Method for calculating up-down eccentric arrangement of shear wall with variable wall thickness

Abstract

The invention discloses a calculation method for up-down eccentric arrangement of a shear wall with variable wall thickness. The calculation method comprises the steps of stress analysis and reinforcement calculation. According to the method, when shear walls with different section thicknesses are eccentrically arranged up and down, the out-of-plane eccentric compression bearing capacity needs to be rechecked and calculated, so that the situation that a bottom-layer wall body and a thin wall body are more difficult to meet can be noticed, and the variable quantity when the wall thickness changes in daily design can also be determined; the position where the wall thickness changes is determined as far as possible at the positions where the floors are located on the two sides, it is also determined that the hogging moment of the support can be increased when the upper portion of the non-flush side floor connected with the wall thickness changing position is pulled, and the lower portion of the flush side floor connected with the wall thickness changing position is pulled, so that a pressed area at the support becomes a pulled area. The numerical value and the anchoring length of the lower reinforcing steel bars of the floor are rechecked, potential safety hazards caused by neglect are eliminated, and the building safety is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of shear walls, and particularly to a calculation method for eccentric arrangement of upper and lower shear walls with variable wall thicknesses. Background Art

[0002] Due to various reasons, such as axial compression ratio limitations, overall lateral stiffness requirements, building functions, etc., the cross-sectional thickness of shear walls may vary up and down. When shear walls with different wall thicknesses are centered vertically, the shear wall is axially compressed out of the plane, and it can be calculated as an axially compressed member. When shear walls with different wall thicknesses are eccentrically arranged vertically with one side flush, how to handle this situation? Article 7.1.9 of the "Technical Specification for Concrete Structures of High-Rise Buildings" JGJ3-2010 stipulates: "Shear walls should be checked for the shear capacity of the inclined section in the plane, eccentric compression or eccentric tension, and the bearing capacity of axial compression out of the plane. Under the action of concentrated loads, the bearing capacity of local compression should also be checked when there is no concealed column in the wall." For the actual situation of eccentric compression of shear walls out of the plane, there is no requirement for calculating the bearing capacity of eccentric compression out of the plane. The current mainstream building software also does not consider this. If this is ignored, there will be certain potential safety hazards. Summary of the Invention

[0003] Aiming at the deficiencies of the existing technology, the present invention provides a calculation method for eccentric arrangement of upper and lower shear walls with variable wall thicknesses, which is used to solve the problem that the existing technology does not consider the situation of eccentric compression of shear walls out of the plane, resulting in certain potential safety hazards.

[0004] To solve the above technical problems, the present invention provides the following technical solutions:

[0005] A calculation method for eccentric arrangement of upper and lower shear walls with variable wall thicknesses, including force analysis and reinforcement calculation;

[0006] S1. Force analysis:

[0007] Let the thickness of the upper wall be t1, the storey height be H1, the thickness of the lower wall be t2, the storey height be H2, the thickness of the floor slab on the non-flush side connected to the location of the wall thickness change be t3, the span of the corresponding floor slab be L1, the thickness of the floor slab on the flush side connected to the location of the wall thickness change be t4, the span of the corresponding floor slab be L2, and the eccentricity between the centerlines of the upper and lower walls be e;

[0008] Let the unit length axial force acting on the centerline of the upper wall transmitted from the root of the upper wall be N, and the moment M generated by the axial force of the upper wall on the lower wall be M = Ne;

[0009] Take the node at the location of the cross-sectional thickness change as the research object for force balance analysis. i1, i2, i3, and i4 are the linear stiffnesses of the upper and lower walls, the non-flush side and the flush side floor slabs at the cross-sectional change location respectively:

[0010] i1=E1l1 / H1=E1bt1 3 / (12H1)

[0011] i2=E2l2 / H2=E2bt2 3 / (12H2)

[0012] i3=E3l3 / L=E3bt3 3 / (12L1)

[0013] i4=E3l4 / L=E3bt4 3 / (12L2)

[0014] When the far ends of the members are rigidly connected, according to the moment distribution principle and the node equilibrium condition, it is obtained:

[0015] M=M1+M2+M3+M4

[0016] M1=Mi1 / (i1+i2+i3+i4)=Nei1 / (i1+i2+i3+i4) (left side of the wall is under tension)

[0017] M2=Mi2 / (i1+i2+i3+i4)=Nei2 / (i1+i2+i3+i4) (the right side of the wall is under tension)

[0018] M3=Mi3 / (i1+i2+i3+i4)=Nei3 / (i1+i2+i3+i4) (the upper part of the floor slab is under tension)

[0019] M4=Mi4 / (i1+i2+i3+i4)=Nei4 / (i1+i2+i3+i4) (the lower part of the floor is under tension)

[0020] The internal forces at the root section aa of the upper wall are bending moment M1 and axial force N;

[0021] The internal forces at the top section bb of the lower wall are bending moment M2 and axial force N;

[0022] In addition to the normal negative bending moment, the floor slab connected to the wall where the wall thickness changes has additional bending moments M3 and M4 caused by the eccentricity of the upper and lower walls at the wall supports;

[0023] S2. Reinforcement calculation:

[0024] The vertical reinforcement values of the upper and lower walls are calculated based on the eccentrically compressed members with symmetrical reinforcement according to M1, N and M2, N. If the calculated value is 0 or less than the reinforcement value calculated based on the minimum reinforcement ratio of the wall distributed reinforcement, the reinforcement can be arranged according to the structural requirements.

