Method to increase durability of steel truss

FIELD: construction.

SUBSTANCE: truss comprises ascending compressed support and intermediate braces, stands and descending stretched braces. Upper and lower belts of the truss are made of equally stable double-tee sections. In the most stressed zone in the middle of the span the upper belt is converted into a tubular one by means of welding of closing sheets at sides to the double-tee section. All compressed elements of the truss lattice are made of oval pipes with the ratio of larger dimension to smaller one equal to three. Oval pipes are aligned with a larger dimension perpendicularly to the truss plane. Compressed braces are detached by two struts in the truss plane. After installation of the truss into the design position, hoses of concrete pipelines are connected to nozzles of closed tubular elements of the truss. Fine-grained expanding concrete is injected into cavities of elements with formation of guncrete elements after concrete setting.

EFFECT: improved durability and reliability of a truss.

5 dwg

 

The proposed invention relates to the survivability of steel trusses for civil and industrial buildings. The need to improve the properties of liveness farms stems from the current state of Affairs in Russia "negative" situation.

A significant number of facilities operated in a state close to the limit or even in an emergency. In Russia, there are buildings that are unsuitable for operation with a high probability of their collapse. Collapse more likely to occur in the metallurgical complex of buildings, and in the last two decades, the rate of failure increases. This trend confirms the urgent need to solve the problem of increasing the survivability and reliability of structures in extreme conditions.

Predisposition steel trusses for accidents increases violation of the rules of operation of the facilities and increase the danger of terrorist attacks.

Often, when designing and building even entertainment and other facilities, where there are a significant number of people, preferred solutions architect with a low and even zero survivability, not an engineer! Such decisions lead to tragic consequences with loss of life, for example, all known cases of collapse in Moscow "water Park" and "Covered market" [1, p.26, 28...31], [1, p.75, is who is 111].

Another example Hobbies architectural expressiveness at the expense of survivability is the project "Indoor speed skating center" in Moscow [2]. In this center in the spring of 2007 Gvozdika emergency situation, which could lead to the collapse of the entire structure. After recovery facilities vitality remained zero. It is obvious that design with low vitality can lead to death and cannot be recommended for entertainment and sports facilities.

Hence, the urgency to improve the survivability of structures undeniable and continues to grow. Undoubtedly, the durability and reliability of a steel truss cover must be raised.

Calculation of steel structures produced by the first and second limiting condition [3, p.60].

The first group of limit States of structures is achieved by the following:

- the loss of carrying capacity and (or) complete uselessness of designs to operate due to: loss of structural elements of sustainability;

- turning designs in geometrically variable element system (mechanism), which in turn leads to a qualitative change of configuration structures [4, p.37];

- fragile, a sudden destruction due to the emergence and development of fatigue cracks under cyclic actions;

- when the excessive growth of plastic Defoe is Macy, which ultimately leads to the destruction of material constructions and structures.

The second group of limit States is characterized by difficulties with the normal operation of the facility or reduction in durability due to the occurrence of unacceptable displacements (deflections, sediment bearings, angles of rotation, vibrations, cracks and so on).

Obviously, the first group of limit States are more dangerous than the second, as the failure develops suddenly, fragile without visible displacements and deformations.

For a similar take "typical" farm with a triangular lattice with the ascending compressed and stretched downward braces [3, s...378, RES], [5, s...26, 2.1]. The support reactions from the farm passed into the area of its lower stretch of the belt. Each farm is connected to the columns by means of flange connections. Mounting bolts transfer the calculated efforts of the interaction of connected elements. Will make these decisions for equivalents.

If the farm is statically determinate, the persistence of her lowest - zero! That is, when the buckling of one of the compressed elements, the farm becomes a mechanism, and it has been coming down suddenly. The rigid connection of the farm with the upper parts of the columns increases the survivability of the whole system, because the system frame construction has become statically indeterminate. Limit state farm in this case comes only PR is off from work for the second weakest element of the system.

Disadvantages similar to the following: the persistence of lattice trusses of [4, p.37] low. The exhaustion of carrying capacity lattice truss comes as a result of buckling, only one of the compressed elements statically determinate farm, making it the mechanism is the collapse of the farm.

The carrying capacity always lose tight, but not stretched rods, as calculated resistance steel VSTS (S), appointed by the yield stress, is equal to Ry=240 MPa [8,p.64], and assigned temporary resistance Ru=360 MPa. Consequently, stretched rods have more than half the stock carrying capacity in relation to the compressed elements!

This is confirmed by studies of Belene E.I. [4], B. I. Belyaeva, Kornienko B.C. [6, c.98] - causes of accidents structures in 44% of cases is the loss of stability of one of the compressed farm elements [6, p.17]. Therefore, to increase the survivability and reliability of truss systems of buildings and structures necessary to increase the carrying capacity (sustainability) of the compressed elements of the farm.

An example of a low survivability steel trusses of corners is an avalanche collapse of the cover casting and reinforcement plant in Penza [7, p.27, 13, p.16, table 1].

Cause a sudden collapse was low survivability farms coatings and a number of related phenomena - BESP gonna coating system, the deficiencies in the system of relations, the use of boiling steel, excessive load on the roof and other

Farm with low survivability was used in casting and reinforcement workshop in Penza. The shop is fully collapsed two spans 18+24=42 m temperature building block of length 96 m When collapse has killed people. The collapse of the coating on the square 42·96=4032 m2happened avalanche.

