CN112989586B - Method for judging failure mode of reinforced concrete hollow pier stud - Google Patents
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- 239000011150 reinforced concrete Substances 0.000 title claims abstract description 43
- 238000000034 method Methods 0.000 title claims abstract description 22
- 238000012937 correction Methods 0.000 claims abstract description 51
- 239000007787 solid Substances 0.000 claims abstract description 28
- 230000006378 damage Effects 0.000 claims abstract description 26
- 238000005452 bending Methods 0.000 claims description 52
- 238000010008 shearing Methods 0.000 claims description 24
- 238000004364 calculation method Methods 0.000 claims description 23
- 230000003068 static effect Effects 0.000 claims description 2
- 238000012360 testing method Methods 0.000 description 69
- 238000013461 design Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 230000003313 weakening effect Effects 0.000 description 3
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 1
- 239000004567 concrete Substances 0.000 description 1
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- 238000010586 diagram Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
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Abstract
A method for judging the failure mode of a reinforced concrete hollow pier stud relates to a reinforced concrete bridgeThe technical field of beams. The scheme is as follows: s1, judging the cross section form of the pier stud; s2, the cross section of the pier column is a thin-wall hollow rectangular section according to a formula
Or
Calculating the shear-span ratio lambda 'of the thin-wall hollow rectangular section pier stud, and obtaining a judgment result of the pier stud failure mode according to the relationship between the shear-span ratio lambda' and the judgment threshold values 1.5 and 2; s3, the cross section of the pier column is not a thin-wall hollow rectangular section, and firstly, according to a formula
Or calculating the shear-span ratio of the solid rectangular pier column by lambda H/H; then looking up a shear span ratio correction coefficient table to obtain a shear span ratio correction coefficient alpha of the pier column corresponding to the hollow section form, and calculating the shear span ratio of the pier column with the hollow section, wherein lambda' is alpha lambda; and obtaining a judgment result of the hollow pier column failure mode according to the relation between the shearing-span ratio lambda' and the judgment threshold values 1.5 and 2. The method is used for judging the damage mode of the reinforced concrete hollow pier stud.
Description
The technical field is as follows:
the invention relates to the technical field of reinforced concrete bridges, in particular to a method for judging a failure mode of a reinforced concrete hollow pier stud.
Background art:
the reinforced concrete hollow pier stud is widely applied to a large-span high-pier reinforced concrete bridge. Due to the influence of section weakening and high-order vibration mode, the shearing resistance of the hollow high pier is reduced, and bending shear damage and even shear damage modes can occur. The existing research finds that the reinforced concrete hollow pier stud with the shear span ratio of more than 3 or even more than 4 still has bending shear damage or even shear damage. This indicates that the calculation formula of the shear span ratio of the medium-low solid pier column cannot correctly reflect the proportional relationship between the maximum normal stress and the maximum shear stress on the hollow section, and therefore cannot be used for judging the failure mode of the hollow section pier column.
The invention content is as follows:
in order to solve the above-mentioned problems in the background art, the present invention is directed to a method for determining a failure mode of a reinforced concrete hollow pier stud.
The technical scheme adopted by the invention is as follows: the method comprises the following steps:
s1, judging the cross section form of the pier stud;
s2, the cross section form of the pier stud obtained by the S1 is a thin-wall hollow rectangle according to a formula
Or
Calculating the shear-span ratio lambda ' of the thin-wall hollow rectangular pier stud, obtaining a judgment result of the pier stud damage mode according to the relation between the lambda ' and the judgment threshold values 1.5 and 2, and when the lambda ' is more than 2, bending damage occurs to the thin-wall hollow rectangular pier stud; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs;
s3, the cross section form of the pier column obtained from S1 is not a thin-wall hollow rectangle, and the calculation formula is based on the shear span ratio of the solid rectangular column
Or lambda is H/H, and a basic value for calculating the shear-span ratio is obtained; deducing the shear-span ratio correction coefficients of other pier columns with different hollow section types to obtain a shear-span ratio correction coefficient table of pier columns with different section forms;
looking up a shear span ratio correction coefficient table to obtain a shear span ratio correction coefficient alpha of the pier column corresponding to the hollow section form, and calculating the shear span ratio of the pier column corresponding to the section, wherein lambda' is alpha lambda;
obtaining a judgment result of a pier column damage mode according to the relation between the shear span ratio lambda 'of the hollow section pier column and the judgment threshold values 1.5 and 2, wherein when the lambda' is more than 2, the hollow section pier column is subjected to bending damage; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention derives the shear-span ratio suitable for the pier columns with different hollow section forms from the ratio of normal stress to shear stress on the section capable of reflecting the essence of the shear-span ratio. The formula has the same mathematical expression form as the shear-span ratio of the solid pier column, and the given ratio of the normal stress to the shear stress on the bottom section of the hollow pier is the same as that of the solid pier, so that the original solid pier column damage mode can be used for judging the threshold value, the re-statistics of the judgment threshold value is avoided, and the application is easy.
