Method of introducing prestress to beam-column joint in triaxial compression

Abstract

There is provided a method of prestressing a beam-column joint with an appropriate ratio among the magnitudes of compression in the directions of X, Y, and Z axes. The method introduces prestress in a beam-column joint with a tensile introducing force generated by tensionally anchoring prestressing tendons that are arranged in PC beams extending along two horizontal directions (or X axis and Y axis) and PC columns extending along the vertical direction (or Z axis) and passed through the beam-column joint to bring the beam-column joint in triaxial compression, the prestress being introduced such that a diagonal tensile force T generated by an input shear force due to a seismic load of an extremely great earthquake that may occur very rarely will be cancelled completely or partially so as not to allow diagonal cracks to occur. The ratio of the prestresses introduced in the directions of the respective axes satisfies the following equation (1):
σx:σy:σz=1:1:0.3−0.9   (1)
where σx, σy, and σz are prestresses introduced in the directions of the X axis, the Y axis, and the Z axis respectively.

Claims

1. A method of introducing prestress in a beam-column joint that introduces prestress in a beam-column joint in a multi-story building structure constructed by prestressed concrete (PC) columns and prestressed concrete (PC) beams with a tensile introducing force generated by tensionally anchoring prestressing tendons that are arranged in the PC beams extending along two horizontal directions (or X axis and Y axis) and the PC columns extending along a vertical direction (or Z axis) and passed through the beam-column joint to bring the beam-column joint in triaxial compression, the prestress being introduced such that a diagonal tensile force generated by an input shear force due to a seismic load of an extremely great earthquake that may occur very rarely will be cancelled completely or partially so as not to allow diagonal cracks to occur, wherein the ratio of the prestresses introduced in the directions of the respective axes satisfies the following equation (1):
σx:σy:σz=1:1:0.3-0.9   (1) where σx, σy, and σz are prestresses introduced in the directions of the X axis, the Y axis, and the Z axis respectively, which are calculated by the following equations:
σx=Px/Ax, σy=Py/Ay, σz=Pz/Az, where Px is the tensile introducing force in the direction of the X axis, Ax is a cross sectional area of the beam at an end with respect to the X axis, Py is the tensile introducing force in the Y axis, Ay is a cross sectional area of the beam at an end with respect to the Y axis, Pz is the tensile introducing force in the Z axis, and Az is a cross sectional area of the column at an end with respect to the Z axis.

2. A method of introducing prestress in a beam-column joint according to claim 1, wherein values of σx, σy and σz fall within the following ranges: 2.0≤σx≤10.0 (N/mm.sup.2) 2.0≤σy≤10.0 (N/mm.sup.2) 0.6≤σz≤9.0 (N/mm.sup.2).

3. A method of introducing prestress in a beam-column joint according to claim 2, wherein at least five layers of the building structure are grouped, and the prestress σz introduced in PC columns in the layers of a same group is uniformized.

4. A method of introducing prestress in a beam-column joint according to claim 3, wherein the prestress is introduced such that when a diagonal tensile force generated in the beam-column joint by the extremely great earthquake is partly cancelled and partly remains, a tensile stress intensity resulting from the remaining diagonal tensile force will be equal to or lower than an allowable tensile stress of the prestressed concrete in the beam-column joint.

5. A method of introducing prestress in a beam-column joint according to claim 2, wherein the prestress is introduced such that when a diagonal tensile force generated in the beam-column joint by the extremely great earthquake is partly cancelled and partly remains, a tensile stress intensity resulting from the remaining diagonal tensile force will be equal to or lower than an allowable tensile stress of the prestressed concrete in the beam-column joint.

6. A method of introducing prestress in a beam-column joint according to claim 1, wherein the prestress is introduced such that when a diagonal tensile force generated in the beam-column joint by the extremely great earthquake is partly cancelled and partly remains, a tensile stress intensity resulting from the remaining diagonal tensile force will be equal to or lower than an allowable tensile stress of the prestressed concrete in the beam-column joint.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIGS. 1A and 1B show a portion of a middle floor of a building including beam-column joints constructed only by PC members according to the present invention. FIG. 1A is a plan view and FIG. 1B is a side view.

(2) FIGS. 2A to 2E illustrate beam-column joints in triaxial compression according to the present invention. FIG. 2A is a plan view; FIG. 2B is a side view; FIG. 2C is an 2C-2C cross sectional view of the beam shown in FIGS. 2A and 2B; FIG. 2D is a 2D-2D cross sectional view of the beam shown in FIG. 2A; and FIG. 2E is a 2E-2E cross sectional view of the column shown FIG. 2B.