The farm is made symmetrical in cross section angular profiles [5], forming in the Assembly of the t section, that is "typical" farm, developed in the middle of the last century. In Russia and in the former USSR built a large number of structures with such farms with low survivability.

As a result of low survivability "typical" farms and the natural aging of structures in the long run the probability of accidents is constantly increasing. The probability of sudden collapse also increases. For example, 13.08.2010 in Samara in an old building converted for trade furniture, collapsed roof. Suffered in the building people!

In the proposed design of the farm will use new ranostay h-section proposed Kid and developed with graduate students [9, p.75, 14]. The main advantage of this profile is his equal resistance with respect to the axes X and Y. Due to this property fuss is AET significant positive effect in farms covering.

The technical problem of the invention is to increase the survivability and reliability of steel trusses for civil and industrial buildings, operating in extreme conditions, with the exception of the sudden buckling of the compressed elements executing them from the oval trubobetonnykh elements with respect to a larger size to a smaller, equal to three, and the translation work of the whole structure of the farm from dangerous stage according to the first final state in a more favourable second limit state.

The technical problem of the invention by way of increasing the survivability and reliability of steel trusses civil or industrial buildings solved as follows.

The way to increase the survivability of steel trusses with ascending compressed reference and intermediate braces, downward slanted and stretched tight enclosures is as follows.

The upper and lower zones of the farm are from revostock I-profile [9, 14].

In the most stressed zone in the middle of the flight of the upper belt is converted into a tubular closed by welding laterally to ranocchiocciola h-profile guard leaves [10, 11].

All compressed frame elements are made of oval tubes with respect to a larger size to a smaller, equal to three[11, 15, 16, 17], orienting big of a courier envelope is ω perpendicular to the plane of the farm, and in the plane of the farm raskrepljajut compressed struts two sprengerae, this reduces their flexibility in three times and significantly increase their carrying capacity (sustainability) 1.5...1.6 times.

After mounting the farm in the design position, attach the hoses beenprovided to the taps closed tubular cavities farm, pump in the cavity elements fine expanding the concrete to produce trubobetonnykh elements after concrete setting.

Increase the survivability of all steel trusses 1.5...1.6 times exclude the possibility of a sudden loss of stability of each of fortified compressed braces and interpret the work of the whole structure of the farm from dangerous stage according to the first final state in a more favourable second limit state.

1 shows a diagram statically determinate farm [12, s] for overlapping span of 30 m Farm has 17 nodes. Left the farm is based on the joint-fixed support (node 1), the right - hinge-bending (node 13).

The upper belt is made of ranocchiocciola I-profile (from node 2 to node 12), i.e. there are ten panels. The last panel (2-3 and 11-12) zero. Farm perceives vertical concentrated forces applied at the nodes 3 and 11. The Central portion of the upper belt from node 5 to node 9 (four panels) is the most compressed.

Pok is related farm without a lantern, so snow load is distributed evenly along the length of the span. A constant load is also distributed uniformly, i.e. the symmetric loading.

The support struts (terminals 1-3 and 11-13) are the most compressed. Equally are compressed vapors ascending diagonals: 5-17 and 9-14, and and 7-15 7-16.

A pair of descending stretch braces 3-17 and 11-14 are equally stretched. Similarly equally stretched a pair of braces 5-16 and 9-15.

All racks (rods: 4-17, 6-16, 8-15 and 10-14) are compressed. All compressed struts made of oval pipe with ratio 3:1, with the larger dimension oriented perpendicular to the plane of the farm.

To align the flexible compressed diagonals are they lashing double sprengerae emanating from the even-numbered nodes(2, 4, 6, 8, 10 and 12). Sprengel divide each compressed diagonal brace into three equal parts. The Central portion of the upper belt from node 5 to node 9 is made trubobetonnykh.

Ranostay h-section turned into trubobetonnykh element as follows.

Figure 2 shows the most compressed area of the upper zone from node 5 to node 9 (four panels: 5-6, 6-7, 7-8, 8-9). Figure 3 - cross-section troublethere plot (5-6-7-8-9).

Ranostay 1 h-section Dnipropetrovsk oblast rounded out in two tubular elements of the steel strip 6 steel. Two strips 6 are welded by automatic welding C is rivnymy seams. The result is two closed cavity 7. Shelves I-beams 1 are connected with the strips 6 continuous welds 8.

Figure 4 shows the node And the reference junction compressed cross stay (pin 1-3) and extended cross stay (rod 3-17) to the top of the belt 1 (solid rod 2-3-4-5-6-7-8-9-10-11-12). Further, the Central section from node 5 to node 9 in turn trubobetonnykh.

Figure 5 shows the node B junction of elongated cross stay (rod 3-17), compressed 5 hours (rod 4-17) and compressed cross stay 3 (rod 5-17) to stretched lower zone 1, consisting of five plays: 13-14, 14-15, 15-16, 16-17, 17-1.

In addition, it should be noted that the supporting brace 2 (item 1-3) lashing in the plane of the truss sprengerae (items 2-18 and 2-19), and the supporting brace 2 with the right hand lashing sprengerae (elements 12-28, 12-29).

Similarly, lashing sprengerae and other compressed struts 5-17 and 9-14 and around the middle and 7-15 7-16.