2. The method for judging the failure mode of the reinforced concrete hollow pier stud can correctly judge the failure mode of the pier stud with the hollow section on the premise of ensuring the usability, can avoid brittle bending shear and shearing failure of the pier stud during engineering design, and is beneficial to improving the safety of civil engineering structures.
3. The process of the invention shows that the weakening of the cross section of the hollow pier column does not affect the internal force of the section of the reinforced concrete pier column, but directly affects the stress distribution rule on the section; the maximum shear stress on the section is obviously increased, and the ratio of the normal stress to the shear stress on the section is reduced, so that the shear-span ratio of the pier column is influenced. This effect is mainly reflected in the increase in section equivalent height in the proposed shear-span ratio formula. The invention can promote the development of the design theory of the hollow section high pier to a certain extent.
Description of the drawings:
for the purpose of clarity, the invention is described in detail in the following detailed description and the accompanying drawings.
FIG. 1 is a block flow diagram of the present method;
fig. 2 is a schematic cross-sectional view of a reinforced concrete pier stud;
fig. 3 is a schematic view of a circular cross-section of an abutment;
fig. 4 is a schematic view of a circular cross-section of the pier stud;
FIG. 5 is a schematic sectional view of a rectangular hollow section (t/h > 0.1) and a thin-wall rectangular hollow section (t/h ≤ 0.1) of a pier stud.
The specific implementation mode is as follows:
the first specific implementation way is as follows: the method assumes the section of the reinforced concrete hollow pier column as a single material section with equivalent strength and rigidity, and deduces the shear-span ratio of the thin-wall box-type pier column by taking the ratio of the normal stress to the shear stress on the assumed equivalent conversion section as a middle quantity. Based on the assumption, the obtained calculation formula of the shear span ratio of the thin-wall pier column and the threshold value thereof can be suitable for hollow pier columns with reasonable reinforcement ratio and hoop ratio within the specification and regulation range. The method comprises the following steps:
s1, judging the cross section form of the pier stud;
s2, the cross section form of the pier stud obtained by the S1 is a thin-wall hollow rectangle according to a formula
Or
Calculating the shear-span ratio lambda ' of the thin-wall hollow rectangular pier stud, and obtaining a judgment result of a pier stud failure mode according to the relationship between the shear-span ratio lambda ' and the judgment threshold values 1.5 and 2, wherein when the lambda ' is greater than 2, the thin-wall hollow rectangular pier stud is subjected to bending failure; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs;
compared with a solid rectangular section, the thin-wall hollow rectangular section is greatly reduced in cross-sectional area and simultaneously influenced by a thin-wall effect, so that the shear stress on the thin-wall hollow rectangular section is sharply increased under the action of the same shear force. If the pier column shear span ratio is calculated based on the proportional relation between the bending moment and the shearing force on the section, the result of the calculation has larger deviation with the real shear span ratio of the thin-wall hollow rectangular pier, so the method can accurately judge the failure mode of the test piece.
S3, the cross section form of the pier column obtained from S1 is not a thin-wall hollow rectangle, and the calculation formula is based on the shear span ratio of the solid rectangular column
And lambda is H/H, and a basic value for calculating the shear-to-span ratio is obtained; deducing the shear-span ratio correction coefficients of other pier columns with different hollow section types to obtain a shear-span ratio correction coefficient table of the pier column with the corresponding section form;
looking up a shear span ratio correction coefficient table to obtain a shear span ratio correction coefficient alpha of the pier column with the corresponding section form, and calculating the shear span ratio of the pier column with the corresponding section, wherein lambda' is alpha lambda;
obtaining a judgment result of a pier column damage mode according to the relation between the shear span ratio lambda 'and the judgment threshold values 1.5 and 2, wherein when the lambda' is more than 2, the hollow pier column is subjected to bending damage; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs.
