CN210002823U

CN210002823U - lifting movable scaffold convenient to fix

Info

Publication number: CN210002823U
Application number: CN201920253832.2U
Authority: CN
Inventors: 宋伟峰
Original assignee: Individual
Current assignee: Individual
Priority date: 2019-02-28
Filing date: 2019-02-28
Publication date: 2020-01-31
Anticipated expiration: 2029-02-28

Abstract

The utility model relates to a scaffold technical field, specifically, relate to lifting mobile scaffold convenient to it is fixed, including bottom surface support, lifting unit and four group locking mechanism, four apex angle departments on bottom surface support top are vertical upwards to be provided with four loop bars, the vertical decurrent four inserted bars that insert the establishment with the cooperation of four loop bars that are provided with of lifting support lower extreme, bottom surface support bottom is provided with four truckles, the utility model discloses a constructor directly stands and to pull up or push down the fastening that realizes locking mechanism and loosen on the scaffold, make constructor not need follow the scaffold and climb down the elasticity mechanism who adjusts the scaffold again, saved the time, make things convenient for constructor to the removal of scaffold position in the construction, labour saving and time saving, guaranteed the smooth and easy nature of construction, realize the regulation of scaffold height through rotatory hexagonal screw, convenient operation, and it is convenient to deposit after using, can save storage space greatly.

Description

lifting movable scaffold convenient to fix

Technical Field

The utility model relates to a scaffold technical field specifically, relates to fixed over-and-under type removal scaffold of being convenient for.

Background

The scaffold is a working platform which is erected for ensuring that each construction process is smoothly carried out, the scaffold is divided into an outer scaffold and an inner scaffold according to the erected position, the scaffold is divided into a wood scaffold, a bamboo scaffold and a steel pipe scaffold according to different materials, the scaffold is divided into a vertical rod type scaffold, a bridge type scaffold, a type scaffold, a suspension type scaffold, a hanging type scaffold, a picking type scaffold and a climbing type scaffold according to the structural form, most of the scaffolds which are adopted for a wall surface with the height of in coating construction like are fixed scaffolds or movable scaffolds, the fixed scaffolds need to be manually lifted and moved after construction is completed, the scaffold is extremely inconvenient to use, time and labor are consumed to influence the construction process, storage is extremely inconvenient after use, a large amount of space is occupied, the mobile scaffolds on the market are fixed in the process of construction although casters are arranged at the bottom, in the use process of constructors, the constructors need to be separated from the scaffolds and then to be loosened to move the scaffolds when the construction position needs to be fixed, the scaffold is very likely to delay the construction time of the scaffold to be conveniently moved, and the scaffold is very likely to prolong the construction time of .

SUMMERY OF THE UTILITY MODEL

To the not enough of prior art, the utility model provides an fixed over-and-under type removal scaffold of being convenient for.

The utility model discloses an over-and-under type removal scaffold convenient to it is fixed, including the bottom surface support, lifting unit and four group's locking mechanism, the bottom surface support is the level setting for the rectangle structure, but lifting support is the level setting of rectangle structure and vertical reciprocating motion directly over the bottom surface support, lifting unit and lifting support are vertical upwards to arrange in proper order, lifting unit is connected with the upper end of bottom surface support and lifting support's lower extreme transmission respectively, four vertical upwards be provided with four loop bars in bottom surface support top, the vertical downward four inserted bars that establish are inserted with the cooperation of four loop bars of lifting support lower extreme, every inserted bar and loop bar all are provided with a plurality of bolt along vertical direction horizontal interval, four group's locking mechanism are rectangle distribution and four apex angles departments of vertical setting on bottom surface support and lifting support's top, every group's locking mechanism's the same structure and all are connected with bottom surface support and lifting support transmission, bottom surface support is provided with four truckles.

Preferably, every group locking mechanism includes the handle, a fixed base, second loop bar and second inserted bar, and the fixed base is vertical setting, and the handle middle part is articulated with fixed base upper portion, and the vertical setting of second inserted bar passes the lifting support at inserted bar side and top and upwards extends, and the extension end of second inserted bar is articulated with the end of handle, and the second loop bar is vertical setting and the top cover is established in the lower part of second inserted bar, and every second inserted bar and second loop bar all are provided with a plurality of second bolt along vertical direction horizontal interval, and the bottom level that bottom surface support downwardly extending just extended end was passed to the bottom of second loop bar is provided with the backup pad.