[0025] At the non - flush side floor slab connected to the location with wall thickness change, the reinforcement value at the wall support is equal to the sum of the calculated value of the negative moment reinforcement under the action of the floor vertical load and the reinforcement value calculated from the additional moment M3 generated by the eccentricity of the upper and lower walls. If the reinforcement value calculated from the sum of the two is less than the calculated value of the minimum reinforcement ratio of the flexural member, then it is reinforced according to the structure.

[0026] Under the action of the floor vertical load, the lower part of the floor slab at the support is in the compression zone, and the calculated reinforcement is 0. Therefore, the lower reinforcement value of the flush side floor slab connected to the location with wall thickness change at the wall support is equal to the reinforcement value calculated from the additional moment M4 generated by the eccentricity of the upper and lower walls. If this value is less than the positive moment reinforcement value in the middle of the floor slab span, then no additional reinforcement is required and it can be extended from the positive moment reinforcement in the middle of the span. If this value is greater than the positive moment reinforcement value in the middle of the floor slab span, then the reinforcement should be provided according to this value, and additional reinforcement should be added on the basis of the positive moment reinforcement in the middle of the span within one - third of the slab span at the support side.

[0027] Preferably, the axial forces N1 transmitted from the floor slabs on both sides of the section change to the lower - layer wall and acting on the center line of the lower - layer wall are much smaller than N, and the influence of N1 is ignored, and N1 is not considered in the calculation.

[0028] Preferably, when there is no floor slab on the flush side of the wall, take t4 = 0 in the above formula.

[0029] Preferably, when there are no floor slabs on both sides of the wall or the influence of the floor slab stiffness is ignored, take t3 = 0 and t4 = 0 in the above formula.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] When the shear walls with different cross - section thicknesses are arranged eccentrically up and down in the present invention, the out - of - plane eccentric compression bearing capacity should be checked and calculated. Thus, it can be noted that the bottom - layer walls and thinner walls are more difficult to meet the requirements, and the change amount during the wall thickness change in daily design can also be clarified. It is determined that the position of the wall thickness change should be preferably selected at the place where there are floor slabs on both sides. It is also determined that the upper part of the non - flush side floor slab connected to the location with wall thickness change is in tension, which will increase the negative moment at the support, and the lower part of the flush side floor slab connected to the location with wall thickness change is in tension, making the compression zone at the support become the tension zone. This ensures the check of the lower - layer steel bar numerical value and the anchorage length of the floor slab, eliminates the potential safety hazards caused by neglect, and improves the building safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic cross - section view of the wall of the present invention;

[0033] Figure 2 It is a schematic diagram of the joint moment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0034] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0035] As Figure 1-2 shown, the present invention provides a technical solution: a calculation method for eccentric arrangement of upper and lower shear walls with varying wall thickness, including force analysis and reinforcement calculation;

[0036] S1. Force analysis:

[0037] Let the thickness of the upper wall be t1, the storey height be H1, the thickness of the lower wall be t2, the storey height be H2, the thickness of the non-parallel side floor connected to the wall thickness change be t3, the span of the corresponding floor be L1, the thickness of the parallel side floor connected to the wall thickness change be t4, and the eccentricity between the center lines of the upper and lower walls be e;

[0038] Let the unit length axial force acting on the center line of the upper wall transmitted from the root of the upper wall be N, and the axial forces transmitted from the left and right sides of the section change to the lower wall and acting on the center line of the lower wall be N1. N1 is much smaller than N, and the influence of N1 is ignored. N1 is not considered in the calculation, and the bending moment M generated by the axial force of the upper wall on the lower wall is M = Ne;

[0039] Take the node at the section thickness change as the research object for force balance analysis. i1, i2, i3, and i4 are the linear stiffnesses of the upper and lower walls, the non-parallel side and the parallel side floors at the section change respectively:

[0040] i1 = E1l1 / H1 = E1bt1 3 / (12H1)

[0041] i2 = E2l2 / H2 = E2bt2 3 / (12H2)

[0042] i3 = E3l3 / L = E3bt3 3 / (12L1)

[0043] i4 = E3l4 / L = E3bt4 3 / (12L2)