In S2
Or
The obtaining process is as follows:
the shear span ratio which is broadly used for judging the pier column failure mode is the proportional relation of bending moment and shearing force on a rectangular section, the calculation formula is as follows,
wherein: m is a cross-section internal bending moment, V is a cross-section internal shearing force, and h is a cross-section effective height;
the shear-span ratio used for judging the pier column failure mode in a narrow sense has the following calculation formula,
wherein H is called the effective height of the pier stud, and H is the effective height of the section;
when H takes the pier column height corresponding to the position of the reverse bend, M is shown in figure 2 1 When the bending moment of the pier bottom section is 0, M is VH;
for a rectangular section pier stud, the relationship between load and stress on the cross section can be expressed as,
wherein M is a section bending moment, V is a section shearing force, sigma max,sr RepresentMaximum normal stress on rectangular cross-section, τ max,sr Represents the maximum shear stress on the rectangular section, b is the width of the rectangular section, the lower corner mark sr represents a solid rectangular section, the formula (3) and the formula (4) are taken into the formula (1) and are finished,
it can be seen from the formula (5) that, for the rectangular section pier stud, the shear-span ratio given by the formula (1) is equivalent to the ratio of the normal stress to the shear stress of 25% on the cross section; according to the shear span ratio threshold λ 1.5 and λ 2, when the rectangular section pier column is subjected to bending moment failure, the ratio of normal stress to shear stress on the section should be greater than 8; when shear failure occurs, the ratio should be less than 6;
for the thin-wall hollow rectangular pier stud, the relation between the load and the stress on the cross section of the thin-wall hollow rectangular pier stud is different from that of the thin-wall hollow rectangular pier stud, and the relation can be specifically expressed as
Wherein q is shear flow on the thin-wall hollow rectangular section; h is the height of the section in the shearing direction (x direction); b is the cross-sectional width in the y direction; t is the wall thickness, as shown in FIG. 5; i is y And S y Respectively the moment of inertia and the static moment for the y-axis,
the shear-span ratio lambda' of the thin-wall hollow rectangular pier column is expressed as 25% of the ratio of the normal stress to the shear stress, namely
The formulas (6) and (7) are put into the formula (9) after finishing, and a calculation formula of the shear span ratio of the thin-wall hollow rectangular section pier stud is obtained
By comparing the formula (2), a narrow calculation formula can be obtained
Equation (10) is the product of shear at bending moment ratio and the effective height of the cross-section; equation (11) is the ratio of the pier column effective height to the cross-section effective height. The formula (10) or the formula (11) can correctly reflect the stress relation on the section of the thin-wall hollow rectangular pier stud, has the same mathematical expression form with the shear span ratio of the solid pier stud, and is easy for engineering application.
The cross section weakening and thin wall effect are analyzed to reduce the shear-span ratio of the pier stud by increasing the cross section shear stress. Comparing the formula (10) with the formula (1) and the formula (11) with the formula (2) respectively, it can be known that the influence is expressed as a change in the effective section height in the shear-span ratio calculation formula. The effective height of the section of the box-type thin-wall pier is not only related to the actual height h of the section, but also related to the width b of the section. That is, the "cross-sectional effective height" is to be understood as the "cross-sectional equivalent height" rather exactly. It is worth noting that when the wall thickness ratio (t/h) of the box-shaped section is less than or equal to 0.1, the wall thickness t does not influence the shear span ratio of the pier column.
