WO2001040594A1 - Bundled bars column - Google Patents
Bundled bars column Download PDFInfo
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- WO2001040594A1 WO2001040594A1 PCT/ID2000/000001 ID0000001W WO0140594A1 WO 2001040594 A1 WO2001040594 A1 WO 2001040594A1 ID 0000001 W ID0000001 W ID 0000001W WO 0140594 A1 WO0140594 A1 WO 0140594A1
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- Prior art keywords
- reinforced concrete
- column
- bars
- strength
- quadrangular
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Classifications
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- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04C—STRUCTURAL ELEMENTS; BUILDING MATERIALS
- E04C5/00—Reinforcing elements, e.g. for concrete; Auxiliary elements therefor
- E04C5/01—Reinforcing elements of metal, e.g. with non-structural coatings
- E04C5/06—Reinforcing elements of metal, e.g. with non-structural coatings of high bending resistance, i.e. of essentially three-dimensional extent, e.g. lattice girders
- E04C5/0604—Prismatic or cylindrical reinforcement cages composed of longitudinal bars and open or closed stirrup rods
-
- E—FIXED CONSTRUCTIONS
- E04—BUILDING
- E04C—STRUCTURAL ELEMENTS; BUILDING MATERIALS
- E04C3/00—Structural elongated elements designed for load-supporting
- E04C3/30—Columns; Pillars; Struts
- E04C3/34—Columns; Pillars; Struts of concrete other stone-like material, with or without permanent form elements, with or without internal or external reinforcement, e.g. metal coverings
Definitions
- Bundled bars column system is a placement of is placed as a corner bundled bars in quadrangular reinforced concrete column structure, both square and or rectangular shape. With an exact calculation, this system is able to increase the capacity of the Pn-Mn interaction curve, both for uniaxial and biaxial bending. So, it is able to save the material or the column cost.
- Bundled bars column system will be mentioned as BUNDCOL system or system only, although in practice, maybe there is a single bar (or bundle) in the middle of h and/ or b face area.
- this system can be implemented not only in quadrangular column, but also in structural wall (shear wall or special wall ⁇ like column) in the C or U, L or T shape.
- this system does not give a significant economical benefit for circular columns or normal beams.
- Uniaxial bending is a load on certain Pn with bending moment in one direction, x- or y ⁇ axis.
- Biaxial bending is a load on certain Pn with two direction bending moment in both x - and y - axes simultaneously.
- Varied drawings of BUNDCOL system are unlimited. They depend on the required of the Pn-Mn interaction curve for quadrangular column. Minimum number of longitudinal bars in symmetrical bars column shall be 8.
- FIGURE 1 a cross section of rectangular column with bundled bars consist of 8 bars, which shows the LA-1X, LA-1Y and LA-2Y distance be maximum and effective toward both the x - and y - axes, in accordance with the present invention.
- Drawings for comparison the capacity calculation 'Prr ⁇ ooiumn between distributed bars with bundled bars, are :
- FIGURE 2A column 450 x 450 mm, 16 D 22 with equally distributed bars (page 8 & 9).
- FIGURE 2B column 450 x 450 mm, 16 D 22 with bundled bars (page 8 & 9).
- FIGURE 3A column 12 x 18 in, 12-88 with distributed bars (page 10).
- FIGURE 3B column 12 x 18 in, 4-tt8, 4-#7 & 2-#6 with bundled bars (page 10).
- FIGURE 4A column 12 x 20 in, 8-tt9 with distributed bars (page 11 ).
- FIGURE 4B column 12 x 20 in, 8-87 & 2-#6 with bundled bars (page 11 ).
- FIGURE 5 column 16 x 24 in, 16-#8 with bundled bars (page 12).
- BUNDCOL system denotes placing longitudinal bars for quadrangular reinforced concrete column, both square or rectangular, which longitudinal bars are placed at the corners of the reinforced concrete column. Practical solution of this principle is that the bars are bundled at the corner of the column.
- BUNDCOL system is a technology breakthrough for analyzing and designing reinforced concrete column.
