support to the free end.

[0021] A further improvement of the present invention is that in step S3, the fire time is the time t at which the three-sided fire-exposed wood-bamboo beam undergoes shear failure along the grain and the remaining bending failure limit load F mv The expression of (t) is:

[0022]

[0023] A further improvement of the present invention is that in step S3, the bearing capacity of the three-sided fire-exposed wood-bamboo beam considering the influence of longitudinal cracking at the time t is expressed as:

[0024]

[0025] Where: F(t) is the bearing capacity.

[0026] The advantages of the present invention are as follows: the method of the present invention takes into account the influence of cracking on the bearing capacity of wood-bamboo beams under fire, and has higher calculation accuracy than the existing determination method of the bearing capacity of wood-bamboo beams under fire that only considers uncracked wood-bamboo beams. The method of the present invention can provide an accurate theoretical reference in the design process of bamboo-wood buildings, thereby increasing the time that wood-bamboo beams can maintain structural integrity under fire conditions, facilitating architectural designers to optimize designs and improve the fire resistance of buildings. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The present invention is a flowchart of a method for calculating the bearing capacity of a longitudinally cracked wood-bamboo beam under fire according to an embodiment of the present invention.

[0028] Figure 2 It is a schematic diagram of the remaining cross-section of a rectangular cracked wooden beam when three sides are exposed to fire in a method for calculating the bearing capacity of a longitudinally cracked wooden or bamboo beam under fire according to an embodiment of the present invention.

[0029] Reference numerals:

[0030] 1——Carbonized layer,

[0031] 2——Cracks before burning,

[0032] 3——Cracks after burning,

[0033] 4——Remaining cross section after combustion. DETAILED DESCRIPTION

[0034] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0035] While some exemplary embodiments of the present invention have been described for the purpose of illustration, it should be understood that the present invention may be implemented in other ways not specifically shown in the drawings.

[0036] The present invention is described in detail below in conjunction with specific embodiments. Figure 2 Take the rectangular wooden beam with three sides exposed to fire as an example. The cross-sectional size of a wooden beam of a historical building is 200mm×300mm, the distance between the support and the free end is 100mm, and the distance between the loading point and the support is 1000mm. The wooden beam is exposed to fire on three sides for 0.5 hours. n =38mm / h, the bending strength, compressive strength, tensile strength and shear strength of the wood along the grain are 42.9MPa, 27.5MPa, 71.9MPa and 7.7MPa respectively.

[0037] according to Figure 1 The calculation steps for the bearing capacity after 0.5 hours of fire are as follows:

[0038] Step S1: Measure the depth d = 55 mm and width w = 15 mm of the longitudinal cracks on the two sides of the wood-bamboo beam, and measure the distance h from the upper and lower edges of the cracks. T =150mm and h B =150mm;

[0039] Step S2: Determine the remaining cross-sectional dimensions of the wood-bamboo beam after burning on three sides for 0.5 hours ( Figure 2 The area indicated by reference numeral 4 in the figure).

[0040] d ef =1.2β n t 0.813 =26mm

[0041] b(t)=b-2d ef =148mm

[0042] h(t)=hd ef =274mm

[0043] After burning, the crack depth d(t) = 55 mm, the width Distance from upper edge hT (t) = h T =150mm, distance from the lower edge h B (t) = h B -d ef =124mm.

[0044] Step S3.1: Calculate the ultimate bending failure load F of the wood-bamboo beam exposed to fire on three sides at time t m (t) I x (t) and y max By querying the surface characteristics in AutoCAD software, you can quickly determine:

[0045] I x (t) = 2.6 × 10 8 mm 4

[0046] y max =150mm

[0047]

[0048] Step S3.2: Calculate the critical crack index of the three-sided fire-exposed wood-bamboo beam at time t when the bending failure changes to shear failure along the grain:

[0049]

[0050] Step S3.3: Calculate the residual bending failure limit load after the three-sided fire-exposed wood-bamboo beam undergoes shear failure along the grain at time t

[0051] Step S6: Calculate the bearing capacity of the three-sided fire-exposed wood-bamboo beam considering the influence of longitudinal cracking at time t:

[0052]

[0053] F(t)=max(η(t)F m (t),F mv (t))=111.54kN.

[0054] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A method for calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire, characterized in that: The following steps are involved: S1: Measure the depth d and width w of the longitudinal cracks in the wood-bamboo beam, and the distance h from the cracks to the upper and lower edges T and h B ; S2: Determine the remaining cross-sectional dimensions and crack dimensions of the three-sided fire-exposed wood and bamboo beam after burning at time t; S3: Calculate the ultimate bending failure load of the wood-bamboo beam exposed to fire on three sides at time t, the critical crack index for the change from bending failure to shear failure along the grain, and the ultimate bending failure load remaining after shear failure along the grain occurs, and finally determine the bearing capacity of the wood-bamboo beam exposed to fire on three sides considering the influence of longitudinal cracking.

2. The method for calculating the bearing capacity of longitudinally cracked bamboo beams under fire according to claim 1 is characterized in that: Step S2 specifically includes: remaining section width b(t)=b-2d ef , height h(t) = hd ef ; In the formula, d ef is the effective carbonization depth of wood and bamboo beams; The crack depth after combustion is d(t)=d, and the expression of width w(t) is: Distance h from the crack to the upper edge T (t) = h T , distance from the lower edge h B (t) = h B -d ef .

3. The method for calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire according to claim 2 is characterized in that: In step S2: effective carbonization depth d of wood-bamboo beam ef =1.2β n t 0.813 , where β n is the carbonization speed, which is determined according to the type of wood and bamboo; t is the fire exposure time.

4. The method for calculating the bearing capacity of longitudinally cracked bamboo beams under fire according to claim 2, characterized in that: In step S3, the bending failure limit load F of the three-sided fire-exposed wood-bamboo beam at time t is m The calculation formula of (t) is: In the formula, I x (t) is the cross-sectional bending moment calculated based on the remaining cross-sectional dimensions of the three-sided fire-exposed wood-bamboo beam after burning at time t, y max is the larger value of the distance between the centroid of the remaining cross section after combustion and the upper edge and the lower edge, f m is the bending strength of wood and bamboo along the grain, and L1 is the distance between the loading point and the support.

5. A method for calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire according to claim 4, characterized in that: Section bending resistance moment I x (t) and the larger value y of the distance between the centroid of the remaining cross section after combustion and the upper edge and the lower edge max This is determined by using the face region feature query function in AutoCAD software.

6. The method for calculating the bearing capacity of longitudinally cracked bamboo beams under fire according to claim 4, characterized in that: In step S3, the expression of the critical crack index ψ(t) of the three-sided fire-exposed wood-bamboo beam at time t, which changes from bending failure to shear failure along the grain, is: In the formula, f c 、f v They are the compressive strength and shear strength along the grain of wood and bamboo respectively; a is the distance from the support to the free end.

7. A method for calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire according to claim 6, characterized in that: In step S3, the fire time is the time t when the three-sided fire-exposed wood-bamboo beam undergoes shear failure along the grain and the remaining bending failure limit load F mv The expression of (t) is:

8. The method for calculating the bearing capacity of longitudinally cracked wood-bamboo beams under fire according to claim 7, characterized in that: In step S3, the bearing capacity of the three-sided fire-exposed wood-bamboo beam considering the influence of longitudinal cracking at time t is expressed as: Where: F(t) is the bearing capacity.

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