The correction coefficients in the cross-section ratio correction coefficient table of the pier studs with different section types in the step S3 are obtained as follows:
taking a circular section as an example, the calculation method of the correction coefficient alpha comprises the following steps:
1) calculating bending moment M and shearing force V on circular section
Where D is the cross-sectional diameter, σ max,c And τ max,c The maximum normal stress and the maximum shear stress on the circular section are respectively represented, and the lower corner mark c represents the circular section;
2) calculating the ratio of normal stress to shear stress on the circular section according to the rectangular section pier stud shear span ratio calculation formula (1)
Wherein a is 1/6; for a circular cross-section, where h is taken as D;
3) defining the shear-span ratio of the circular section by the ratio of the normal stress to the shear stress on the rectangular section
4) Calculating a correction factor alpha
The second embodiment is as follows: the difference from the first embodiment is that the correction coefficients in the table of the shear ratio correction coefficients of the pier columns of different section types in S3 are obtained as follows:
1) calculating the bending moment M and the shearing force V on the section of the circular ring
Wherein D is the outer diameter of the ring, σ max,a And τ max,a Respectively representing the maximum normal stress and the maximum shear stress on the circular section, and the lower corner mark a represents the circular section;
2) calculating the ratio of the normal stress to the shear stress on the section of the circular ring according to the calculation formula (1) of the shearing-span ratio of the pier column with the rectangular section
For a circular cross-section, where h is taken as D,
3) the ratio of normal stress to shear stress on the rectangular section is used to define the shear-span ratio of the circular section
4) Calculating a correction factor alpha
The third concrete implementation mode: the difference from the first or second embodiment is that the correction coefficients in the table of the cross-section ratio correction coefficients of the pillars of different section types in S3 are obtained as follows:
taking a hollow rectangular section as an example
1) Calculating bending moment M and shearing force V on hollow rectangular section
Wherein D is the outer diameter of the ring, σ max,b And τ max,b Respectively representing the maximum normal stress and the maximum shear stress on the hollow rectangular section, and the lower corner mark b represents the hollow rectangular section;
2) calculating the ratio of the normal stress to the shear stress on the hollow rectangular section according to a calculation formula of the shear-span ratio of the pier column with the rectangular section, namely formula (1)
For a box-shaped cross-section,
3) defining the shear-span ratio of the hollow rectangular section by the ratio of normal stress to shear stress on the rectangular section
4) Calculating a correction factor alpha
The table 1, the shear span ratio correction coefficient table of the hollow reinforced concrete pier, is obtained from the above.
TABLE 1
Specific example 1: the present embodiment is described with reference to fig. 2, and the failure mode of the reinforced concrete hollow pier stud test piece 1 is determined, and the known dimensional information of the reinforced concrete hollow pier stud includes an effective pier stud height H of 4.0, an effective section height H of 1.0, and a section width b of 0.89; the cross section of the test piece 1 is a thin-wall hollow rectangular section, and then a formula is adopted
Directly obtaining the calculated shear-span ratio lambda' of the pier column as 1.44; and if lambda' is less than 1.5, judging that the test piece has shear failure. According to the disclosure of the relevant literature, the test piece undergoes shear failure after an actual failure test.
Specific example 2: the present embodiment is described with reference to fig. 2, and the failure mode of the reinforced concrete hollow pier stud test piece 2 is determined, and the known dimensional information of the reinforced concrete hollow pier stud includes an effective pier stud height H of 4.25, an effective section height H of 1.0, and a section width b of 0.89; the cross section of the test piece 2 is a thin-wall hollow rectangular section, and then a formula is adopted
Directly obtaining the calculated shear-span ratio lambda' of the pier column as 1.53; and lambda' is more than or equal to 1.5 and less than or equal to 2, and the test piece is judged to be subjected to bending shear damage. According to the disclosure of relevant documents, the test piece is subjected to actual damage experiments, and then bending shear damage occurs.
Specific example 3: the present embodiment is described with reference to fig. 2, and the failure mode of the reinforced concrete hollow pier stud test piece 3 is determined, and the known dimensional information of the reinforced concrete hollow pier stud includes an effective pier stud height H of 4.0, an effective section height H of 1.0, and a section width b of 0.89; the cross section of the test piece 3 is a thin-wall hollow rectangular section, and then a formula is adopted
Directly obtaining the calculated shear-span ratio lambda' of the pier column as 1.44; and when the lambda' is less than 1.5, judging that the test piece has bending shear failure. According to the disclosure of the relevant documents, the test piece undergoes shear failure after an actual failure test.
