CN102033023A - Method for calculating shear strength of multi-ribbed composite wall - Google Patents

Abstract

The invention provides a method for calculating the shear bearing capacity of densely ribbed composite walls, comprising the following steps: step 1, determining the position of the horizontal weak layer; step 2, calculating the shear bearing capacity of the concrete grid of the horizontal weak layer; step 3, Calculate the shear bearing capacity of the horizontal weak layer filled blocks; step 4, calculate the influence coefficient of the sash constraint effect and the influence coefficient of the wall height-to-width ratio; step 5, calculate the shear bearing capacity of the densely ribbed composite wall. The calculation method of the shear bearing capacity of the densely ribbed composite wall of the present invention can better conform to the failure characteristics and failure rules of the densely ribbed composite wall under the action of horizontal load, so that the calculation of the bearing capacity is more accurate.

Description

A Calculation Method of Shear Capacity of Composite Wall with Ribs

technical field

The invention relates to a calculation method of structural bearing capacity, in particular to a calculation method of shear bearing capacity of densely ribbed composite walls.

Background technique

The densely ribbed composite wall is made of reinforced concrete with small cross-section and reinforcement as the frame, embedded with aerated silicate block or other light-weight masonry with certain strength, mainly made of industrial waste such as slag and fly ash It is made of blocks and is mainly used in densely ribbed structures. For a long time, people have not done enough research on the shear mechanism of densely ribbed composite walls and the calculation method of shear capacity. The existing calculation methods for the shear capacity of densely ribbed composite walls refer to concrete shear walls and reinforced masonry walls And the proposed approximate calculation method.

For example, a bearing capacity calculation formula is:

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; Re</span>}}}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0.035</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.035</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.08</span>}\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ]</span>$

In the formula: λ is the shear-span ratio of the wall, and 1.5 and 2.2 are taken as the limit value; f _c is the design value of the compressive strength of the concrete in the wall panel; A _c is the cross-sectional area of the concrete rib column and the connecting column in the wall panel and; f _q is the design value of the compressive strength of the blocks in the wall panel; A _q is the sum of the cross-sectional areas of the blocks in the wall panel; f _y is the design strength of the longitudinal reinforcement in the shear plane of the wall panel; A _s is the wall The sum of the areas of rib beam longitudinal reinforcement in the shear plane of the slab; N is the design value of the axial pressure of the wall, which should satisfy N≤0.2fbh. The formula for calculating the bearing capacity is established on the assumption that the multi-ribbed composite wall complies with the failure criterion of the oblique section. It can be called the formula for calculating the shear bearing capacity based on the failure criterion of the oblique section. There is only one main oblique crack in the direction of 45° in the densely ribbed composite wall; (2) Assuming that the entire cross-section of the rib beam is uniformly tensioned, there is only tension but no section bending moment in the entire cross-section of the rib beam.

However, the structural form of the densely ribbed composite wall is different from solid walls such as concrete walls and masonry walls. When the densely ribbed composite wall reaches the limit state of shear bearing capacity, diffuse cracks appear in all the blocks in the grid, and the rib columns on both sides Bending and shearing failure occurs at the bottom of the column (the rib column on the tension side shows tensile bending failure, and the rib column on the compression side shows compression bending failure), the middle rib column has relatively few or no cracks, and vertical cracks penetrate through the ends of rib beams , the entire wall does not have a real 45° main oblique crack that runs through the wall. Due to the weak strength of the filling block, the main failure surface of the multi-ribbed composite wall under the horizontal load is a certain horizontal weak layer, such as the bottom sash unit or the middle sash unit, and the failure surface is concentrated in the middle of the sash unit layer position, rather than a 45° oblique section.

It can be seen that there are two unexplainable problems in the traditional formula for calculating the shear capacity of densely ribbed composite walls based on the failure criterion of oblique sections: first, it is difficult to explain theoretically that there is no main force for densely ribbed composite walls under horizontal loads. The failure phenomenon of oblique cracks; secondly, with the decrease of the strength of the infill block, the tensile force borne by the rib beam gradually decreases and the bending moment borne gradually increases, that is, there is a local bending moment in the rib beam section, and the failure criterion of the oblique section The assumption that the entire cross-section of the rib beam bears the tensile force obviously cannot reasonably explain the stress variation characteristics of the rib beam section, and often overestimates the tensile effect of the rib beam and underestimates the shear effect of the infill blocks under constraints. Therefore, the traditional shear capacity calculation method based on the assumption of oblique section failure is difficult to accurately calculate the shear capacity of densely ribbed composite walls.

Contents of the invention

The technical problem to be solved by the present invention is to provide a calculation method for the shear bearing capacity of densely ribbed composite walls, which can better conform to the failure characteristics and failure laws of densely ribbed composite walls under horizontal loads, so that the calculation of bearing capacity more precise.