- This system can be applied in structural wall (shear wall or special wall -like column) by the same principle calculation.
- structural wall shear wall or special wall -like column
- longitudinal bars placement especially at the farthest four outer corners from the plastic centroid.
- longitudinal bars placement especially at the three outer corners of the long face.
- longitudinal bars placement especially at the two outer corners of the T top side, then at the other four outer corners.
- the formula used in the interaction capacity Pn-Mn calculation is a standard formula which is commonly used with static principle.
- the modulus of elasticity of non presressed reinforcement may be taken as 200.000 MPa ( 29,000 ksi).
- BUNDCOL system form is made in the form of spread-sheet direct and exact calculation, with interlaced formula so that any change of an axis angle which perpendicular to the neutral axis and or the depth of the neutral axis, has a direct influence to the value of the Pn-M column biaxial capacity.
- BUNDCOL system form can shorten the calculation process of trial & error cubic equation by using personal computer, so it could omit the conservative or unconservative criteria for biaxial bending. Some of calculation process of distance and strain is not displayed in order to make the complete calculation in one page.
- This form can be applied to calculate Pn-Mn column capacity for uniaxial or biaxial bending. And, it can be applied also for unsymmetrical bars column, eventhough with different size of bars.
- the interaction curve Pn-Mn column capacity for biaxial bending is an exact calculation like in uniaxial bending. It is need an acuracy to determine the formulation of each bar distance and the concrete compression block, in the inclination and depth of the neutral axis.
- BUNDCOL system could make use of the short bars (from the waste of the bars cutting) as a bar splicer.
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- Architecture (AREA)
- Civil Engineering (AREA)
- Structural Engineering (AREA)
- Reinforcement Elements For Buildings (AREA)
Abstract
The BUNDCOL system, which the most longitudinal bars be placed in the corner of the quadrangular reinforced concrete column as bundled bars, could increase the curve capacity of Pn-Mn column interaction in both uniaxial and biaxial bending. By this system, the distance between each bar (LA-1X, LA-1Y and LA-2Y) will be maximum and effective toward both the x- and y- axes. With BUNDCOL forms, a direct and exact spread-sheet calculation with interlaced formulas, with the computer can shorten the calculation process of trial & error cubic equation, and omit the conservative or unconservative criteria for biaxial bending formerly. This system can reduce the quantity and/or the dimension of the material, means the reduction of the cost. The other advantage is the availability of the wider space. By the same calculation principle, this system can be applied in structural wall (shear wall or special wall-like column).
Description
BUNDLED BARS COLU N Technical Field
Bundled bars column system is a placement of
is placed as a corner bundled bars in quadrangular reinforced concrete column structure, both square and or rectangular shape. With an exact calculation, this system is able to increase the capacity of the Pn-Mn interaction curve, both for uniaxial and biaxial bending. So, it is able to save the material or the column cost.
To be concise. Bundled bars column system will be mentioned as BUNDCOL system or system only, although in practice, maybe there is a single bar (or bundle) in the middle of h and/ or b face area.
With the same calculation principle, this system can be implemented not only in quadrangular column, but also in structural wall (shear wall or special wall ■ like column) in the C or U, L or T shape. However, this system does not give a significant economical benefit for circular columns or normal beams. Uniaxial bending is a load on certain Pn with bending moment in one direction, x- or y ■ axis. Biaxial bending is a load on certain Pn with two direction bending moment in both x - and y - axes simultaneously.
This system is valid in SI version (Newton-meter) or Inch-Pound units. Background Art Up to now, in Indonesia or in the world there has never been any calculation for bundled bars in quadrangular column section. The reason is because the potential of the strength inclination capacity in the Pn-Mn interaction curve, has not been noticed or realized. The load characteristic of many column in practice, combination of an axial load with bending moment in both x and y - axes simultaneously, that makes this system capable of increasing the significant Pn- Mn column capacity (this means cost saving). This system also provides wider space for placing longitudinal bars.