Specific example 4: with reference to fig. 3, the failure mode of the reinforced concrete hollow pier stud test piece 4 is determined, and the size information of the known reinforced concrete hollow pier stud includes an effective pier stud height H of 1.0 and an effective section height H of 0.25; the cross section of the test piece 4 is circular, the calculated shear span ratio lambda of the rectangular solid pier stud is calculated to be 4 according to the formula lambda H/H, a shear span ratio correction coefficient table is checked, the shear span ratio correction coefficient alpha of the cross section of the circular solid pier stud is obtained to be 3/2, and the shear span ratio lambda' of the circular section pier stud of the test piece 4 is calculated to be 6; and lambda' is more than 2, and the test piece is judged to be subjected to bending failure. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 5: with reference to fig. 3, the failure mode of the reinforced concrete hollow pier stud test piece 5 is determined, and the size information of the known reinforced concrete hollow pier stud includes an effective pier stud height H of 2.0 and an effective section height H of 0.25; the cross section of the test piece 5 is circular, the calculated shear span ratio lambda of the rectangular solid pier stud is calculated to be 8 according to the formula lambda H/H, a shear span ratio correction coefficient table is checked, the shear span ratio correction coefficient alpha of the cross section of the circular pier stud is obtained to be 3/2, and the shear span ratio lambda' of the circular section pier stud of the test piece 5 is calculated to be 12; and lambda' is more than 2, and the test piece is judged to be subjected to bending failure. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 6: with reference to fig. 3, the failure mode of the reinforced concrete hollow pier stud test piece 6 is determined, and the size information of the known reinforced concrete hollow pier stud includes an effective pier stud height H of 3.5 and an effective section height H of 1; the cross section of the test piece 6 is circular, the calculated shear-span ratio λ of the rectangular solid pier column is calculated according to the formula λ ═ H/H, the shear-span ratio correction coefficient table is checked, the shear-span ratio correction coefficient α ═ 3/2 of the cross section of the circular pier column is obtained, and the shear-span ratio λ' ═ α λ ═ 5.25 of the circular section pier column of the test piece 6 is calculated; and determining that the test piece is bent and damaged if the lambada' is more than 2. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 7: with reference to fig. 4, the failure mode of the reinforced concrete hollow pier stud test piece 7 is determined, and given the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 7 is circular, the effective height H of the pier stud is 3.5, the outer diameter D of the cross section of the circular ring is 1, and the inner diameter D of the cross section of the circular ring is 0.75; calculating the calculated shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula lambda of H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula lambda of H/HFormula (II)
Wherein
Calculating a shear-span ratio correction coefficient of the circular-ring-shaped section pier column, obtaining a shear-span ratio correction coefficient alpha of the circular-ring-shaped pier column as 0.65, and calculating a shear-span ratio lambda' of the circular-ring-shaped section pier column of the test piece 7 as 2.28; and lambda' is more than 2, and the test piece is judged to be subjected to bending failure. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 8: with reference to fig. 4, the failure mode of the reinforced concrete hollow pier stud test piece 8 is determined, and knowing the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 8 is circular, the effective height H of the pier stud is 3.5, the outer diameter D of the cross section of the circular ring is 1, and the inner diameter D of the cross section of the circular ring is 0.5; calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula lambda H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula
Wherein in it
Calculating a shear-span ratio correction coefficient of the circular-ring-shaped section pier column, obtaining a shear-span ratio correction coefficient alpha of the circular-ring-shaped section pier column as 0.86, and calculating a shear-span ratio lambda' of the circular-ring-shaped section pier column of the test piece 8 as 3.01; and lambda' is more than 2, and the test piece is judged to be subjected to bending failure. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 9: with reference to fig. 4, the failure mode of the reinforced concrete hollow pier stud test piece 9 is determined, and knowing the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 9 is circular, the effective height H of the pier stud is 4.9, the outer diameter D of the cross section of the circular ring is 1.4, and the inner diameter D of the cross section of the circular ring is 0.98; calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula lambda H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.5 according to the formula
Wherein
Calculating a shear-span ratio correction coefficient of the circular-ring-shaped section pier column, obtaining a shear-span ratio correction coefficient alpha of the circular-ring-shaped pier column as 0.68, and calculating a shear-span ratio lambda' of the circular-ring-shaped section pier column of the test piece 9 as 2.38; and lambda' is more than 2, and the test piece is judged to be subjected to bending failure. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 10: with reference to fig. 5, the failure mode of the reinforced concrete hollow pier stud test piece 10 is determined, and knowing the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 10 is a hollow rectangle, the effective height H of the pier stud is 2.88, the effective height H of the section is 0.36, and the width b of the section is 0.5; calculating the shear-span ratio lambda of the rectangular solid pier column to be 8 according to the formula lambda H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 8 according to the formula
Wherein
Calculating a shear-span ratio correction coefficient of the hollow rectangular pier column, obtaining the shear-span ratio correction coefficient alpha of the hollow rectangular pier column as 0.42, and calculating the shear-span ratio lambda' of the hollow rectangular pier column of the test piece 10 as 3.36; and determining that the test piece is bent and damaged if the lambada' is more than 2. According to the disclosure of the relevant documents, the test piece undergoes bending failure after an actual failure test.