An example of a specific implementation

Collecting loads on farm (lamp design no)

Nodal forces found from the constant uniformly distributed on the surface load q=·123,84 GN/m (1,a):

Pq=q d=·123,84·3=371,5 GN;

from a uniformly distributed snow load (Penza) s=192 GN/m;

S=S·d=216·3=648 GN;

Definition efforts rods farm

The calculation of farm PR is produced by the program SNFERMA from independent loading: constant and snow loads. Efforts in farm elements determined from concentrated forces applied at the nodes in the farm. The estimated value of the effort, each stud farm, find, running the adverse combination effects.

The purpose of the cross sections of the rods in the farm

The purpose of the cross sections of the rods of the upper compressed zone

The cross section of each of the compressed core is assigned such that the first limiting condition, the loss of stability was not achieved. If the farm is statically determinate, then off from work only one rod turns the farm into the mechanism and it has been coming down. Appointed by the tubular section of the upper belt farm (pin 6-7) and compare it with the cross-section of corners.

- Estimated compressive force in the upper zone N=-11244,5 GN

The actual bearing capacity of the Central compressed upper zone of the farm depends on the coefficient of working conditions γ, the stability factor φminestimated resistance steel Ryand cross-sectional area And

F=γ·φmin·Ry·A.

- Select the required cross-sectional area of the upper compressed zone of the new I-beam profile is equal to the resistance with respect to the axes x and y.

A=ΝγφRy=11244,5 0,950,8230=64,33with am2

Appointed ranostay h-section PI23K1 with cross sectional area A=66,69 cm2, the radii of inertia ix=iy=7,17 cm and a mass per unit length m=52,35 kg/m

Find the flexibility of the top of the compressed zone of ranocchiocciola h-profile PI23K1 respect to the axes x and y when the hinge fastening its ends:

λx=λy=lxefix=3007,17=41,8460γ=0,95

Then given the flexibility

λx=λxRyE=41,84230206000=1,3982,5

Then the minimum stability factor is more convenient to define postcoitally standards [8, p.9] in dependence of the flexibility of the rod for one of three formulas:

ppand0λ2,5φ=1-of 0.066λλ;

ppand2,5λ4,5φ=1,46-0,34λ+0,021λ2;

ppandλ4,5φ=332/[λ2(51-λ)].

Find the minimum coefficient of resistance by the formula

φxmin=/mo> 1-of 0.066λλ=1-of 0.0661,3981,398=0,8910,8

Adjust the calculated resistance Rywhen the thickness of the elements is less than 10 mm, Ry=240 MPa.

Check resistance [8, p.9]

N<F=γ·φmin·Ry·A⇒N=11244,5<F=0,95·0,891·240·66,69=13547,9 Mr.

Conclusion: the current compressive force N is 83% of the carrying capacity of the upper zone F=γ·φmin·Ry·A. There is excess supply on the sustainability of 17%. Reduce the section.

Appointed ranostay I-profile [9], [14]

PI20K2, A=59,86 cm2, ix=iy=6.3 cm, m=47 kg/m

The flexibility of the top of the compressed zone of ranocchiocciola I-beam profile with respect to the axes x and y:

λx=λy=lxefix=3006,8=44,1260γ=0,95

Then given the flexibility

λ/mrow> x=λxRyE=44,12240206000=1,5062,5

Thenφxmin=1-of 0.066λλ=1-of 0.0661,5061,506=of 0.8780,8

Check resistance [8, p.9].

Adjust the calculated resistance Rywhen the thickness of the elements is less than 10 mm, Ry=240 MPa.

N<F=γ·φmin·Ry·A⇒N=11244,5<F=0,95·0,878·240·59,86=11983,3 Mr.

Acting compressive force N=11244,5 GN is 93,8% of the carrying capacity of the upper zone F=γ·φmin·Ry·A. To have provided margin of stability of 6.2%.

The upper zone of the pipe

Set the coefficient of working conditions γ with flexibility

λx=lxefix60γ=0,95 and the stability factor φ=0,9 [8, table].

The required area of the cylindrical section of the upper belt.

A=ΝγφRy=11244,50,950,9230=57,18with am2

Check its resistance doing about any axis. Acting compressive force must be less than the maximum value limited by the rules.

- Apply pipe Ø245·8, A=59,54 cm2, ix=8,39 cm, m=46,76 kg/m

The flexibility of the cylindrical rod relative to any axis:

λ=lefi=3008,39=35,7660,7γ=0,95

Given the flexibility

λ=λRyE =35,76230206000=1,19482,5

The stability factor φminfind on the flexibilityλ=1,19482,5according to the formula [8, p.9]:

φmin=1-of 0.066λλ=1-of 0.0661,19781,1978=0,9138

Check resistance

N<F=γ·φmin·Ry·A⇒N=11244,5<F=0,95·0,9138·230·59,54=11888,0 Mr..

Resistance is provided as the estimated compressive strength N=11244,5 GN in the upper zone of the cylindrical section ⌀245·8 less than the actual bearing capacity.

Check resistance can be performed in the compression stress

σ=NA=11244,559,54=188,9<γφ minRy=0,950,9272230=202,6MPand

stability is provided.

In the future we will compare the effective gripping force N with the actual bearing capacity of the rod N<F=γ·φmin·Ry·A.

For comparison, we analyze how the stability of the upper belt [8, p.9] when changing sections.

- When the tube ⌀273·8 (the cross-sectional area A=66,62 cm2the radius of gyration ix=9,39 cm and mass m=52,28 kg/m).