The column formula for uniaxial bending capacity on the compression- controlled area was developed in 1 942. Although the formula is not quite accurate, the basic analysis and design of column was exist for a long time. The equivalent rectangular stress block factor βi = 0.85 was formulated in around 1930, that is followed by ACI 318-95 (for fc' $ 4 ksi) and SK SNI T-15-1 991 -03 (for fc' 30 Mpa), and has still been used widely up to now.
The investigation or design of a square or rectangular section subjected to
.
2
charts, formulas and computer analyses have been aes^fcpSc^^and published, but no one was a direct calculation without a trial & error cubic equation.
One method of analysis for square or rectangular column with axial compression and biaxial bending moment is to use the basic principles of equilibrium with the same strength assumption like that for the case of axial compression and bending about one axis only. This method essentially involves a trial and error process for obtaining the position of an inclined neutral axis, hence any such method is sufficiently complex that no formula may be developed for practical use.
Some references that will be compared to BUNDCOL system can be separated into two groups :
1 ) Based on AC with Bresler chart, Parme et al chart, and Design Aids :
- Reinforced Concrete Design, Wang & Salmon 6/e 1998, example 13.21.3. - Design of Concrete Structures, Arthur H. Nilson 12/e 1997, example 8.5.
2) Based on other chart, with D.G. Row & T. Paulay Chart :
- Reinforced Concrete Structures, R. Park & T. Paulay 1975, example 5.8.
It is worth noting that, the initial design of biaxial bending in the references, need to be checked with another chart/ formula to confirm it toward the design adequacy. Then, the final design has a conservative or unconservative criteria from an exact theoretical.
BUNDCOL system that was being application in patent process, is a technology breakthrough with direct and exact calculation, in significant increasing of the strength/ capacity of Pn-Mn interaction curve, for square or rectangular column and structural wall. This additional strength/ capacity means economical cost. Brief Description of Drawings
Varied drawings of BUNDCOL system are unlimited. They depend on the required of the Pn-Mn interaction curve for quadrangular column. Minimum number of longitudinal bars in symmetrical bars column shall be 8.
A figure of the drawings using this system, - which should accompany the abstract -, is :
FIGURE 1 : a cross section of rectangular column with bundled bars consist of 8 bars, which shows the LA-1X, LA-1Y and LA-2Y distance be maximum and effective toward both the x - and y - axes, in accordance
with the present invention. Drawings for comparison the capacity calculation 'Prr^ ooiumn between distributed bars with bundled bars, are :
FIGURE 2A : column 450 x 450 mm, 16 D 22 with equally distributed bars (page 8 & 9).
FIGURE 2B : column 450 x 450 mm, 16 D 22 with bundled bars (page 8 & 9).
FIGURE 3A : column 12 x 18 in, 12-88 with distributed bars (page 10).
FIGURE 3B : column 12 x 18 in, 4-tt8, 4-#7 & 2-#6 with bundled bars (page 10).
FIGURE 4A : column 12 x 20 in, 8-tt9 with distributed bars (page 11 ). FIGURE 4B : column 12 x 20 in, 8-87 & 2-#6 with bundled bars (page 11 ).
FIGURE 5 : column 16 x 24 in, 16-#8 with bundled bars (page 12).
Disclosure of the invention
BUNDCOL system denotes placing longitudinal bars for quadrangular reinforced concrete column, both square or rectangular, which longitudinal bars are placed at the corners of the reinforced concrete column. Practical solution of this principle is that the bars are bundled at the corner of the column.
By placing the most of the reinforcement at the corner of the column, the distance between each bar will be maximum and effective toward both the x - and y- axes. This placing reinforcement is applied in accordance to the valid Building Code stipulation occured. With the distance or the lever arm of each of the bar is maximum, the internal moment in each bar is maximum too. Hence, sum of internal moment will be maximum, and will cause the increase of interaction curve Pn-Mn column capacity both uniaxial and biaxial bending.
It will not be an advantageous (contradiction with the principle above), if there still any bundled bars in the middle of the face, especially for the column that is not large. It is because these columns bars mentioned above will only be maximum or effective toward one direction.