(3) FIGS. 3A illustrates an arrangement of prestressing tendons in a beam-column joint. FIG. 3B illustrates directions of triaxial compressive stress on the beam-column joint.

(4) FIGS. 4A and 4B illustrate relationship between stresses in a beam-column joint and cracks occurring therein.

(5) FIGS. 5A to 5C show a semi pressure contact PC structure including a beam-column joint formed by cast-in-situ concrete. FIG. 5A is a plan view, FIG. 5B is a side view, and FIG. 5C is a cross sectional view of a beam.

Embodiments for Carrying Out the Invention

(6) FIGS. 1A and 1B show a portion of a building to which the present invention is applied. FIGS. 1A and 1B are, respectively, a plan view and a side view of beam-column joints in a middle floor of a multi-story building.

(7) PC columns 1 and PC beams 2 in the structure shown in FIGS. 1A and 1B are precast members. The PC columns 1 are set upright on the foundation (not shown). Prestressing steel rods 3 serving as prestressing tendons are passed through the PC column 1 and tensionally anchored (in other words, fixed in a tensioned state). The PC beams 2 are set on corbels 11 provided on the PC columns 1. Prestressing cables 31 provided in the PC beams 2 serving as prestressing tendons are passed through the beam-column joints and tensionally anchored.

(8) As shown in FIGS. 1A and 1B, the prestressing steel rods 3 and the prestressing cables 31 serving as prestressing tendons are passed through the beam-column joint in two horizontal directions (X, Y) and the vertical direction (Z) and tensionally anchored to introduce prestress in the beam-column joint 10.

(9) Components and features of the structure that are not directly relevant to the present invention are similar to those in conventional structures and will not be described in detail. For example, as in conventional structures, the PC columns and the PC beams are connected together using the prestressing tendons fixed in a tensioned state, and top concrete and a slab are formed on top of the precast PC beams to form composite beams.

(10) The PC columns and the PC beams mentioned in the description of the present invention are prestressed concrete structural components.

(11) Pressure connection of a precast PC column and a precast PC beam achieved only by prestressing tendons without the use of reinforcing bars will be referred to as full pressure connection, and connection achieved by both reinforcing bars and prestressing tendons will be referred to as semi pressure connection.

(12) FIGS. 2A and 2B show the same structure in a plan view including the X and Y axes and a side view including the X and Z axes, respectively. In FIGS. 2A and 2B, to facilitate understanding of the present invention, the illustration of the prestressing tendons is eliminated, and prestresses o (σx, σy, σz) acting on the beam-column joints are indicated by arrows to show that the beam-column joints 10 are in triaxial compression.

(13) FIGS. 2C to 2E show the cross sectional shapes of the beams extending along the X axis and Y axis and the column extending along the Z axis at their end faces as a 2C-2C cross sectional view, a 2D-2D cross sectional view, and a 2E-2E cross sectional view respectively.

(14) In the method according to the present invention, the operation of tensioning and anchoring secondary cables serving as prestressing tendons provided in the beam members and passed through the beam-column joints is performed before providing the top concrete 20. Therefore, the cross sectional areas Ax, Ay at the end of the beam do not include the top concrete 20. In other words, the cross sectional areas Ax, Ay at the end of the beams that will be used in calculation of the prestresses σx, σy do not include the cross sectional area of the top concrete 20.

(15) Similarly, the beam-column joint 10 (or panel zone) mentioned in the description of the present invention does not include the top concrete 20. In other words, the beam-column joint 10 refers to only the hatched portion in FIGS. 2A and 2B.

(16) It is assumed that prestress σ (σx, σy, σz) is introduced only by tensioning of the prestressing tendons, and the influences of eccentricity of the centroid of the prestressing tendons in the cross sections of the beam members will be ignored.

(17) Therefore, the prestress σ (σx, σy, σz) is calculated only by P/A, and influences of P.Math.e are not taken into account, where P is the effective tension introducing force by the prestressing tendons, “A” is the cross sectional area (Ax, Ay, Az) at the end of each of the beam and the column member as described above, and “e” is the eccentricity of the centroid of the prestressing tendons from the centroid axis of the beam or column member in its cross section.

(18) In this specification, the terms “PC column” and “PC beam” are used to refer to those which are prestressed over their entire length, which may include components that are prestressed by primary prestressing tendons (i.e. those prestressed in the factory) and components that are prestressed by secondary prestressing tendons (i.e. those prestressed at the site of construction).