The estimated length oflef=μl=1300with am

λx=300ix=3009,39=31,95=λy60,7γ=0,95

λ=λRyE=31,95230206000=1,0675,5

φmin=1-of 0.066λλ=1-of 0.0661,06751,0675=0,9272

N<F=γ·φmin·Ry·A⇒N=11341,5<F=0,95·0,9272·230·66,62=13497,2 Mr..

- When the tube ⌀299·8 (a=73,12 cm2, ix=10.3 cm, m=57,41 kg/m)

λx=300ix=30010,3=29,13=λy60,7γ=0,95

λ=λRyE=29,13230206000=0,97322,5

φmin=1-of 0.066λλ= 1-of 0.0660,97320,9732=0,937

N<F=γ·φmin·Ry·A⇒

N=11244,5<F=0,95·0,937·230·73,12=14970 Mr..

The stability of the upper belt in the middle of the span in the plane of the farm relative to the x axis and of the plane of the farm relative to the y-axis is provided.

- When the tube ⌀325·8 (A=79,64 cm2, ix=11,22 cm, m=62,54 kg/m)

λx=300ix=30011,22=26,74=λy60,7γ=0,95

λ=λRyE=26,74230206000=0,89342,5

φmin=1-of 0.066λλ=1-of 0.0660,89340,8934=0,944

Check the resistance of the rod [8, p.9] the x-axis

N<11341,5<γ·φmin·Ry·A=0,95·0,944·230·79,64=16431 Mr..

The stability of the upper belt in the middle of the span in the plane of the farm relative to the x axis and of the plane of the farm relative to the y-axis is provided.

- When the tube ⌀351·8 (a=86,19 cm2, ix=12,14 cm, m=67,67 kg/m)

λx=lxefix=30012,14=24,7=λy60,7γ=0,95

Given the flexibility ofλ=λRyE=24,7230206000=0,82572,5

Thenφmin=1-of 0.066λλ=1-of 0.0660,82570,8257=0,95

Check the resistance of the rod of the upper belt relative to any axis [8, p.9]

N<F=γ·φmin·Ry·A⇒N=11341,5<F=0,95·0,866·230·86,19=16309 Mr.

N=11244,5 (69,5%) F=16309 GN (100%) margin of stability of 30.5%.

For comparison, we adopt the cross-section of two symmetrical isosceles corners. In this case, set φ=0,8 [8, table] and the coefficient of working conditions γ with flexibilityλx=lxefix60γ=0,8

The required area of the symmetric cross-sections of the two isosceles corners

A=ΝγφRy=11244,50,80,8230=76,4with am2

2∠160·14, m=64 kg/m, A=2·43,3·=86,6 cm2, ix=4,92, iy=7,05 cm

The flexibility of the compressed rod with respect to the axes x and y:

λx=lxefix=3004,92=60,9860, λy=3007,05=42,5560,7

The stability factor φ accept for maximum flexibility,

λxmax=60,9860γ=0,8.Given the flexibility

λx=λxRyE=60,98230206000=2,0372,5

Thenφxmin=1-of 0.066λλ=1-of 0.0662,0372,037=0,8080,8

Check resistance [8, p.9]

N<F=γ·φmin·Ry·A⇒N=11244,5<F=0,8·0,808·230·86,6=12876,9 Mr..

Acting compressive force N with the hat 88% of the carrying capacity of the rod F=γ·φ min·Ry·A. To have provided margin of stability of 12%.

The stability of the upper belt in the middle of the span in the plane of the farm to the x-axis and y are provided.

Thus, materialmany compressed upper zone of the corners 2L160·14 1.45 times the intensity zone of the tube ⌀245·8. The efficiency of replacement of parts of the compressed upper zone of the cylindrical pipe high!

The purpose of the cross sections of the rods of the upper compressed zone of revostock I-profiles PI20K2 further into trubobetonnykh

Concrete grade250300350400450500550
kBOJ1,921,831,731,661,591,551,50
RCR, MPa10,7913,2415,217,1719,1321,09
RCRkgf/cm2110135155175195215

Fill two cavities ranocchiocciola ibeam PI20K2 (A=59,86 cm2, ix=6.8 cm, m=47 kg/m) reference cross stay fine-grained expanding concrete grade M250 prism strength RCR=10,79 MPa.

The area of the concrete core tee

AndBOJ=2(a×b)=2(12,725×13,75)=349,94 cm2. The moment of inertia of the concrete kernel

JbI=2[bh312+AbI(tct2+a2)2]=2[12,72513,75312+349,93(0,872+12,72 2)2]=37851,77with am4

The radius of inertia of the concrete kernelibI=JbIAndbI=37851,77349,93=10,4with am

The coefficients ofk=kbIRbIRy=1,9210,79240=0,08632;μ=ATpAbI=59,86349,93=0,171

Given the flexibility

λPp=lefibI k+μ0,25k+0,5μ=30010,40,08632+0,1710,250,08632+0,50,71=26,625φ=0,942

Bearing capacity troublethere rod

N≤(ABOJRBOJkBOJ+ATrRy)φ⇒11244,5(349,93·10,79·1,92+59,86·240)0,942=20362, 11 Mr.

Sustainability troublethere rod increased in comparison with a steel rod in 20362,11/11244,5=1,81 times.

Compare the consumption of compressed upper zone of ranocchiocciola h-profile PI20K2 and of the tubular profile ⌀351·8, i.e. the second and third lines of the table. It is easy to see that with almost the same material resistance zone of ranocchiocciola h-profile AC only slightly inferior to the tubular profile ⌀351·8. The results of the comparison of variants of the upper belt when compressive force in it N=11244,5 GN are given in table 10.