For the large column with the size of b and or h > 450 mm, of course there should be a singular bar (or bundle bars) in the middle of b and or h face area. These bars are needed in order to make the distance between crossties or legs of overlapping hoops maximum 350 mm on center, to fit transverse reinforcement for full ductility, Seismic Design point 3.14.4.4). (3) SK SNI T -15-1991 -03 (or maximum 14 in. ACI 318-95 Special Provision for Seismic Design 21.4.4.3). However, it is needed to be acquired that the distance between each bar can be effective toward both x - and y - axes.
Formerly, it was not realized that there is a srαj anL4-K_ s?tfal increase in
'"Λ«," V y interaction curve capacity Pn-Mn column, connec βcti-ie the characteristic loading combination of an axial load with bending moment at x - and y - axes, which is applying bundled bars at least in one of the corners of the quadrangular column. Apart from the increase of the interaction curve capacity, - that means an economical advantage - there is also more wider space for placing the longitudinal bars, when it needed or desired to use more bars on the similar or different total bars area, in the proportionally design (for example, a column with b or h less than 300 mm, use a small bar, maximum D22).
BUNDCOL system is a technology breakthrough for analyzing and designing reinforced concrete column. This system can be applied in structural wall (shear wall or special wall -like column) by the same principle calculation. On column or structural wall with C or U shape, longitudinal bars placement especially at the farthest four outer corners from the plastic centroid. For column or structural wall with L shape, longitudinal bars placement especially at the three outer corners of the long face. And for column or structural wall with T shape, longitudinal bars placement especially at the two outer corners of the T top side, then at the other four outer corners.
The formula used in the interaction capacity Pn-Mn calculation is a standard formula which is commonly used with static principle.
The nominal bending strength Mn computation based on :
- The strength of members shall be based on satisfying the applicable conditions of equilibrium and compatibility of strain. c « £u d/(£u +£y)
- Strain in the reinforcement and in the concrete shall be assumed directly proportional to the distance from the neutral axis.
- The maximum usable strain £u at the extreem concrete compression fiber shall be assumed = 0.003.
- The modulus of elasticity of non presressed reinforcement may be taken as 200.000 MPa ( 29,000 ksi).
Table 1 Capacity computation of uniaxial Pn-Mn column interaction curve
BUNDCOL system form is made in the form of spread-sheet direct and exact calculation, with interlaced formula so that any change of an axis angle which perpendicular to the neutral axis and or the depth of the neutral axis, has a direct influence to the value of the Pn-M column biaxial capacity. BUNDCOL system form can shorten the calculation process of trial & error cubic equation by using personal computer, so it could omit the conservative or unconservative criteria for biaxial bending. Some of calculation process of distance and strain is not displayed in order to make the complete calculation in one page. This form can be applied to calculate Pn-Mn column capacity for uniaxial or biaxial bending. And, it can be applied also for unsymmetrical bars column, eventhough with different size of bars.
Examples of the calculation on page 8 & 9, are the uniaxial capacities comparison between the bundle bars system and the equally distributed bars of square column in SI version (Newton-meter) units, follows the valid Indonesia concrete standard, SK SNI T -15-1991 -03.
The interaction curve Pn-Mn column capacity for biaxial bending is an exact calculation like in uniaxial bending. It is need an acuracy to determine the formulation of each bar distance and the concrete compression block, in the inclination and depth of the neutral axis.
In order to make it easy to compare between BUNDCOL system and the formerly, a distributed bars, the difference is displayed in the form of the bars saving that is gained, by using the similar column dimension and strength/ properties material. Comparative calculation of Pn-Mn biaxial capacity on page 10, 11 , and 12 are in Inch-Pound units, following the Building Code Requirements for S ructural Concrete (ACI 318-95) and Commentary (ACI 318R-95).
If more bars are needed or desired on the similar or different total bars area, the example is used from Design Handbook Volume 2 Columns reference. On page 165 for column with b = 12 in, 4 bars of #8 cannot be applied cause of
the requirements of the clear spacing between longitudinal bars and ) .sp^S©^' of the bars where they are present.
The wider space for placing longitudinal bars, also make eaiser to concreting. Relating to the lap splices, BUNDCOL system could make use of the short bars (from the waste of the bars cutting) as a bar splicer.