Specific example 11: with reference to fig. 5, the failure mode of the reinforced concrete hollow pier stud test piece 11 is determined, and knowing the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 11 is a hollow rectangle, the effective height H of the pier stud is 1.4, the effective height H of the section is 0.45, and the width b of the section is 0.9; calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.11 according to the formula lambda H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.11 according to the formula
Wherein
Calculating a shear-span ratio correction coefficient of the box-section pier column, obtaining the shear-span ratio correction coefficient alpha of the box-section pier column as 0.27, and calculating the shear-span ratio lambda' of the hollow rectangular pier column of the test piece 11 as 0.84; when lambda' is less than 1.5, the test piece is judged to have shear failure. After the actual failure test, the test piece was subjected to shear failure.
Specific example 12: with reference to fig. 5, the failure mode of the reinforced concrete hollow pier stud test piece 12 is determined, and given the size information of the reinforced concrete hollow pier stud, the cross section of the test piece 12 is a hollow rectangle, the effective height H of the pier stud is 1.4, the effective height H of the section is 0.45, and the width b of the section is 1.5; calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.11 according to the formula lambda H/H, and calculating the shear-span ratio lambda of the rectangular solid pier column to be 3.11 according to the formula
Wherein
Calculating a shear-span ratio correction coefficient of the hollow rectangular pier stud, obtaining the shear-span ratio correction coefficient alpha of the hollow rectangular pier stud as 0.48, and calculating the shear-span ratio lambda' of the hollow rectangular pier stud of the test piece 12 as 1.49; and lambda' is less than 1.5, and the test piece is judged to be subjected to shear failure. After the actual failure test, the test piece was subjected to shear failure.
Verification results according to specific embodiments 1 to 12 show that the shear-span ratio correction formula and the failure mode judgment threshold provided by the invention for the pier columns with different cross sections can quickly and effectively judge the failure modes of the pier columns with different cross section forms; can carry out the prejudgement to the destruction mode of pier stud at the beginning of the design to effectively avoid the pier stud to take place brittle shear failure.
Claims (3)
1. A method for judging the failure mode of a reinforced concrete hollow pier stud is characterized by comprising the following steps: the method comprises the following steps:
s1, judging the cross section form of the pier stud;
s2, the cross section form of the pier stud obtained from S1 is thin-walled hollow rectangle according to the formula
Or
Wherein: m is the internal bending moment of the section, V is the internal shearing force of the section, H is the effective height of the section, H is the effective height of the pier column, b is the width of the rectangular section,
calculating the shear-span ratio lambda ' of the thin-wall hollow rectangular pier stud, obtaining a judgment result of the pier stud damage mode according to the relation between the lambda ' and the judgment threshold values 1.5 and 2, and when the lambda ' is more than 2, bending damage occurs to the thin-wall hollow rectangular pier stud; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs;
s3, the cross section form of the pier column obtained from S1 is not a thin-wall hollow rectangle, and the calculation formula is based on the shear span ratio of the solid rectangular column
Or lambda is H/H, and a basic value for calculating the shear-span ratio is obtained; deducing the shear-span ratio correction coefficients of other pier columns with different hollow section types to obtain a shear-span ratio correction coefficient table of the pier columns with different section forms;
looking up a shear span ratio correction coefficient table to obtain a shear span ratio correction coefficient alpha of the pier column corresponding to the hollow section form, and calculating the shear span ratio of the pier column corresponding to the section, wherein lambda' is alpha lambda;
obtaining a judgment result of a pier column damage mode according to the relation between the shear span ratio lambda 'of the hollow section pier column and the judgment threshold values 1.5 and 2, wherein when the lambda' is more than 2, the hollow section pier column is subjected to bending damage; when lambda' is less than 1.5, shearing failure occurs; when the lambda' is more than or equal to 1.5 and less than or equal to 2, the bending shear damage occurs;
in S2
Or
The process is as follows:
the shear-span ratio which is broadly used for judging the pier column failure mode is the proportional relation of bending moment and shearing force on a rectangular section, the calculation formula is as follows,
wherein: m is a cross-section internal bending moment, V is a cross-section internal shearing force, and h is a cross-section effective height;
the shear-span ratio used for judging the pier column failure mode in a narrow sense has the following calculation formula,
wherein H is called the effective height of the pier stud, and H is the effective height of the section;