(19) The primary prestressing tendons are not illustrated in the drawings. Prestressing by primary prestressing tendons is conducted in the factory, and tensioning may be performed by either pre-tensioning or post tensioning. Tensioning of the secondary prestressing tendons is performed at the site of construction by post-tensioning. In the following description, prestressing cables used as secondary prestressing tendons will also be referred to as secondary cables.

(20) FIGS. 3A and 3B show how prestress is introduced in the beam-column joint 10 in triaxial compression according to the present invention. FIG. 3A is a perspective view illustrating prestressing tendons set in the beam-column joint 10, and FIG. 3B is a view illustrating how triaxial compressive stress acts on the beam-column joint.

(21) As shown in FIGS. 3A and 3B, in order to satisfactorily cancel diagonal tensile force generated due to the earthquake by establishing triaxial compression of the beam-column joint, it is necessary to introduce prestresses (σx, σy, σz) in the beam-column joint 10 in three axial directions. Moreover, relationship among the introduced prestresses (σx, σy, σz) is very important. Specifically, advantageous effects achieved by the constraint of the beam-column joint 10 is greatly affected by whether the prestresses (σx, σy, σz) are in a well-balanced relationship.

(22) Advantageous effects of the present invention will now be described with reference to FIGS. 4A and 4B. FIGS. 4A and 4B illustrate relation between the stress in the beam-column joint 10 and the occurrence of cracks.

(23) FIG. 4A shows a panel zone of a conventional RC construction on which a seismic load is acting on the building as a right action. Though not shown in the drawings, when a seismic load is acting on the building as a left action, the locations and directions of the stress, deformation, and cracks are reverse to those in FIG. 4A.

(24) In the beam-column joint 10 of a conventional RC construction, when a great earthquake occurs, an input shear force (not shown) acts on the structural frame in the horizontal direction due to the seismic load, and the input shear force generates bending moments Mx and Mz on the ends of the beams and the columns respectively in the X-Z plane. On the column 1 is acting a vertical stationary load (N) as an axial force, the magnitude of which is not uniform but varies depending on the floor level. On the other hand, no axial force acts on the beam generally. Because constraint against the bending moments caused by the seismic load cannot be provided, there arises a relative displacement between the columns 1 on the vertically upper end and the lower end of the beam-column joint (or panel zone), and the ends of the horizontally left and right beams deform rotationally to make the beam-column joint 10 rhomboidal as shown in FIG. 4A. In consequence, the bending moments Mx, Mz acting on the ends of the beams and the columns generate a tensile stress on one side of the cross section of the beams and the columns and a compressive stress on the other side, though not shown. This tensile stress generates resultant diagonal tensile forces (T and Tc) along a diagonal and at corners of the beam-column joint, leading to the occurrence of cracks along the diagonals (including a diagonal crack 4 along the diagonal and diagonal cracks 41 at corners). This eventually causes a brittle shear failure, which probably leads to fatal collapse of the entire structural frame.

(25) There may be cases where one of the diagonal crack 4 along the diagonal and the diagonal cracks 41 at corners occurs and cases where both of them occur. The occurrence of diagonal crack(s) along a diagonal mentioned in the description of the present application includes both the cases.

(26) FIG. 4B shows a beam-column joint 10 in triaxial compression by prestress introduced according to the present invention. While FIG. 4B shows only the X-Z plane, the following description also applies to the Y-Z plane, though not shown in the drawings.

(27) As shown in FIG. 4B, a seismic load tends to generate diagonal tensile forces in the beam-column joint (or panel zone) 10 including tensile forces T along a diagonal and tensile forces Tc at corners as in the above-described conventional structure. However, because the beam-column joint (or panel zone) 10 is strongly constrained from outside by virtue of the prestress σ (σx and σz in FIG. 4B) introduced thereto, the beam-column joint 10 does not deform unlike with the conventional structure. Moreover, setting the ratio of prestresses as specified by equation (1) according to the present invention leads to a resultant compressive force Cp on a diagonal and resultant compressive forces Cc at corners. Furthermore, if the values of stresses σx, σy, and σz in equation (1) are limited within respective appropriate ranges, effective and favorable resultant compressive forces Cp and Cc will be generated to cancel the tensile forces T and Tc completely or partially, thereby preventing the occurrence of diagonal cracks.