[0044] Under the condition that the far ends of the members are all rigidly connected, according to the principle of moment distribution method and the node balance condition, it can be obtained that:

[0045] M = M1 + M2 + M3 + M4

[0046] M1 = Mi1 / (i1 + i2 + i3 + i4) = Nei1 / (i1 + i2 + i3 + i4) (the left side of the wall is in tension)

[0047] M2 = Mi2 / (i1 + i2 + i3 + i4) = Nei2 / (i1 + i2 + i3 + i4) (the right side of the wall is in tension)

[0048] M3 = Mi3 / (i1 + i2 + i3 + i4) = Nei3 / (i1 + i2 + i3 + i4) (the upper part of the floor slab is in tension)

[0049] M4 = Mi4 / (i1 + i2 + i3 + i4) = Nei4 / (i1 + i2 + i3 + i4) (the lower part of the floor slab is in tension)

[0050] The internal forces at the cross-section a-a of the root of the upper wall are the bending moment M1 and the axial force N;

[0051] The internal forces at the cross-section b-b of the top of the lower wall are the bending moment M2 and the axial force N;

[0052] In addition to the normal negative bending moment, there are additional bending moments M3 and M4 generated by the eccentricity of the upper and lower walls at the support of the floor slab connected to the wall where the wall thickness changes;

[0053] When there is no floor slab on one side of the wall where the walls are flush, take t4 = 0 in the above formula;

[0054] When there is no floor slab on both sides of the wall or the influence of the floor slab stiffness is ignored, take t3 = 0 and t4 = 0 in the above formula;

[0055] S2, reinforcement calculation:

[0056] The calculated values of the vertical steel bars of the upper and lower walls are obtained by calculating the eccentrically compressed members with symmetric reinforcement according to M1, N and M2, N. If the calculated value is 0 or less than the reinforcement value calculated according to the minimum reinforcement ratio of the wall body distribution steel bars, the reinforcement can be arranged according to the structural requirements;

[0057] The reinforcement value at the support of the non-flush side floor slab connected to the wall where the wall thickness changes is equal to the sum of the calculated value of the negative bending moment steel bars under the action of the vertical floor load and the calculated value of the reinforcement for the additional bending moment M3 generated by the eccentricity of the upper and lower walls. If the reinforcement value calculated according to the sum of the two is less than the calculated value of the minimum reinforcement ratio of the flexural member, the reinforcement is arranged according to the structure;

[0058] Under the action of vertical floor loads, the lower part of the floor slab at the support is in the compression zone and the calculated reinforcement is 0. Therefore, the reinforcement value at the lower part of the flat side floor slab connected to the wall thickness change at the wall support is equal to the reinforcement value calculated according to the additional moment M4 generated by the eccentricity of the upper and lower walls. If this value is less than the positive moment reinforcement value in the middle of the floor slab span, no additional reinforcement is required and it can be extended from the positive moment reinforcement in the middle of the span. If this value is greater than the positive moment reinforcement value in the middle of the floor slab span, the reinforcement needs to be provided according to this value, and additional reinforcement needs to be added on the basis of the positive moment reinforcement in the middle of the span within one-third of the slab span at the support side.

[0059] Using the function of EXCEL, an automated calculation table is compiled, and walls with cross-section changes at different positions are selected for calculation. After repeated trial calculations, it is finally determined that the wall thickness change does not exceed 50mm each time, gradually transitioning from 250mm to 350mm. In this way, the distributed reinforcement of the shear walls in the upper and lower layers at the cross-section change is configured according to the structure, and the floor slab reinforcement can also be configured according to the reinforcement under vertical loads. The results are as follows in the table:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] In a certain residential community project, the above results are used to conduct a check and calculation of the out-of-plane eccentric compression bearing capacity of the shear walls with wall thickness changes. See the following table:

[0066]

[0067]

[0068] Obviously, the calculated reinforcement value of the root section of the upper wall is 981mm 2 , and Φ14@150 must be configured, which is much larger than the conventional wall distributed reinforcement Φ8@200.

[0069] When shear walls with different cross-sectional thicknesses are arranged eccentrically up and down, the out-of-plane eccentric compression bearing capacity shall be checked and calculated. Otherwise, there may be potential safety hazards. Usually, the bottom layer walls and thinner walls are more difficult to meet the requirements and should be paid more attention to. In daily design, when the wall thickness changes, try to control the change not to exceed 50mm each time. The floor slab at the location where the wall thickness changes plays a certain role in balancing the eccentric moment. The location where the wall thickness changes should be preferably selected at the place where there are floor slabs on both sides. The upper part of the non-parallel side floor slab connected to the location where the wall thickness changes is in tension, which will increase the negative moment at the support. The lower part of the parallel side floor slab connected to the location where the wall thickness changes is in tension, making the compression zone at the support become a tension zone. Attention should be paid to checking the numerical value and anchorage length of the lower reinforcement of the floor slab.