Table 10
Comparison of variants of the upper belt
And, cm2ix minm, kgλxγλxφxminF, GNN/F
AC59,866,84744,120,951,506of 0.87811983,30,938
⌀245·859,548,3946,7635,760,951,1950,91411888,00,954
2∠160·1286,64,9468610,82,0370,808 12876,90,88
Pipe EK349,9310,492,1826,620,94-0,94220362,110,552

Compare the cross-section of a pipe and two corners. The upper zone of the tube ⌀245·8 stable belt part 2 ∠ 160·14 1,267 times.

The purpose of the cross-section of the compressed reference cross stay

The estimated compressive strength of the reference diagonal rod (rod 1-3)

N1-3=-6582,4 GN (table 1).

Set φ=0,9 [8, table] and the coefficient of working conditions γ with flexibilityλx=lxefix60γ=0,95

The actual load-carrying capacity (sustainability) F=γ·φmin·Ry·And depends on the adopted section of the upper belt.

Find the required cross-sectional area (Fig.4) of the pipes, of circular cross-section:A1-3=Ν1-3γφRy=/mo> 6582,40,80,8240=42,85with am2

Select the section of ranocchiocciola [9] [14] I-profile [8, p.9]

- PI20K1, A=52,69 cm2, ix=iy=6,39 cm, m=41,36 kg/m

The flexibility of the rod relative to any axis at length was 4.02 m, µ=1:

λx=lxefix=4026,39=62,9460γ=0,8

The stability factor find on the flexibility [8, p.9]:λ=λRyE=62,94240206000=2,14832,5

thenφmin=1-of 0.066λλthe =1-of 0.0662,34272,3427=0,7922

N<F=γ·φmin·Ry·A⇒N1-3=6582,4<F=0,8·0,7922·240·52,69=8013,9 Mr..

Conclusion: the stability of support of the cross stay ranocchiocciola I-beam profile is provided. Margin of stability of 17.1%.

Find the required cross-sectional area of the pipe, round

A1-3=Ν1-3γφRy=6582,40,950,8240=36,1with am2

Apply pipe, round

- Ø273·4,5, A=38 cm2, ix=9.5 cm, m=29,8 kg/m

Check the resistance of the tubular support cross stay round do about any axis. Acting compressive force must be less than the maximum value limited by the rules.

The flexibility of the tubular rod relative to any axis at length was 4.02 m, µ=1:

λx= xefix=4029,5=42,3260γ=0,95

The stability factor φminfind on the flexibility [8, p.9]: N1-3=6582,4 GN

λ=λRyE=42,32240206000=1,44432,5

then by the formula [8, p.9]

φmin=1-of 0.066λλ=1-of 0.0661,44431,4443=0,88540,8

N<F=γ·φmin·Ry·A⇒N1-3=6582,4<F=0,95·0,8854·240·38=7671,4 Mr..

Stability of cylindrical support cross stay ⌀273·4,5 are provided. Margin of stability of 16.5%.

Turn the tubular section of the compressed reference cross stay in trubobetonnykh element.

Concrete grade250300350400450500550
kBOJ1,921,831,731,661,591,551,50
RCR, MPa10,7913,2415,217,1719,1321,09
RCRkgf/cm2110135155175195215

Bearing capacity trubobetonnykh columns N<(ABOJRBOJkBOJ+ATrRy

where aBOJand aTr- the area of the concrete core and steel tube;

kBOJfactor of increasing the strength of the concrete in the pipe;

RBOJ=RCRand Ry- estimated resistance of concrete and steel.

φ is the coefficient of resistance of the rod troublethere rod.

Given the flexibility ofλPp=lefibIk+μ0,25k+0,5μ,

wherek=kbIRbIRy;μ=ATpAbI;lef- the estimated length of the rod;

ibI=JbIAndbIconcrete kernel.

The stability factor φ compressed troublethere rod

Given g is bcost λ CR102030405060
Grade of concrete 2500,9880,9630,9310,8880,8500,791
Grade of concrete 5000,9880,9740,9500,9220,8930,852
Given the flexibility λCR708090100110120
Grade of concrete 2500,7280,6540,5910,5270,4610,400
Grade of concrete 5000,800,7310,6630,5880,518 0,450

Fill pipe Ø273·4,5 (=38 cm2, ix=9.5 cm, m=29,8 kg/m) reference cross stay fine-grained expanding concrete grade M250 prism strength RCR=10,79 MPa.

The diameter of concrete core dBOJ=D-2t=27,3-2·0,9=25,5 see

The area of the concrete core and steel tubeAbI=πd24=π25,524=510,71with am2

The moment of inertia of the concrete kernelJbI=πd464=π25,5464=20755,4with am4

The radius of inertia of the concrete kernelibI=JbIAndbI=20755,4510,71=6,375with am

The coefficients ofmath display="block"> k=kbIRbIRy=1,9210,79240=0,08632;μ=ATpAbI=38510,71=0,074406

Given the flexibility

λPp=lefibIk+μ0,25k+0,5μ=4026,3750,08632+0,069420,250,08632+0,50,074406=104,3φ=0 ,553,

Bearing capacity troublethere rod

N≤(ABOJRBOJkBOJ+ATrRy)φ⇒6582,4(510,71·10,79·1,92+38·240)0,553=10894,3 Mr.