Preferably, every the fixing base all includes the supporting seat, two baffles, two sets of braking component and dustproof cover plate, the supporting seat is vertical setting, two baffles are vertical interval and set up on the supporting seat top, dustproof cover plate level sets up the top at two baffles, the level is provided with pivot and articulates with the middle part of handle between two baffles, two sets of braking component structures are the same and be vertical setting side of keeping away from each other at two baffles respectively, every braking component of group all includes the ratchet, the rocker, extension spring and straight-bar, the ratchet is vertical setting, the rocker level sets up the below at the ratchet, end level of rocker is provided with articulated shafts, the vertical pawl that upwards is provided with in top middle part of rocker, the vertical setting of straight-bar is ends in addition of rocker, the vertical setting of extension spring is just established on the cover, the both ends of extension spring respectively with the top of straight-bar and the bottom fixed connection of dustproof cover plate, the top of straight-bar passes dustproof cover plate.

Preferably, every the inserted bar top all is provided with fixed axles with the articulated department of handle to the axis direction of fixed axle is mutually perpendicular with the length direction of handle, the handle is close to the vertical through-hole that supplies inserted bar to insert to establish that is provided with in top of inserted bar end, the handle is passed at the fixed axle both ends and is outwards extended, the handle both sides all are provided with the gliding bar of confession fixed axle extension end and dodge the hole, the equal vertical fixed cylinder of being provided with of extension end at fixed axle both ends is detained, and the diameter that the cylinder was detained is greater than the width that the hole was dodged to the bar.

Preferably, lifting unit includes an upper fixed plate, bottom plate and hexagonal screw, bottom plate and upper fixed plate set up along vertical ascending direction interval, four apex angle departments on upper fixed plate top are provided with the down tube of the fourth outside expansion, the top of every down tube and lifting support's bottom fixed connection, four apex angle departments in bottom plate bottom are provided with the second down tube of four outside expansions, the bottom of every second down tube and ground support's top fixed connection, the vertical setting of hexagonal screw is at bottom plate bottom middle part, the screw thread end of hexagonal screw passes the bottom plate and upwards extends and pass the upper fixed plate simultaneously, the hexagonal screw is articulated with the bottom plate and with upper fixed plate threaded connection.

Preferably, an extension frame is arranged on the side of the lifting support in the length direction , and the end of the extension frame is hinged with the lifting support.

Preferably, stairs are vertically arranged downwards on the side, away from the bottom end , of the lifting support, a second stair is vertically arranged upwards on the side, away from the top end , of the bottom support, the stairs and the second stair are not on the same plane, and the sum of the lengths of the stairs and the second stair is smaller than the sum of the lengths of the inserted bar and the inserted bar.

Has the advantages that: the utility model discloses a constructor directly stands and will handle the fastening that pull up or push down to realize locking mechanism on the scaffold frame and loosen, thereby make constructor need not climb down from the scaffold frame and adjust the take-up unit of scaffold frame again, the time is greatly saved, the removal of constructor to scaffold frame position in the construction has been made things convenient for, and is time-saving and labor-saving, thereby the smooth and easy nature of construction has been guaranteed, realize the regulation of scaffold frame height through rotatory hexagonal screw, and convenient for operation, and it is very convenient to deposit after using, and the storage space can be greatly saved.

Drawings

The accompanying drawings, which are incorporated herein and constitute part of this application and are included to provide a further understanding of the application, section of the application, illustrate embodiments of the application and together with the description serve to explain the application and not to limit the application.

Fig. 1 is a schematic perspective view of the present invention;

fig. 2 is a schematic perspective view of the present invention;

fig. 3 is a side view of the present invention;

FIG. 4 is an exploded perspective view of the locking mechanism;

FIG. 5 is an enlarged view taken at A in FIG. 4;

FIG. 6 is an enlarged view at B in FIG. 4;

the reference numbers indicate that the bottom surface bracket 1, the lifting bracket 2, the th loop bar 1a, the th inserted bar 2a, the th inserted pin 5, the caster 6, the fixed seat 4a, the handle 4b, the second loop bar 4c, the second inserted bar 4d, the second inserted pin 7, the support plate 8, the support seat 4aa, the baffle 4ab, the dust-proof cover plate 4ac, the ratchet 9, the pawl 9a, the rocker 10, the tension spring 11, the straight bar 12, the button 13, the through hole 14, the strip-shaped avoiding hole 15, the cylindrical buckle 16, the upper fixing plate 3a, the lower fixing plate 3b, the hexagonal screw 3c, the th inclined bar 3d, the second inclined bar 3e, the extension frame 17, the th staircase 18 and the second staircase 19.