In order to solve the above problems, the present invention discloses a method for calculating the shear bearing capacity of densely ribbed composite walls, including the following steps: Step 1, determine the position of the horizontal weak layer; Step 2, calculate the shear bearing capacity of the concrete sash of the horizontal weak layer ; Step 3, calculate the shear bearing capacity of the horizontal weak layer filled blocks; Step 4, calculate the influence coefficient of the sash constraint effect and the influence coefficient of the wall aspect ratio; Step 5, calculate the shear bearing capacity of the densely ribbed composite wall.

为水平薄弱层第i根肋柱的柱顶、柱底弯矩设计值；H₀为水平薄弱层肋柱的净高度。Further, the formula for calculating the shear bearing capacity of the horizontal weak layer concrete sash in step 2 is: in,

is the design value of column top and column bottom bending moment of the i-th rib column in the horizontal weak layer; _H0 is the net height of the rib column in the horizontal weak layer.

Further, the formula for calculating the shear bearing capacity of the horizontal weak layer filled blocks in step 3 is: V _m = (f _{m, t} + μσ _m ) A _m , where f _{m, t} is the tensile strength of the filled blocks ; A _m is the sum of the horizontal cross-sectional area of the block; σ _m is the average vertical compressive stress borne by the block;

Further, the calculation formula of the compression-shear composite force influence coefficient is μ=0.83-0.7σ _m /f _m , where f _m is the compressive strength of the masonry.

其中，l_m为框格内填充砌块的净长度，h₀为框格内填充砌块的净高度。Further, the formula for calculating the influence coefficient of the sash constraint effect in step 4 is:

Among them, l _m is the net length of the filling block in the sash, and _h0 is the net height of the filling block in the sash.

Further, the calculation formula of the wall aspect ratio influence coefficient in step 4 is φ=1-0.711g(H _w /B _w ), where H _w is the height of the densely ribbed composite wall, and B _w is the densely ribbed composite wall The width of the wall.

其中，V_c为水平薄弱层混凝土框格的抗剪承载力；V_m为水平薄弱层填充砌块的抗剪承载力；

为框格约束效应影响系数；φ为墙体高宽比影响系数。Further, the formula for calculating the shear bearing capacity of the densely ribbed composite wall in step 5 is:

Among them, V _c is the shear bearing capacity of the concrete grid in the horizontal weak layer; V _m is the shear bearing capacity of the filled blocks in the horizontal weak layer;

is the influence coefficient of grid constraint effect; φ is the influence coefficient of wall height-to-width ratio.

Further, the order of steps 2, 3, and 4 can be changed arbitrarily.

Compared with the prior art, the present invention has the following advantages:

The shear bearing capacity calculation method of the invention is calculated based on the failure criterion of the horizontal weak layer, and can accurately calculate the shear bearing capacity of the densely ribbed composite wall. Because the final load-bearing capacity of the densely ribbed composite wall is determined by the load-bearing capacity of the first layer of sash with the smaller load-bearing capacity and the most unfavorable force, that is, its final failure form is manifested as a certain horizontal layer (usually the bottom horizontal frame grids) were severely damaged, while the grids of other layers were relatively slightly damaged. From the macroscopic damage phenomenon of the multi-ribbed composite wall, it was shown that the blocks of the bottom grid were severely cracked, and the blocks of the upper layers were all cracked, and the cracks of the blocks were dispersed, but There is no main diagonal crack. Therefore, the failure criterion of the horizontal weak layer can explain the macroscopic failure phenomenon of the multi-ribbed composite wall, and provide a more accurate calculation basis for the seismic design of the multi-ribbed composite wall structure.

Description of drawings

Fig. 1 is a flow chart of the calculation method for the shear bearing capacity of a densely ribbed composite wall according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of the structure of the densely ribbed composite wall in the calculation method of the shear bearing capacity of the densely ribbed composite wall according to the embodiment of the present invention.

Detailed ways

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Please refer to Fig. 1, the method for calculating the shear capacity of a densely ribbed composite wall of the present invention is based on the failure criterion of a horizontal weak layer to calculate the shear capacity of a densely ribbed composite wall, comprising the following steps:

Step (1), determining the position of the horizontal weak layer;

Step (2), calculate the shear capacity of the concrete sash in the horizontal weak layer:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}$

分别为水平薄弱层第i根肋柱的柱顶、柱底弯矩设计值；H₀为水平薄弱层肋柱的净高度。In the formula:

are the design values of the column top and column bottom bending moments of the i-th rib column in the horizontal weak layer, respectively; _H0 is the clear height of the rib column in the horizontal weak layer.