Sustainability troublethere rod increased in comparison with a steel rod in 10894,3/6971,3=1,563 times.

Assigned support brace from the oval in cross section of the pipe

Oval rod obtained from the pipe Ø273·4,5, And=38 cm2, ix=9.5 cm, m=29,8 kg/m

Vertical and horizontal sizes of oval profile (axis passing through the middle of the wall thickness)

2a=1,5Aπt0=1,538π0,45=40,319with amand=20,16b=a3=6,72with am

2b=12,144 see

Vertical and horizontal dimensions of the oval profile

2a+t0=40,319+0,45=40,77; 2b+t0=2·6,72-0.45=11,694 see

Moments of inertiaJX=3A16(2a2+5 6t0)=33816(220,162+560,45)=5792,55with am4JY=π4[a(a3)3-(a-t02)(a3-t02)3]=π4[20,16(20,163)3-(20,16-0,452)(20,163-0,452)3]=655,82with am4

Moments of resistance

WX=Jxa+ 0,5t0=5792,5520,16+0,50,45=284,16with am3WY=JYb+0,5t0=655,826,72+0,50,45=94,43with am3

the radii of the core sectionρX=WxA=284,1638=of 7.48;ρY=WYA=94,4338=2,485with am,

the radii of inertiaiX=JxAnd=5792,5538=12,346;iY= JYAnd=655,8238=4,154with am.

Geometric and the estimated length of the reference cross stay out of the plane of the farm, is l =402; lef=µ· l=402

Geometric and the estimated length of the reference cross stay in the plane of the farm (two Sprengel) is equal to µ=1, l=402/3=134; lef=µ· l=134.

Maximum flexibility in the plane of the farm when the length of lef=134,λY=lefiY=1344,154=32,2660

The flexibility of the plane of the farm when the length of lef=402 cm

λX=lefiX=40212,346=32,5632,26

Filled oval profiles of fine-grained expanding concrete and turn the rods in trubobetonnykh.

External dimensions of the cross section of the concrete kernel largest and smallest 2a-t0=40,319-0.45=39,87; 2b-t0=2·6,72-0.45=13,89 see

The area of the CoE is to be placed concrete kernel

AbI=π4(2a-t0)(2b-t0)=π4(40,319-0.45)(6,72-0.45)=366,17cm2

The moment of inertia of the concrete kernel

JbIY=AbI4(b-t02)2=366,174(3,36-0,452)2=3129,64with am4

The radius of inertia of the concrete kernelibIY=JbIYAndbI=3129,64366,17=3,924with m

k=kbRbRy=1,9210,79240=0,08632;μ=ATpAb=38366,17=0,103776

Given the flexibility

λPp=lefibk+μ0,25k+0,5μ=1343,9240,08632+0,1037760,250,08632+0,50,103776=54,94φ=0,879,

Bearing capacity troublethere rod

N≤(ABOJRBOJkBOJ+ATrRy)φ⇒6582,4(366,17·10,79·1,92+38·240)0,879=14684,6 Mr.

Ostoich the stability troublethere rod increased in comparison with a steel rod in 14684,6/6971,3=2,106 times.

The support brace of the two corners (for comparison)

The required cross-sectional area at φ=0,8:

A=Ν1-3γφRy=6582,40,80,8230=44,7with am2

Assigned to the symmetric cross-section of a pair of corners 2L160·10,

A=2·31,4=62,8 cm2the radii of inertia ix=4,96, iy=6,97 cm

m=2·24,7=49,4 kg/m

The flexibility of the supporting cross stay relative to the x-axis at length 402,2 cm, µ=1:

λx=lxefix=4024,96=81,0960γ=0,8

The stability factor φ find on the flexibility:

λ=λRyE=81,09240206000=2,70952,5

then form the Les [8, p.9]

φmin=1,46-0,34λ+0,021λ2=1,46-0,342,7095+0,0212,70952=0,6929

N<F=γ·φmin·Ry·A⇒N1-3=6582,4F=0,950,692923062,8=9507,8gN.

Conclusion: the stability of the reference cross stay from a couple of corners 2L 160·10 is provided. The compressive strength of the reference diagonal rod N1-3=-6582,4 GN.

Compare the consumption of compressed reference cross stay of ranocchiocciola h-profile RC and tubular profiles Ø245·8 and Ø200·5 mm, that is, the first, second and third lines of the table.

Comparison of matrilocal compressed reference cross stay
And cm2ix minm, kgλxγ λxφxminF, GNN/F
RC52,696,3941,3662,940,82,14830,72228013,90,821
Ø245·537,126,9829,1457,620,951,92540,82376971,270,944
2∠160·1062,84,9649,481,090,82,70950,69299507,80,724

The carrying capacity of supporting cross stay of revostock h-profile AC has a greater margin of resistance, but inferior tubular pros who Yu ⌀351·8. However, the design of the nodes in the first case is easier. The consumption of compressed reference cross stay of over 2 L 160·14 the worst of all options.

The purpose of the cross-section of the compressed struts and braces

The purpose of the compressed sections of the braces and struts produced as well as the compressed section of the upper belt farm, stretch braces - as well as the span of the lower belt. Estimated length elements definel0=µ·lwherelthe distance between lashing points, and µ is the coefficient of reduction of the length.

For the top and bottom of the trusses and support braces in the plane and from the plane of the farm, the coefficient of reduction of length µ=1.