Detailed Description

In addition, is provided to simplify the drawing and to simplify the description provided herein, in which conventional structures and components are shown in simplified schematic form.

In addition, the descriptions related to "", "second", etc. in the present invention are only used for descriptive purposes, not specifically referring to the order or sequence, and not for limiting the present invention, but only for distinguishing the components or operations described in the same technical terms, and not for indicating or implying relative importance or implicitly indicating the number of the indicated technical features.

Referring to kinds of lifting movable scaffolds convenient to fix shown in fig. 1-6, including bottom surface support 1, lifting support 2, lifting unit and four groups of locking mechanisms, bottom surface support 1 is the level setting for the rectangular structure, lifting support 2 is the rectangular structure and can vertical reciprocating motion's level setting directly over bottom surface support 1, lifting unit and lifting support 2 are vertical upwards to arrange in proper order, lifting unit is connected with the upper end of bottom surface support 1 and the lower extreme transmission of lifting support 2 respectively, four apex angle departments at bottom surface support 1 top are vertical upwards to be provided with four loop bars 1a, lifting support 2 lower extreme is vertical downwards provided with four inserted bar 2a of inserting with four loop bar 1a cooperations and inserting, every inserted bar 2a and loop bar 1a all are provided with a plurality of bolts 5 along vertical direction horizontal interval, four groups of locking mechanisms are four apex angle departments that rectangular distribution and vertical setting is on the top of bottom surface support 1 and lifting support 2, every group of locking mechanism's structure is the same and all is provided with transmission support 1 and lifting support 2 bottom surface and is connected four truckles bottom casters 1 and 6 distributions.

Each set of locking mechanism comprises a handle 4b, a fixed seat 4a, a second sleeve rod 4c and a second inserting rod 4d, wherein the fixed seat 4a is vertically arranged, the middle part of the handle 4b is hinged with the upper part of the fixed seat 4a, the second inserting rod 4d is vertically arranged beside the second inserting rod 2a, the top end of the second inserting rod extends upwards through the lifting support 2, the extending end of the second inserting rod 4d is hinged with the end of the handle 4b, the second sleeve rod 4c is vertically arranged, the top end of the second inserting rod is sleeved on the lower part of the second inserting rod 4d, each second inserting rod 4d and the second sleeve rod 4c are horizontally provided with a plurality of second inserting pins 7 at intervals along the vertical direction, the bottom end of the second sleeve rod 4c extends downwards through the bottom surface support 1, and the bottom end of the extending end is horizontally provided with a support plate 8, when a construction worker needs to adjust the construction position, the construction worker pushes down the ends ends of the four handles 4b far away from the second inserting rod 4d, the middle part is hinged with the middle part of the second inserting rod 4b hinged with the fixed seat 4b, the second inserting rod 4c moves upwards, the second inserting rod 4c and the second inserting rod 4c moves towards the ground, the lower end of the second inserting rod 4c, the scaffold is hinged with the scaffold, the scaffold is the scaffold, the scaffold 4b moves the scaffold, the scaffold 4b moves towards the scaffold, the scaffold 4b moves towards the scaffold, the scaffold 4d, the scaffold is the scaffold.