Table 2 The summary of the comparative analysis
This Pn-Mn column capacity calculation for uniaxial or biaxial bending is an observe for a short column with symmetrical bars, not considering the capacity reduction caused by slenderness effect of a column yet. In slender column, the advantages of an increased reinforced concrete strength or material savings by BUNDCOL system could be gained, in accordance with the formula for slender column, which are depends on the uniaxial bending capacity.
For column with unsymmetrical bars, the minimum advantages which be gained, was observed in several conditions. Table 3 The summary of the comparative analysis at a minimum advantages
The result of an increased reinforced concrete strength on the formerly same bars area, at least in the amount of 3.516 % in one axis (with the other axis is constant) at fc' (compressive strength of concrete) ^ 130 MPa. The bars
savings, at least in the amount of 5.845 %
reinforced concrete strength. The concrete savings in the equivaleiat^ totced concrete strength formerly, at least in the amount of 3.0 % at fc' i 55 MPa. And the forms savings in the equivalent reinforced concrete strength formerly, at least in the amount of 1.52 % at fc' ^ 55 MPa.
Column 450 x 450 mm. fc' = 25 MPa. Grade 400, 16 D- 22 Pn = 1898.1 N. b =450 h= 450 dc 56 mm g 3.00 % FIGURE^. (= Pb bundled) fc' = 25 fy 400 MPa Equally distributed bars
0.85 fc' = 21.25 MPa BUNDCOL Foπnl
X = y-axis d = 394.0 mm File : c45x45E sh.l c = 0.5939 d= 234.006 mm d-c= 159.994 a= 198.9048 125.55 la
£sl = 0.003 x( 234 - 56.0 y 234.01 = 2.282 .10^3 fsl = 400.0 MPa
Notes : The calculation of the equally distributed bats as comparison, has already calculated Hie internal moment bars on the middle
&ce, MCs2 ~MT4, that is usually ignored in conventional calculation. This happens because the bare resultants have moment lever ar =0 toward the axis. Balanced Condition FIGURE 2B x = y- axis d = 389.0 mm dc 61 mmpg 3.00 % Bundled bars
Alt. 1 Pn = Pb c = 0.60 d= 233.4 mm d-c= 155.6 a-- 198.39 125.81 la
Constant Pn, Mn increase in both axes, each axis = 13.68 %
Alt.2 e 0.2715 m. c = 0.6246 d= 242.974 mm d-c= 146.026 a, 206.5275 121.74 la
Constant e, Pn- Mn increase in both axes, each axis 10.90 %
Column 450 x 450 mm. fc" = 25 MPa. Grade 400, 16 D- 22 Pn= 1898.1 kN. b =450 h= 450 dc 56 mmpg 3.00 % FIGUREMA (=Pb bundled) fr = 25 fy 400 MPa Equally distributed bars
0.85 fc' = 21.25 MPa Conventional calculation x = y - axis d = 394.0 mm BUNDCOL Forml
C = 0.6027 d= 237.456 mm d-c= 156.544 a= 201.8378 124.08 la
£s2 = 0.003 x( 237 - 140.5 )/ 237.46 = 1.225 .10 fs2= 244.987 MPa
Note : The calculation of the equally distributed bars as comparison, is without calculate the internal moment bars on the middle face, MCs2 ~MT4, that is usually ignore in practice. This happens because the bars resultants have moment lever arm =0 toward the axis.