For compressed braces and struts of the lattice in the plane of the farm µ=0,8 and from the plane of the farm µ=1.

The purpose of the cross-section of the compressed hours (rod 4-17)

Check stability of tubular square section of the rack are doing relative to the y-axis (out of plane). Acting compressive force must be less than the maximum value limited by the rules.

Find the required cross-sectional area (Fig.4) of the pipe, square in cross-section:

A4-17=Ν4-17γφRy=1019,50,8 0,7240=to 7.59with am2

Apply pipe, square in cross section

□90·3, A=10.1 cm2, ix=3,92 cm, m=8,83 kg/m

The flexibility of the tubular rod relative to any axis with length

300 cm, µ=1:λx=lxefix=3003,92=76,5360γ=0,8

The stability factor φ find on the flexibility

λ=λRyE=76,53240206000=2,6122,5;2,6124,5,

then by the formula [8, p.9]

φmin=1,46-0,34λ+0,021λ2=1,46-0,342,612 +0,0212,6122=0,71520,7

N<F=γ·φmin·Ry·A⇒N1-3=1019,5<F=0,8·0,7152·240·10,1=1386,8 Mr..

Conclusion: the stability of tubular rack is provided with a reserve.

The purpose of the cross-section of the compressed hours trubobetonnykh (rod 4-17)

Fill pipe □90·3 (A=10.1 cm2, ix=3,92 cm, m=8,83 kg/m) fine-grained expanding concrete grade M250 prism strength RCR=10,79 MPa.

The area of the concrete core and steel tube

AbI=a×b=8,4×8,4=70,56with am2

The moment of inertia of the concrete kernelJbI=bh312=8,48,4312=414,9with am4

The radius of inertia of the concrete kernelibI=JbIAndbI =414,970,56=2,42with am

The coefficients ofk=kbIRbIRy=1,9210,79240=0,08632;μ=ATpAbI=the 10.170,56=0,143

Given the flexibility

λPp=lefibIk+μ0,25k+0,5μ=3002,420,08632+0,1430,250,08632+0,50,143=194,62φ=0,553

Bearing capacity rubbettino the hours

N≤(ABOJRBOJkBOJ+ATrRy)φ⇒1019,5(70,56·10,79·1,92+10,1·240)0,553=2336,33 Mr.

Sustainability troublethere rod increased in comparison with a steel rod in 2336,33/1019,5=2,291 times.

The purpose of the cross-section of the compressed hours trubobetonnykh (rod 5-17)

Oval rod obtained from the tube ⌀273·4,5, A=38 cm2, ix=9.5 cm, m=29,8 kg/m

Vertical and horizontal sizes of oval profile (axis passing through the middle of the wall thickness)

2a=1,5Aπt0=1,538π0,45=40,319with amand=20,16b=a3=6,72with am;2b=12,144with am.

Vertical and horizontal dimensions of the oval profile

2a+t0=40,319+0,45=40,77; 2b+t0=2·6,72-0.45=11,694 see

Moments of inertiaJX=3A16(2a2+56t 0)=33816(220,162+560,45)=5792,55with am4

JY=π4[a(a3)3-(a-t02)(a3-t02)3]=π4[20,16(20,163)3-(20,16-0,452)(20,163-0,452)3]=655,82with am4

Moments of resistance

WX=JXa+0,5 t0=5792,5520,16+0,50,45=284,16with am3WY=JYb+0,5t0=655,826,72+0,50,45=94,43with am3

the radii of the core sectionρX=WXA=284,1638=of 7.48;ρY=WYA=94,4338=2,485with am

the radii of inertia

iX=JXAnd=5792,5538=12,346;iY= JYAnd=655,8238=4,154with am

Geometric and the estimated length of the reference cross stay out of the plane of the farm equal tol=402;lef=µ·l=402 see

Geometric and the estimated length of the reference cross stay in the plane of the farm (two Sprengel) is equal to µ=1l=402/3=134;lef=µ·l=134 see

Maximum flexibility in the plane of the farm if the length oflef=134 cm

λY=lefiY=1344,154=32,2660

The flexibility of the plane of the farm with a length lef=402 cm

λX=lefiX=40212,346=32,5632,26

Filled oval profiles of fine-grained expanding concrete and turn the rods in trubobetonnykh.

External dimensions of the cross section of the concrete kernel largest and smallest 2a-t0=40,319-0,45=39,87; 2b-t0=2·6,72-0,45=13,89cm.

The cross-sectional area of the concrete core

AbI=π4(2a-t0)(2b-t0)=π4(40,319-0,45)(6,72-0,45)=366,17cm2

The moment of inertia of the concrete kernel

JbIY=AbI4(b-t02)2=366,174(3,36-0,452)2=3129,64with am4

The radius of inertia of the concrete kernelibIY=JbIYAndbI=3129,64366,17 =3,924with am

k=kbRbRy=1,9210,79240=0,08632;μ=ATpAb=38366,17=0,103776

Given the flexibility

λPp=lefibk+μ0,25k+0,5μ=1343,9240,08632+0,1037760,250,08632+0,50,103776=54,94φ=0,879

Bearing capacity troublethere rod

N≤(ABOJRBOJkBOJ+ATrRy)φ⇒4464,5366,17·10,79·1,92+38·240)0,82=1370,72 Mr.

Sustainability trubobetonnykh hours increased in comparison with steel stand in 13707,2/4464,5=3,072 times. Effect high!