Step (3), calculate the shear bearing capacity of the horizontal weak layer filled block;

V _m = (f _{m, t} + μσ _m ) A _m

In the formula: f _{m, t} is the tensile strength of the filled block; A _m is the sum of the horizontal cross-sectional area of the block; σ _m is the average vertical compressive stress borne by the block; The formula for calculating the influence coefficient of compression-shear composite force is: μ=0.83-0.7σ _m /f _m , where f _m is the masonry compressive strength.

φ＝1-0.711g(H_w/B_w)Step (4), calculate the influence coefficient of the sash constraint effect Wall aspect ratio influence coefficient φ;

φ＝1-0.711g(H _w /B _w )

In the formula: l _m is the net length of the filling block in the sash, h ₀ is the net height of the filling block in the sash. H _w is the height of the ribbed composite wall, and B _w is the width of the densely ribbed composite wall.

Step (5), calculating the shear capacity V _u of the densely ribbed composite wall;

Referring to Fig. 2, the calculation method of the shear capacity of the densely ribbed composite wall of the present invention will be described in detail below in conjunction with examples: the densely ribbed composite wall bears horizontal loads on the top of the wallboard without vertical loads. Among them, the rib beams 10 and rib columns 20 of the densely ribbed composite wall are all reinforced: longitudinal bars 4Φ6, stirrups Φ4, and the spacing is 200mm. The wall thickness of the ribbed composite wall is 160mm, the length B _w is 2400mm, and the height H _w is 2450mm. There are three filling blocks 30, the net length l _m of each filling block 30 is 633mm, and the net height _h0 is 633mm. The cross-sectional height h _lz of the rib column 20 is 100 mm, and the cross-sectional height h _ll of the rib beam 10 is 100 mm. In addition, the distance h _s from the tensile end of a single rib beam to the bending center is 80mm. The mechanical properties of the material are: the design value of the tensile strength of the steel bar is 210Mpa, the design value of the compressive strength of the concrete is 14.3Mpa, and the design value of the compressive strength of the filled block is 0.35Mpa. According to the calculation steps given in Figure 1, the shear bearing capacity of the densely ribbed composite wall shown in Figure 2 is calculated, and the calculation steps are as follows:

Step (1), determine the location of the horizontal weak layer. Since the reinforcement and cross-sectional size of the three-layer frame of the densely ribbed composite wall are the same, the weak layer is taken at the bottom layer with the greatest stress;

则底层中间两根肋柱的柱顶及柱底弯矩均为0.95KNm，底层两侧两根肋柱的柱顶弯矩为0.95/2KNm，柱底弯矩为0.95KNm。水平薄弱层肋柱的净高度H₀与填充砌块的净高度h₀相等，则此处水平薄弱层肋柱的净高度H₀为633mm。根据前述步骤(2)中的公式可以得出水平薄弱层混凝土框格的抗剪承载力为：In step (2), calculate the shear capacity of the concrete sash in the horizontal weak layer. The bending moment distributed by the two rib columns in the middle of the bottom floor at the end of the upper column is equal to the bending moment at the end of the rib beam, and the bending moment distributed by the rib columns on both sides of the bottom floor at the end of the upper column is equal to half of the bending moment at the end of the rib beam. The bending moment distributed by the ribbed column at the bottom of the column is equal to the bending moment at the end of the ribbed beam. The yield bending moment at the beam end of the rib beam is calculated according to the following formula:

Then the bending moment of the top and bottom of the two rib columns in the middle of the bottom floor is 0.95KNm, the bending moment of the top of the two rib columns on both sides of the bottom floor is 0.95/2KNm, and the bending moment of the bottom of the column is 0.95KNm. The net height H ₀ of the horizontal weak layer rib column is equal to the net height h ₀ of the filling block, so the net height H ₀ of the horizontal weak layer rib column here is 633mm. According to the formula in the aforementioned step (2), it can be concluded that the shear bearing capacity of the concrete frame in the horizontal weak layer is:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 10.51</span>}\mathrm{<span\; class="notranslate">\; kN</span>}<span\; class="notranslate">\; .</span>$

In step (3), calculate the shear bearing capacity of the filled blocks. Since there is no vertical load, then V _m =f _{m, t} A _m =633mm×160mm×3×0.35Mpa=106.33kN.

则框格约束效应影响系数

密肋复合墙的长度B_w为2400mm，高度H_w为2450mm，故此处墙体高宽比影响系数φ＝1-0.711g(H_w/B_w)＝1-0.71×1g(2450/2400)＝0.994。Step (4), calculate the influence coefficient of the sash constraint effect Wall aspect ratio influence coefficient φ. Since the net length l _m and net height h ₀ of the filling blocks are both 633mm, here

Influence Coefficient of Sash Constraint Effect

The length B _w of the densely ribbed composite wall is 2400mm, and the height H _w is 2450mm, so the influence coefficient of the wall aspect ratio here is φ=1-0.711g(H _w /B _w )=1-0.71×1g(2450/2400) = 0.994.