(28) There may be cases where the tensile force T on a diagonal is cancelled by the resultant compressive force Cp only partially and the tensile force T partly remains. According to the present invention, prestressing tendons are set and anchored in such a way as to introduce specific prestresses according to equation (1) so that the resultant compressive forces will make the tensile stress intensity (i.e. tensile stress per unit area) on a cross section of the concrete lower than the allowable tensile stress intensity of the concrete used to construct the beam-column joint, even if the tensile force T partly remains, thereby preventing diagonal cracks of concrete from occurring.

(29) For example, if the design standard strength Fc of the concrete used to construct the beam-column joint 10 is 60N/mm.sup.2, the allowable tensile stress ft of the concrete is as follows: ft=1/30Fc=2N/mm.sup.2. Prestress is introduced in such a way as to make a tensile stress intensity resulting from the aforementioned partially remaining tensile force T (if it remains) lower than the allowable tensile stress intensity of the concrete. This also applies to the tensile forces Tc occurring at corners.

(30) In conventional PC structures constructed using precast PC columns and precast PC beams, a beam member and a column member are connected together by full pressure connection. Specifically, prestressing tendons passing through the column are tensionally anchored to the end of the beam. It is considered sufficient that the tension introducing force for this purpose be set in such a way as to meet requirements of PC pressure connection of the end of the beam to the column. Likewise, in conventional PC structures, to connect two column members together by PC pressure connection, prestressing tendons are arranged along the axial direction of the columns and required prestressing force is introduced.

(31) In conventional structures, no consideration has been given to relationship between the prestressing in the X and Z directions or Y and Z directions for the purpose of generating a resultant compressive force Cp on a diagonal of the beam-column joint (or panel zone). In other words, in conventional structures, stress introducing forces in the respective directions have been applied only for the purpose of achieving full pressure connection of the members, but no consideration has been given to the ratio among the magnitudes of the stress introducing forces. Therefore, it is not secured that an effective resultant compressive force Cp is always generated on a diagonal of the beam-column joint (or panel zone). Likewise, no consideration has been given to generation of compressive forces at corners of the beam-column joint (or panel zone).

(32) FIGS. 5A to 5C show a case where a PC structure is constructed by layered construction. In this case, columns and beams are prepared as precast members, and beam-column joints (or panel zones) 10 are constructed by concrete cast in situ. Precast beam members may be joined together by fixing reinforcing bars extending from the precast beam members to a beam-column joint. Regarding precast column members, though not shown in the drawings, reinforcing bars extending from a precast column member are extended through a beam-column joint, so that the upper precast column member may be connected with another precast column member, using a mortar-filled joint or the like in some cases, as shown in FIG. 5 of Patent Literature 3 (Japanese Patent No. 4041828). In such cases, while the beam members and the column members are made of PC structure, the beam-column joints 10 are made of RC structure.

(33) In some conventional layered constructions, the amount of reinforcing bars is reduced to provide prestressing tendons, and tension introducing forces are applied. In such cases, connections of members are achieved by semi pressure connection instead of full pressure connection, leading to a much smaller number of prestressing tendons required than in full pressure connection. Hence, the prestress introduced in the beam-column joint is much lower. Therefore, in layered constructions, it is not possible to generate effective resultant compressive forces (Cp and Cc) in beam-column joints (or panel zone) 10.

(34) In PC structures constructed by the conventional layered construction, beam-column joints are made of RC (reinforced concrete) or PRC (prestressed reinforced concrete), which are more vulnerable to diagonal cracking than ordinary beam-column joints made of PC. Therefore, the need for reinforcement by prestressing is higher in structures using semi pressure connection than in structures using full pressure connection.

(35) In the method according to the present invention, prestressing tendons are arranged along three axial directions (X, Y, Z) in a beam-column joint as in conventional methods. Moreover, the present invention definitely teaches a specific method of introducing prestresses with a reduced prestress σz along the vertical direction, which is determined taking account of axial force acting on the column. Specifically, appropriate prestresses are introduced according to equation (1). Moreover, the present invention limits numerical ranges for the values of prestresses σx, σy, and σz that are suitable for the design standard strength of concretes commonly used in PC structures such that effective resultant compressive forces (Cp and Cc) that are not too large nor too small will be generated in the beam-column joint(or panel zone).

(36) The process of layered construction according to an embodiment of the present invention, shown in FIGS. 5A to 5C will now be described.