Balanced Condition FIGURE 2B x = y- axis d = 389.0 mm dc 61 mmpg 3.00 % Bundled bars
Alt. 1 Pn = Pb C = 0.60 d= 233.4 mm d-C= 155.6 = 198.39 125.81 la
Constant Pn, M increase in both axes, each axis = 20.01 %
Alt 2 e 0.2572 m. C = 0.6360 d= 247.404 mm d-C= 141.596 a: 210.294 119.85 la
Constant e, Pn- Mn increase in both axes, each axis = 15.77 %
Column 12 x 18 in. fc* = 4 ksi, fy = 60 ksi, 4# 8 , 4#7 & 2#6 ύz 2.5 "
Z -axis observation (angle, 1 :1.153 ) Pn 237.71 kips, pg = 2.98 % hmh 2*V1.75/0.87-(l 2h/0.87-α^yvi.75 13.736 -3.307 = 10.430 " FIGURE A d©'= dc*V1.752/0.87-(dc/0.87-dcyvi.752= 3.8156 -0.289 = 3.5266 " d@'=dc*abl/ab3+(dc+dlj-dc 0.87yvi.752= 3.8156 0.466 hm-c 6.9029 " d@'= 4.2821 0.755 d = 17.332 " 1 : 1.153 18.315 0.85 hm= 10.430 "t 9.065 hich-Pound units d = 17.332 in. Base: 17.569 " 1.3641 " -0.369 1-a ι 4.6320 "
Ast 6.44 in.2 C = 0.5903 d= 10.231 in. ά- 7.1015 a= 8.696 La2 1.5487 " 57.011 ≤ 60.0 ksi
50.587 ksi ( = 29 x 1.7444 )
&S6- 3.0 x( 7.101 - 5.288 )/ 10 31 = 0.5317 .10^3 fse- 15.420 ksi BUNDCOL Foπn3
Clockwise turned W - axis to get Pn= 237.71 kips er= 0.9175 Mnr resultant 218.10 1 : 1.153 angle Pu = 166.4 kips Pn = 237.71 kips Safety factor βz= 102.97 % Mux = 137.6 ft-kipsφ= 0.7 Mnx 196.57 ft-kips = 218 10 e«= 102.99 % Muy= 55.2 ft-kips Mny= 78.86 ft-kips 211.80
Mnr= 211.80 ft-kips Sf = 102.98 % Example 13.21.3 C.K. Wang&C.G. Salmon [6/e 1998] pp. 524-528 : Bars saving : 32.07 %
* With tension controlled formula, p = p , bars at It is capable to support the the two short face, the initial asumptiαn pg = 0.04 load and biaxial moment.
Column size determine 12 x 18 in. and pg = 0.044, hsX 9.48 in.2 (12-#8)
* Check with Bresler Reciprocal Load Method and FIGURE 3B by using ACI Strength Handbook, equation (13.21.6) Pi= 277 > 237.7 kips OJC
* Check with Panne Load Contour Method Mny= 110 > 78.9 ft-kips OJ
* J.C. Smith "Computer & Structures'* program [ 1973] Pn= 284 > 237.7 kips OX.
* C.K. Wang "Three-Level Iteration" program [1988] Pn= 277 > 237.7 kips OX
Column 12 x 20 in. fc' = 4 ksi, fy = 60 ksi, 8-# 7 & 2#6dx2.437$*
Z - axis observation ( angle, 1 :1.527 ) Pn 392.86 kips, pg = 2.37 % hm= h/2*V1.43/0.65-(l/2h/0.65-h2yV1.4_: 18.253 -7.755 = 10.498 " FIGU ED d®'= dc*V1.43/0.655-(dc 0.655-dcyvl.43= 4.4492 -1.075 = 3.375 " d©'=(dc+db)abl/ab3-K(dc+dbyab3-dcyabl 6.0463 -2.192 hπ^c 7.123 " d@*= 3.8539 0.479 d = 17.621 "
1 : 1.527 21.904 0.85 hm = 10.498 "1 10.039
Inch-Pound units d= 17.621 in. Base: 21.438 " 0.4591 " -0.213 1-a i 3.9476 "
Ast 5.68 in.2 C = 0.6560 d= 11.560 in. d-C 6.0619 a= 9.826 l-a2 0.5657 "
£s'l = 3 x( 11.56 - 3.375 )/ 11.56 = 2.1242 .10^3 fsl = 61.602 ≤ 60.0 ksi
£s2= 3 x( 11.56 - 3.854 V 11.56 = 1.9998 .10^3 fs2 = 57.994 ksi (= 29 x 1.9998 ) T- 3 x( 6.062 - 5.961 )/ 11.56 = 0.0263 .10^3 fs7 = 0.762 ksi BUNDCOL Form3 έslO- 3 x( 6.062 ) / 11.56 = 1.5732 .10^3 fslO 45.623 ksi File : k40x60ffi sh.5
Clockwise turned W - axis to get Pn= 392.86 kips Cr= 0.56523 Mnr resultant 222.05 1 : 1.527 angle Pu = 275.0 kips Pn = 392.86 kips Safety factor ey= 6 in. Mux = 137.5 ft-kips φ = 0.7 Mnx 196.43 ft-kips = 222.05 e 3 in. Muy = 68.75 ft-kips Mny= 98.21 ft-kips 219.61
Qz= 101.11 % Mm= 219.61 ft-kips Sf= 101.11 % 101.11 % Bars saving : 29.00 % It is capable to support the Example 8.5, Arthur H. Nilson [ 12/e 1997] pp.290-291 : FIGURE 4B load and biaxial mome
* Check with Bresler Reciprocal Load Method Ast= 8.0 in.2 ( 8-#9 ) and by using ACI Strength Handbook, φ Pn= 281 > 275 kips OX.