when the height of the pier column corresponding to the position of the reverse bending point is obtained by H, the bending moment M at the section of the pier top is obtained 1 When M is 0, the bending moment of the pier bottom section is M, VH;
for a rectangular section pier stud, the relationship between load and stress on the cross section can be expressed as,
wherein M is a bending moment in the cross section, V is a shearing force in the cross section, sigma max,sr Denotes the maximum normal stress on a rectangular section, τ max,sr Represents the maximum shear stress on a rectangular section, b is the width of the rectangular section, and the lower corner mark sr represents a solid rectangular section(3) And formula (4) in formula (1), can be obtained by finishing,
it can be seen from the formula (5) that, for the rectangular section pier stud, the shear-span ratio given by the formula (1) is equivalent to the ratio of the normal stress to the shear stress of 25% on the cross section; according to the shear span ratio threshold λ 1.5 and λ 2, when the rectangular section pier stud is subjected to bending moment failure, the ratio of the normal stress to the shear stress on the section should be greater than 8; when shear failure occurs, the ratio should be less than 6;
for the thin-wall hollow pier column with the rectangular section, the relation between the load and the stress on the cross section of the thin-wall hollow pier column is different from that of the thin-wall hollow pier column with the rectangular section, and the relation can be specifically expressed as
Wherein q is shear flow on the thin-wall hollow rectangular section; h is the height of the section in the shearing action direction; b is the cross-sectional width in the y direction; t is the wall thickness; i is y And S y The moment of inertia and the static moment, σ, respectively, for the y-axis max，B Denotes the maximum normal stress, τ, on the hollow rectangular section max，B The maximum shear stress on the hollow rectangular cross-section is shown,
the shear-span ratio lambda' of the thin-wall hollow rectangular pier column is defined as 25 percent of the ratio of the normal stress to the shear stress, namely
The formulas (6) and (7) are put into the formula (9) after finishing, and a calculation formula of the shear span ratio of the thin-wall hollow rectangular pier stud is obtained
By comparing the formula (2), a narrow calculation formula can be obtained
Equation (10) is the product of shear at bending moment ratio and the effective height of the cross section; formula (11) is the ratio of the effective height of the pier stud to the effective height of the cross section;
the correction coefficient α in the shear span ratio correction coefficient table for the pillars of different hollow section types in S3 is obtained as follows:
1) calculating the bending moment M and the shearing force V on the section of the pier column aiming at different section forms;
2) when the ratio of the normal stress to the shear stress on different hollow sections is obtained, the ratio of the normal stress to the shear stress on different hollow sections is calculated only according to a calculation formula of the shear span ratio of the pier column with the rectangular section;
3) defining the shear-span ratio of the pier columns with different hollow sections according to the ratio of the normal stress to the shear stress on the rectangular sections;
4) the correction coefficient α is calculated.
2. The method for judging the failure mode of the reinforced concrete hollow pier stud according to claim 1, wherein the method comprises the following steps:
the method for calculating the correction coefficient alpha of the circular ring section comprises the following steps:
1) calculating the bending moment M and the shearing force V on the circular section
Wherein D is the outer diameter of the ring, σ max,a And τ max,a Respectively representing the maximum normal stress and the maximum shear stress on the section of the circular ring, and a lower corner mark a represents the section of the circular ring;
2) calculating the ratio of the normal stress to the shear stress on the section of the circular ring according to the calculation formula (1) of the shear span ratio of the pier column with the rectangular section
For a circular cross-section, where h is taken as D,
3) the shear-span ratio of the section of the circular ring is defined by the ratio of the normal stress to the shear stress on the rectangular section
4) Calculating a correction coefficient alpha
3. The method for judging the failure mode of the reinforced concrete hollow pier stud according to claim 1, wherein the method comprises the following steps:
the calculation method of the correction coefficient alpha of the hollow rectangular section comprises the following steps:
1) calculating bending moment M and shearing force V on hollow rectangular section
σ max，B And τ max，B Respectively representing the maximum normal stress and the maximum shear stress on the hollow rectangular section, and a lower corner mark B represents the hollow rectangular section;
2) according to a calculation formula of the shear-span ratio of the pier column with the rectangular cross section, namely formula (1), calculating the ratio of normal stress to shear stress on the hollow rectangular cross section
For a hollow rectangular cross-section,
3) defining the shear-span ratio of the hollow rectangular section by the ratio of normal stress to shear stress on the rectangular section
4) Calculating a correction factor alpha
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