Each of the fixing seats 4a includes a supporting seat 4aa, two baffle plates 4ab, two sets of braking components and a dustproof cover plate 4ac, the supporting seat 4aa is vertically arranged, the two baffle plates 4ab are vertically arranged at the top end of the supporting seat 4aa at intervals, the dustproof cover plate 4ac is horizontally arranged at the top ends of the two baffle plates 4ab, rotating shafts are horizontally arranged between the two baffle plates 4ab and hinged to the middle of the handle 4b, the two sets of braking components are identical in structure and vertically arranged on sides, away from the two baffle plates 4ab, each set of braking components includes a ratchet 9, a rocker 10, a tension spring 11 and a straight rod 12, the ratchet 9 is vertically arranged, the rocker 10 is horizontally arranged below the ratchet 9, is horizontally arranged at the end of the rocker 10, a pawl 9a is vertically arranged upwards in the middle of the top end of the rocker 10, the straight rod 12 is vertically arranged upwards at the other end of the rocker 10, the tension spring 11 is vertically arranged and sleeved on the straight rod 12, two ends of the tension spring 11 respectively abut against the top end of the bottom end of the dustproof cover plate 12 and fixedly connect with the bottom end of the straight rod 12, the handle 13 b, the straight rod 13 b, when a scaffold is moved to a scaffold, the scaffold is moved, the handle 13 d, the scaffold is moved, the scaffold, the handle 13 d is moved, the handle is moved, the handle 13 d, the handle, the scaffold is moved, the handle is lifted scaffold, the handle is moved, the handle 4a is moved, the handle 13 d, the handle is separated from the handle, the scaffold, the handle is moved, the scaffold.

fixed shafts are arranged at the hinged positions of the top end of each inserted rod 2a and the handle 4b, the axis direction of each fixed shaft is perpendicular to the length direction of the handle 4b, a through hole 14 for the inserted rod 2a to be inserted is vertically arranged at the top end of the handle 4b close to the end of the inserted rod 2a, two ends of each fixed shaft penetrate through the handle 4b to extend outwards, strip-shaped avoiding holes 15 for the extending ends of the fixed shafts to slide are arranged at two sides of the handle 4b, cylindrical buckles 16 are vertically and fixedly arranged at the extending ends of the two ends of each fixed shaft, the diameter of each cylindrical buckle 16 is larger than the width of each strip-shaped avoiding hole 15, when a constructor lifts or presses the handle 4b upwards or downwards, the distance between the end of the handle 4b close to the second inserted rod 4d and the second inserted rod 4d is constantly changed, in the process, the fixed shafts can slide back and forth in the strip-shaped avoiding holes 15 to change the distance between the handle 4b and the second inserted rod 4d, so that the second inserted rod 4d can slide upwards or the strip-shaped avoiding holes can not fall off when the handle 4b moves downwards, and the strip-shaped avoiding holes 16 can not fall off.

The lifting assembly comprises an upper fixing plate 3a, a lower fixing plate 3b and hexagonal screws 3c, the lower fixing plate 3b and the upper fixing plate 3a are arranged at intervals along a vertical upward direction, four vertex angles at the top end of the upper fixing plate 3a are provided with four outwards-expanded -th oblique rods 3d, the top end of each -th oblique rod 3d is fixedly connected with the bottom end of the lifting support 2, four outwards-expanded second oblique rods 3e are arranged at four vertex angles at the bottom end of the lower fixing plate 3b, the bottom end of each second oblique rod 3e is fixedly connected with the top end of the ground support, the hexagonal screws 3c are vertically arranged in the middle of the bottom end of the lower fixing plate 3b, the threaded ends of the hexagonal screws 3c penetrate through the lower fixing plate 3b to extend upwards and simultaneously penetrate through the upper fixing plate 3a, the hexagonal screws 3c are hinged with the lower fixing plate 3b and are in threaded connection with the upper fixing plate 3a, when the height between scaffolds needs to be adjusted, at the moment, a constructor a worker can adjust the height between the hexagonal screws 3b and the hexagonal wrench 3c when the upper fixing plate and the hexagonal screws 3c and the hexagonal wrench, the hexagonal wrench is required to adjust the height, the whole upper fixing plate 3a distance between the hexagonal screws 3a bolt 3a, so that the bolt 3b and the bolt 3c is not to be rotated, and the bolt 3c, and the bolt is.

The extension frame 17 is arranged on the side of the lifting support 2 in the length direction , and the end of the extension frame 17 is hinged with the lifting support 2. the extension frame 17 is foldable, so that the folded part can be directly erected on an adjacent object when necessary, the use space of the scaffold is enlarged, and the use distance of the scaffold is prolonged.