(37) Firstly, precast PC columns 1 are set upright on the foundation (not shown), and prestressing steel rods 3 serving as prestressing tendons are passed through the PC columns 1 and tensionally anchored. Then, precast PC beams 2 are set on corbels 11 provided on the PC columns 1, and bottom reinforcing bars 5 extending from ends of adjacent PC beams 2 are connected by reinforcing bar joints. The bottom reinforcing bars 5 may be connected by lap joint without using reinforcing bar joints, alternatively. Then, wires and reinforcing bars are arranged in the beam-column joints (or panel zones) 10, and concrete having a compression strength equal to or higher than the PC beams 2 is poured in situ up to the level as high as the upper face of the precast PC beams 2 and cured. After the concrete is cured, prestressing cables 31 serving as prestressing tendons arranged in the PC beams 2 are tensionally anchored to introduce prestress in two horizontal directions (X, Y). Then, upper top reinforcing bars 5 are set on top of the precast PC beams 2, and top concrete and a slab are formed together. Normally, the concrete of the PC beams 2 and the slab have different strength, specifically the PC beams 2 have higher strength. Therefore, cast-in-situ concrete in the beam-column joint (or panel zone) 10 is poured and cured in two stages.

(38) After the top concrete 20 is cured, a precast PC column 1 of the upper floor is set on the beam-column joint 10, and prestressing steel rods 3 serving as prestressing tendons are connected by couplers and tensionally anchored to introduce prestress in the vertical direction (or Z direction). When reinforcing bars extend into the PC column 1 of the upper floor, the reinforcing bars are passed through the beam-column joint before pouring concrete, and after the concrete is poured and cured, the reinforcing bars are connected with the column member of the upper floor by connecting the reinforcing bars by mortar-filled joints.

(39) In the case of the beam-column joint (or panel zone) 10 constructed by layered construction described above, the cross sectional area Ax, Ay at the end of the beam does not include the top concrete, as with the embodiment shown in FIGS. 1A and 1B, where all the components used are precast members. Therefore, relationship represented by equation (1) applies to this case also.

(40) The method of introducing prestress in a beam-column joint according to the present invention can also be applied to PC structures constructed by cast-in-situ prestressed concrete in which all of the PC columns, PC beams, and beam-column joints (panel zone) 10 are constructed by concrete that is cast in situ, though not shown in the drawings.

(41) In this case, the cross sectional area Ax, Ay at the end of the beam shall be construed as the cross sectional area at the time when prestressing tendons are tensionally anchored to introduce prestress. For example, in cases where the slab has not been formed on the beam at the time of tensional anchoring, the cross sectional area Ax, Ay shall be construed not to include the slab. In cases where tensional anchoring is performed after the beam and the slab are formed, the cross sectional area Ax, Ay shall be construed to include the slab.

(42) In a mode of the present invention, at least five layers (or stories) of a building are grouped, and the same prestress is introduced in the beam-column joints in the same group of layers. This mode will be described in the following.

(43) The axial force acting on columns varies depending on layers (or floor levels) of the building. Therefore, it is preferable that the prestress introduced in the columns be adjusted according to the variations in the axial force to uniformize the sum of the axial force and the prestress. However, controlling the tension is a very troublesome and difficult task. In this mode of the present invention, an allowable range (σz=0.3−0.9) is set for the ratio of the stress introduced in the columns to the stress introduced in the beams, to allow the same stress to be set for the columns in five layers in the same group. This facilitates the design and construction of the beam-column joints.

(44) For example, in a ten-story building of PC structure, a certain number of prestressing steel rods are provided in each column in the first to fifth floors. Because the axial force decreases in the columns in the sixth to tenth floors, the number of prestressing steel rods provided in each column in the sixth to tenth floors is increased to compensate the decrease accordingly. This mode provides a practical method of introducing prestress that allows the sum of the axial force and the prestress acting on columns in these layers to readily fall within the allowable range (σz=0.3−0.9) while enabling simplification in design and construction of the building.

(45) An extremely great earthquake is so rare as to occurs once in the lifetime of a building at most. Even if it occurs, the building will not be significantly damaged unless diagonal cracks occur. Therefore, in the present invention, when a part of the diagonal tensile force generated at the beam-column joint remains, the tensile stress intensity may be set to be equal to or less than the allowable tensile stress of concrete. This is applied when priority is given to reducing construction costs by reducing PC tendons.

REFERENCE SINGS LIST

(46) 1: PC column 10: beam-column joint (or panel zone) 11: corbel 2: PC beam 20: top concrete 3: prestressing steel rod 31: prestressing cable 4: diagonal crack 41: diagonal crack at corner 5: reinforcing bar T: tensile force Tc: tensile force Cp: resultant compressive force Cc: resultant compressive force at corner