* Check with Load Contour Method, equation (8.19) : 1.002 ~ 1.0 OX
Column 16 x 24 in. fc' = 4 ksi, fy = 60 ksi, 16# 8 dc: 2.50"
Z - axis observation ( angle, 1 :1.354 )Pn= 571.43 kips, pg = 3.29 % hmh/2*V1.55/0.74-(l/2h 0.74-b/2)/V1.55= 20.054 -6.464 = 13.590 " FIGURED. d©'=dc*V1.545/0.74-(dc/0.74-dc)/V1.545= 4.1780 -0.679 = 3.499 " d®'= dc*abl/ab3+(dc+db-dcΛ).74)/V1.545= 4.1780 0.1222 hm-c 10.091 " d©'= 4.3002 0.8012 d = 23.681 "
1 : 1.339 26.739 0.85 hm= 13.59 '1 12.820
Inch-Pound units d = 23.681 in. Base: 25.619 " 0.771 " -0.537 1-a l 5.4021 "
Asfc 12.64 in.2 C = 0.6102 d= 14.450 in. d-C = 9.232 a= 12.282 2 1.0393 M sl = 3 x( 14.450 -3.499 ); 14.450 = 2.2736 .1(3^-3 fs = 65.933 $ 60.0 ksi £s4 = 3 x( 14.450 - 7.906 ). 14.450 = 1.3586 .10Λ-3 fs = 39.401 ksi ( = 29 x 1.3586 ) £slO^ 3 x( 9.232 - 8.813 )/ 14.450 = 0.0869 .10^-3 fiio= 2.519 ksi BUNDCOL Form3
Clockwise turned W - axis to get Pn = 571.43 kips er= 0.96327 Mm- resultant = 550.44 1 : 1.339 angle Pu = 400.0 kips Pn= 571.43 kips Safety factor e y= 10 in. Mux = 333.33 ft-kips = 0.7 Mnx 476.19 ft-kips - 550.44 ex= 5 in. Muy= 166.67 ft-kips Mny= 238.10 ft-kips 532.40 ez= 103.38 % ew= 103.43 % Mπr= 532.40 ft-kips Sf= 103.39 %
Example 5.8 R Park & T. Paulay [1/e 1975] pp. 169-172 : With Row & Paulay design chart, reinforcements required : 17.6 in.2 . . . (16 -# . . .?) This method will give a conservative results, and it is claimed Bars saving : 28.18 % mat the linearly interpolation is accurate to within 2.5%. It is capable to support the (This book doesn't give a final design in size and number of the bars) load and biaxial moment.
Claims
1. Longitudinal bars placing system for quadrangular 
column and/ or reinforced concrete structural wall, wherein the most longitudina bars be placed at least in one of the corners as bundled bars to get an increased reinforced concrete strength in comparison with the reinforced concrete strength on the formerly same bars area, and to get the bars area, concretes or forms savings in the equivalent reinforced concrete strength with the formerly reinforced concrete strength, and also to get the wider space for placing the longitudinal bars.