The stairway 18 is vertically arranged downwards on the side of the lifting support 2 far away from the bottom end of the extension frame 17, the second stairway 19 is vertically arranged upwards on the side of the bottom surface support 1 far away from the top end 0 of the extension frame 17, the th stairway 18 and the second stairway 19 are not on the same plane 4 2, and the sum of the lengths of the st stairway 18 and the second stairway 19 is less than the sum of the lengths of the th inserted bar 2a and the th inserted bar 1 a. when the distance between the scaffolds is adjusted, the distance between the 8657 th stairway 18 and the lifting support 2 is increased or decreased, the sum of the lengths of the nd stairway 18 and the second stairway 19 is less than the sum of the lengths of the 5393 rd inserted bar 2a and the th inserted bar 1a when the distance between the bottom surface support 1 and the lifting support 2 is changed, and the sum of the lengths of the 539 3 rd inserted bar 2 th stairway 18 and the second stairway 19 is less than the sum of the lengths of the th inserted bar 2 when the distance between the ground surface support and the lifting support 2 is maximum, so that the distance between the second stairway 18 and the lifting.

When the scaffold needs to be moved, the constructor needs to loosen the four sets of locking mechanisms, in the process, the constructor directly stands on the scaffold to press the two buttons 13 downwards, at the same time, the straight rod 12 below the buttons 13 starts to move downwards, the end of the rocker 10 is hinged to the hinge shaft, the bottom end of the straight rod 12 abuts against the free end of the rocker 10, at the same time, the free end of the rocker 10 starts to move downwards to drive the pawl 9a to move downwards, at the same time, the pawl 9a and the ratchet 9 are separated from each other, at the same time, the ratchet 9 can rotate freely to drive the handle 4b to rotate freely, at the same time, the constructor pushes down the end of the four handles 4b far from the second inserting rod 4d, at the same time, the middle of the handle 4b is hinged to the upper portion of the fixing seat 4a, the other end of the handle 4b starts to move upwards, the other end of the handle end of the handle 4b is hinged to the second inserting rod 4d, the second inserting rod 4d, the second inserting rod drives the second inserting rod 4c to move upwards, the second inserting rod 4c is hinged to move, the hexagonal bolt 4c, when the second inserting rod 4c is required to move, the hexagonal bolt 4b, the bolt 4c, the bolt 4b is hinged to move, the bolt 4b is fixed plate 4b, the bolt 4c, the bolt 4b is fixed plate, the bolt 4c, the bolt 4b is fixed plate 4b, the bolt 4c, the bolt 4b, the bolt 4c, the bolt 4b is fixed bolt 4c, the bolt 4 c.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