中，计算得到出密肋复合墙的抗剪承载力

Step (5), V _c , V _m , φ, Into the formula

In the calculation, the shear bearing capacity of the densely ribbed composite wall is obtained

The shear bearing capacity calculation method of the invention is calculated based on the failure criterion of the horizontal weak layer, and can accurately calculate the shear bearing capacity of the densely ribbed composite wall. Because when the sashes of the densely ribbed composite wall from the bottom to the top are all subjected to the shear force of the same magnitude, the sashes of each layer will undergo shear deformation, and each small sash of each layer will have an opposite effect. Corner crossing oblique cracks. However, the final bearing capacity of the densely ribbed composite wall is determined by the bearing capacity of the first layer of sash with the smaller bearing capacity and the most unfavorable stress, that is, the final failure form of the densely ribbed composite wall is a certain horizontal layer ( Usually the horizontal sash at the bottom) is severely damaged, while the other layers of sash are relatively slightly damaged. From the macroscopic damage phenomenon of the densely ribbed composite wall, it is shown that the blocks of the bottom sash are severely cracked, and the blocks of the upper layers are all cracked. The block cracks are diffuse, but there are no main diagonal cracks. Therefore, the failure criterion of the horizontal weak layer can explain the macro-failure phenomenon of the multi-ribbed composite wall, and provides a more accurate calculation basis for the seismic design of the multi-ribbed composite wall structure.

It can be understood that the order of the above steps (2), (3) and (4) can also be changed. The method for calculating the shear bearing capacity of the densely ribbed composite wall of the present invention is also applicable to the calculation of the shear bearing capacity of grid-type composite walls such as grid shear walls and dense-frame shear walls.

The calculation method of the shear bearing capacity of a kind of densely ribbed composite wall provided by the present invention has been introduced in detail above. In this paper, specific examples have been used to illustrate the principle and implementation of the present invention. The description of the above examples is only It is used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation and scope of application. In summary, this The content of the description should not be construed as limiting the present invention.

Claims (8)

1. A shear-resistant bearing capacity calculation method for a multi-ribbed composite wall is characterized by comprising the following steps:

step 1, determining the position of a horizontal weak layer;

step 2, calculating the shear-resistant bearing capacity of the horizontal weak layer concrete sash;

step 3, calculating the shear-resistant bearing capacity of the horizontal weak layer filling building block;

step 4, calculating a sash constraint effect influence coefficient and a wall body height-width ratio influence coefficient;

and 5, calculating the shear resistance and bearing capacity of the multi-ribbed composite wall.

2. The calculation method according to claim 1, wherein the shear-resistant bearing capacity calculation formula of the horizontal weak layer concrete sash in the step 2 is as follows:

wherein,

designing bending moments of the column top and the column bottom of the ith rib column of the horizontal weak layer; h₀The net height of the rib column of the horizontal weak layer.

3. The calculation method as claimed in claim 1, wherein the shear-resistant bearing capacity calculation formula of the horizontal weak layer filling block in the step 3 is as follows: v_m＝(f_m，t+μσ_m)A_mWherein f is_m，tThe tensile strength of the filling building block is high; a. the_mIs the sum of the horizontal cross section areas of the building blocks; sigma_mThe average vertical compressive stress borne by the building blocks; mu is the compression-shear composite stress influence coefficient.

4. The calculation method according to claim 3, wherein the calculation formula of the compression-shear composite force influence coefficient is μ -0.83-0.7 σ_m/f_m，f_mThe compressive strength of the masonry is obtained.

5. The calculation method according to claim 1, wherein the lattice constraint effect influence coefficient in the step 4 is calculated by the formula:

wherein l_mThe net length of the filled building blocks in the sash, h₀The net height of the filled building blocks in the sash.

6. The calculation method according to claim 5, wherein the calculation formula of the wall aspect ratio influence coefficient in step 4 is 1-0.711g (H)_w/B_w) Wherein H is_wHeight of the multi-ribbed composite wall, B_wThe width of the dense rib composite wall.

7. The calculation method according to claim 1, wherein the shear-bearing capacity of the multi-ribbed composite wall in the step 5 is calculated by the formula:wherein, V_cThe shear-resistant bearing capacity of the horizontal weak layer concrete sash; v_mFilling the horizontal weak layer with the shear-resistant bearing capacity of the building block;

the influence coefficient of the sash constraint effect is defined; phi is the influence coefficient of the aspect ratio of the wall.

8. The computing method according to any one of claims 1 to 7, wherein the order of steps 2, 3, 4 is arbitrarily changed.

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