2. Longitudinal bars placing system for quadrangular reinforced concrete column and/ or reinforced concrete structural wall according to claim 1 , wherein the result of an increased reinforced concrete strength on the formerly same bars area, at least in the amount of 3.51 G % in one axis (with the other axis is constant) at compressive strength of concrete ^ 130 MPa.
3. Longitudinal bars placing system for quadrangular reinforced concrete column and/ or reinforced concrete structural wall according to claim 1 , wherein the result of the bars area savings in the equivalent reinforced concrete strength from the formerly reinforced concrete strength, at least in the amount of 5.845 % at compressive strength of concrete ; 130 MPa.
4. Longitudinal bars placing system for quadrangular reinforced concrete column and/ or reinforced concrete structural wall according to claim 1 , wherein the result of the concretes savings in the equivalent reinforced concrete strength from the formerly reinforced concrete strength, at least in the amount of 3.0 % at compressive strength of concrete 55 MPa.
5. Longitudinal bars placing system for quadrangular reinforced concrete column and/ or reinforced concrete structural wall according to claim 1 , wherein the result of the forms savings in the equivalent reinforced concrete strength from the formerly reinforced concrete strength, at least in the amount of 1.52 % at compressive strength of concrete ^ 55 MPa.
6. Longitudinal bars placing system for quadrangular reinforced concrete column and/ or reinforced concrete structural wall according to claim 1 , wherein the reinforced concrete structural wall could be in the C or U, L or T shape.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| AU15460/01A AU1546001A (en) | 1999-11-30 | 2000-11-29 | Bundled bars column |
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| IDP991110A ID27139A (en) | 1999-11-30 | 1999-11-30 | CAUSED KUSMARGONO |
| IDP991110 | 1999-11-30 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| WO2001040594A1 true WO2001040594A1 (en) | 2001-06-07 |
Family
ID=11004992
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/ID2000/000001 Ceased WO2001040594A1 (en) | 1999-11-30 | 2000-11-29 | Bundled bars column |
Country Status (3)
| Country | Link |
|---|---|
| AU (1) | AU1546001A (en) |
| ID (1) | ID27139A (en) |
| WO (1) | WO2001040594A1 (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007019598A1 (en) * | 2005-08-19 | 2007-02-22 | University Of Wollongong | Reinforced concrete structural members |
| RU2393303C1 (en) * | 2009-06-01 | 2010-06-27 | Государственное образовательное учреждение высшего профессионального образования "Уральский государственный университет путей сообщения" (УрГУПС) | Joint of precast columns |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2321643A1 (en) * | 1973-04-28 | 1974-11-07 | Hochtief Ag Hoch Tiefbauten | REINFORCED CONCRETE POST |
| WO1997035078A2 (en) * | 1996-03-19 | 1997-09-25 | Damjanic, Frano | Bearing elements of completely reinforced lightweight concrete structures |
-
1999
- 1999-11-30 ID IDP991110A patent/ID27139A/en unknown
-
2000
- 2000-11-29 AU AU15460/01A patent/AU1546001A/en not_active Abandoned
- 2000-11-29 WO PCT/ID2000/000001 patent/WO2001040594A1/en not_active Ceased
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2321643A1 (en) * | 1973-04-28 | 1974-11-07 | Hochtief Ag Hoch Tiefbauten | REINFORCED CONCRETE POST |
| WO1997035078A2 (en) * | 1996-03-19 | 1997-09-25 | Damjanic, Frano | Bearing elements of completely reinforced lightweight concrete structures |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007019598A1 (en) * | 2005-08-19 | 2007-02-22 | University Of Wollongong | Reinforced concrete structural members |
| RU2393303C1 (en) * | 2009-06-01 | 2010-06-27 | Государственное образовательное учреждение высшего профессионального образования "Уральский государственный университет путей сообщения" (УрГУПС) | Joint of precast columns |
Also Published As
| Publication number | Publication date |
|---|---|
| ID27139A (en) | 2001-03-01 |
| AU1546001A (en) | 2001-06-12 |
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