The lifting type movable scaffold convenient to fix is characterized by comprising a bottom surface support (1), a lifting support (2), a lifting assembly and four groups of locking mechanisms, wherein the bottom surface support (1) is of a rectangular structure and is horizontally arranged, the lifting support (2) is of a rectangular structure and can be vertically reciprocated horizontally and is arranged right above the bottom surface support (1), the lifting assembly and the lifting support (2) are vertically and upwards sequentially arranged, the lifting assembly is respectively in transmission connection with the upper end of the bottom surface support (1) and the lower end of the lifting support (2), four top corners of the top end of the bottom surface support (1) are vertically and upwards provided with four sleeve rods (1a), the lower end of the lifting support (2) is vertically and downwards provided with four sleeve rods (2a) which are matched and inserted with the four sleeve rods (1a), each sleeve rod (2a) and each sleeve rod (1a) are horizontally provided with a plurality of bolts (5) at intervals along the vertical direction, the four groups of locking mechanisms are distributed in a rectangular shape, the vertical arrangement, the bottom surface support (1) and four lifting mechanisms are connected with four caster wheels (6) of the bottom surface support (1) and are distributed with four lifting support (1) and four lifting mechanisms (6).
2. A conveniently fixed lifting mobile scaffold, according to claim 1, wherein each set of said locking mechanism comprises a handle (4b), a fixed seat (4a), a second loop bar (4c) and a second inserted bar (4d), the fixed seat (4a) is vertically disposed, the middle of the handle (4b) is hinged with the upper part of the fixed seat (4a), the second inserted bar (4d) is vertically disposed beside the inserted bar (2a) and the top end thereof passes through the lifting bracket (2) to extend upwards, the extending end of the second inserted bar (4d) is hinged with the end of the handle (4b), the second loop bar (4c) is vertically disposed and the top end thereof is sleeved on the lower part of the second inserted bar (4d), each second inserted bar (4d) and second loop bar (4c) are horizontally provided with a plurality of second inserted pins (7) at intervals along the vertical direction, the bottom end of the second loop bar (4c) passes through the bottom surface (1) to extend downwards and the bottom end of the extending end thereof is provided with a support plate (8).
3. The lifting mobile scaffold convenient to fix of types as claimed in claim 2, wherein each of the fixing seats (4a) includes a supporting seat (4aa), two baffles (4ab), two sets of braking components and a dust-proof cover plate (4ac), the supporting seat (4aa) is vertically disposed, the two baffles (4ab) are vertically spaced at the top end of the supporting seat (4aa), the dust-proof cover plate (4ac) is horizontally disposed at the top end of the two baffles (4ab), rotating shafts are horizontally disposed between the two baffles (4ab) and hinged to the middle portion of the handle (4b), the two sets of braking components are identical in structure and are respectively vertically disposed at sides of the two baffles (4ab) away from each other, each set of braking components includes a ratchet wheel (9), a rocker (10), a tension spring (11) and a straight rod (12), the ratchet wheel (9) is vertically disposed, the rocker (10) is horizontally disposed below the ratchet wheel (9), end of the rocker (10) is horizontally disposed with , the middle portion of the top end of the rocker (10) is vertically upwardly disposed with a pawl (9a straight rod (12), the extension spring (12) is vertically disposed on the top end of the straight rod (12), and the vertical extension spring (12) is disposed above the vertical cover plate (13) and the vertical end of the vertical rod (12), the extension spring (12) and the extension spring (12) is disposed on the vertical end of the straight rod (4 ac).
4. lifting mobile scaffold convenient for fixing, according to claim 3, wherein fixing shafts are provided at the hinged position of the top end of each inserting rod (2a) and the handle (4b), and the axial direction of the fixing shafts is perpendicular to the length direction of the handle (4b), a through hole (14) for inserting the inserting rod (2a) is vertically provided at the top end of the handle (4b) near the end of the inserting rod (2a), both ends of the fixing shafts pass through the handle (4b) to extend outwards, bar-shaped avoiding holes (15) for sliding the extending ends of the fixing shafts are provided at both sides of the handle (4b), cylindrical buckles (16) are vertically and fixedly provided at both extending ends of the fixing shafts, and the diameter of the cylindrical buckles (16) is larger than the width of the bar-shaped avoiding holes (15).
5. A conveniently fixed lifting mobile scaffold, according to claim 1, wherein the lifting assembly comprises an upper fixing plate (3a), a lower fixing plate (3b) and a hexagonal screw (3c), the lower fixing plate (3b) and the upper fixing plate (3a) are spaced vertically upward, four outwards expanding oblique rods (3d) are arranged at four top corners of the top end of the upper fixing plate (3a), the top end of each oblique rod (3d) is fixedly connected with the bottom end of the lifting bracket (2), four outwards expanding second oblique rods (3e) are arranged at four top corners of the bottom end of the lower fixing plate (3b), the bottom end of each second oblique rod (3e) is fixedly connected with the top end of the ground bracket, the hexagonal screw (3c) is vertically arranged in the middle of the bottom end of the lower fixing plate (3b), the threaded end of the hexagonal screw (3c) passes through the lower fixing plate (3b) and extends upward while passing through the upper fixing plate (3a), and the hexagonal screw (3c) is hinged with the lower fixing plate (3b) and is threadedly connected with the upper fixing plate (3 a).
6. kinds of easy-to-fix liftable mobile scaffold as claimed in claim 5, wherein the side of the length direction of the lifting support (2) is provided with an extension frame (17), and the end of the extension frame (17) is hinged with the lifting support (2).
7. kinds of conveniently fixed lifting mobile scaffold according to claim 6, characterized in that the lifting support (2) is provided with the th stairs (18) vertically downwards far away from the bottom end side of the extending frame (17), the bottom support (1) is provided with the second stairs (19) vertically upwards far away from the top end side of the extending frame (17), the th stairs (18) and the second stairs (19) are not on the same plane, and the sum of the lengths of the th stairs (18) and the second stairs (19) is smaller than the sum of the lengths of the th inserted bar (2a) and the th sleeved bar (1 a).