[0070] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device.

[0071] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A calculation method for the eccentric arrangement of the upper and lower parts of a shear wall with variable wall thickness, characterized in that: It includes force analysis and reinforcement calculation; S1. Force analysis: Let the thickness of the upper wall be t1, the storey height be H1, the thickness of the lower wall be t2, the storey height be H2, the thickness of the non-parallel side floor slab connected to the wall thickness change be t3, the corresponding span of the floor slab be L1, the thickness of the parallel side floor slab connected to the wall thickness change be t4, and the corresponding span of the floor slab be L2. The eccentricity of the center lines of the upper and lower walls is e; Let the axial force per unit length acting on the center line of the upper wall transmitted from the root of the upper wall be N, and the moment M generated by the axial force of the upper wall on the lower wall is M = Ne; Take the node at the section thickness change as the research object for force balance analysis. i1, i2, i3, and i4 are the linear stiffnesses of the upper and lower walls, the non-parallel side and the parallel side floor slabs at the section change respectively: i1 = E1l1 / H1 = E1bt1 3 / (12H1) i2 = E2l2 / H2 = E2bt2 3 / (12H2) i3 = E3l3 / L = E3bt3 3 / (12L1) i4 = E3l4 / L = E3bt4 3 / (12L2) Under the condition that the far ends of the members are all rigidly connected, according to the principle of moment distribution method and the node balance condition, it can be obtained that: M = M1 + M2 + M3 + M4 M1 = Mi1 / (i1 + i2 + i3 + i4) = Nei1 / (i1 + i2 + i3 + i4) (the left side of the wall is in tension) M2 = Mi2 / (i1 + i2 + i3 + i4) = Nei2 / (i1 + i2 + i3 + i4) (the right side of the wall is in tension) M3 = Mi3 / (i1 + i2 + i3 + i4) = Nei3 / (i1 + i2 + i3 + i4) (the upper part of the floor slab is in tension) M4 = Mi4 / (i1 + i2 + i3 + i4) = Nei4 / (i1 + i2 + i3 + i4) (the lower part of the floor slab is in tension) The internal forces of the section a-a at the root of the upper wall are the moment M1 and the axial force N; The internal forces of the section b-b at the top of the lower wall are the moment M2 and the axial force N; In addition to the normal negative moment, there are additional moments M3 and M4 generated by the eccentricity of the upper and lower walls at the support of the floor slab connected to the wall thickness change; S2. Reinforcement calculation: The upper and lower walls are calculated as eccentric compression members with symmetrical reinforcement according to M1, N and M2, N to obtain the calculated values of the vertical reinforcement of the upper and lower walls. If the calculated value is 0 or less than the reinforcement value calculated according to the minimum reinforcement ratio of the wall body distributed reinforcement, the reinforcement can be carried out according to the structural requirements; The reinforcement value of the non-parallel side floor slab connected to the wall thickness change at the support of the wall is equal to the sum of the calculated value of the negative moment reinforcement under the action of the floor vertical load and the reinforcement value calculated by the additional moment M3 generated by the eccentricity of the upper and lower walls. If the reinforcement value calculated by the sum of the two is less than the calculated value of the minimum reinforcement ratio of the flexural member, the reinforcement is carried out according to the structure; Under the action of the floor vertical load, the lower part of the floor slab support is the compression zone and the calculated reinforcement is 0. Therefore, the lower reinforcement value of the parallel side floor slab connected to the wall thickness change at the support of the wall is equal to the reinforcement value calculated by the additional moment M4 generated by the eccentricity of the upper and lower walls. If this value is less than the positive moment reinforcement value of the floor slab span, no additional reinforcement is required and it can be extended from the positive moment reinforcement of the span; if this value is greater than the positive moment reinforcement value of the floor slab span, the reinforcement needs to be provided according to this value. Additional reinforcement needs to be added on the basis of the positive moment reinforcement of the span within one-third of the slab span at the support side.

2. A calculation method for the eccentric arrangement of the upper and lower parts of a shear wall with variable wall thickness according to claim 1, characterized in that: The axial forces N1 transmitted from the floor slabs on both the left and right sides at the section change to the lower wall and acting at the center line of the lower wall are much smaller than N. Ignoring the influence of N1, N1 is not considered in the calculation.

3. A calculation method for the eccentric arrangement of the upper and lower parts of a shear wall with variable wall thickness according to claim 1, characterized in that: When there is no floor slab on one side where the wall is flush, take t4 = 0 in the above formula.

4. A calculation method for eccentric arrangement of upper and lower shear walls with variable wall thickness according to claim 1, characterized in that: When there is no floor slab on both sides of the wall or the influence of the floor slab stiffness is ignored, take t3 = 0 and t4 = 0 in the above formula.

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