The purpose of the cross-section of the lower stretch of the belt (rod 15-16)

The calculated tensile strength N15-16=11744,2 GN.

The required cross-sectional area of the lower stretch of the belt (5):

ATp=Ν15-16γcRy=11744,20,95240=51,5with am2

Select a section of the lower stretch of the belt from the new I-beam profile is equal to the resistance of the x-axis and y-axis. Appointed ranostay h-section

RK, A=52,69 cm2, ix=iy=6,39 cm, m=41,36 kg/m

The flexibility of the lower stretch of the belt from ranocchiocciola h-profile of the plane relative to the axis y:

λy=lyefix=12006,39=187,8250

Flexibility less than the limit λbefore =250. The durability test of the lower belt tension:

σ=N15-16A=11744,252,69=222,9<γcRy=0,95240=228mPand

The strength of the lower belt stretching from ranocchiocciola I-beam profile is provided.

After mounting the farm in the design position, attach the hoses beenprovided to the taps closed tubular cavities elements farm, pump, introduced in the cavity of fine-grained elements extending concrete with education trubobetonnykh elements after concrete setting.

Increase the survivability of all steel trusses 1.5...1.6 times exclude the possibility of a sudden loss of stability of each of fortified compressed elements and interpret the work of the whole structure of the farm from dangerous stage according to the first final state in a more favourable second limit state.

For reduction of consumption of steel stretched frame elements are made of low-alloy steel.

1 shows a diagram of the farm, in which the durability is improved by the proposed method with compressed top 1 is Ojas of ranocchiocciola I-beam profile. Ascending a short supporting struts, intermediate compressed 3 braces in the plane of the farm raskrepljajut two sprengerae, this reduces their flexibility in the plane of the farm three times. All racks 5 and compressed struts made trubobetonnykh. Descending intermediate stretched 4 struts ranocchiocciola I-profile [9, 14].

The farm is equipped with a system of cross ties on the top and bottom zones and vertical cross ties. Each temperature compartment buildings in the coating system has a spatial connection blocks (in the middle of the Bay and its ends). Intermediate farms are connected with spatial shear wall blocks, spacers and runs. Therefore, all farm lashing from the plane of the links.

Bearing capacity and survivability of all steel trusses increase 1.5...1.6 times, turning all compressed elements in trubobetonnykh and excluding this possibility of sudden loss of stability of each of trubobetonnykh compressed elements, and diagonals have oval section 3:1. The entire design of the farm was transferred from dangerous stage according to the first final state in a more favourable stage for the second limit state.

References

1. Kancheli NR. Building spatial design: a Training manual. M.: Publishing house of the SSA, 2003. 112 C.

2. Drobot DO Revocationdate metal structures, abstract of Cand. thesis, M.: MSSU, 2010.

3. Metal structures: textbook. / Ehimare, Vsigachev, Wigodsky and others, Ed. by Wiesen. - 9th ed., wiped. - M.: Academy, 2007. 688 C.

4. Belenja E.I. Limit state of lateral frames of single-storey industrial buildings. M: Gastrolyzer, 1958. 124 S.

5. Light metal design: a Handbook of designer Ed. IEC. - 2nd ed. - M.: stroiizdat, 1979. 196 C.

6. Belyaev B. I., Kornienko B.C. causes of the accidents of steel structures and ways of their elimination. M.: stroiizdat, 1968. 207 S.

7. Nezhdanov K.K. ABOUT reducing the risk of avalanche breakdowns covering industrial buildings in emergency / Kid, Nasosy // Industrial engineering, 1991. No. 7. - P.27-29.

8. SNiP II-23-81*. Steel structures. - M.: Federal state unitary enterprise of CSE, 2005. 90 C.

9. Nezhdanov K.K., Nezhdanov A.K., Kaledin SURDS New range of hot-rolled I-beam column profiles // structural mechanics and computation structures, 2010. No. 2, p.75.

10. Nezhdanov K.K., V.A. Tumanov, Nezhdanov A.K. Method of strengthening reinforced concrete columns, no longer bearing capacity. Patent of Russia №2274719. M, CL. E04G 23/02 Application for invention No. 2004116828 from 19.02.2004. Bull. No. 11. Published 20.04.2006.

11. Nezhdanov K.K., Karev M.A., Nezhdanov A.K., Sapelkin A.A. Frame two-span of the building. Patent of Russia №2319817. M, CL. AS 3/38 (01.2006) Application for invention No. 205116385/03(018711)Bul. No. 8. Published 20.03.2008.

12. Metal structures: a Handbook of designer Ed. Nspminnesota. M.: stroiizdat, 1980. 776 C.

13. Lashchenko mathematical SCIENCES. The crash of metal structures of buildings and structures.

Leningrad: stroiizdat, 1969. 184 C.

14. Nezhdanov K.K., Nezhdanov A.K., Kaledin SURDS hot rolled I-beam column profile. Patent Of Russia. RU # 2411091 C1. B21B /08(2006.1). Application No. 2009 116982, 04.05.2009. Published 10.02.2001. Bulletin no.4.

15. Nezhdanov K.K., Karev M.A., Nezhdanov A.K., Sapelkin AA "Frame two-span of the building." Patent of Russia №2 319817. AS 3/38 (2006.01). The invention application No. 2005 116385/03 (018711). Bull. No. 8. Published 20.03.2008. Trubobetonnykh.

16. Nezhdanov K.K., V.A. Tumanov, Ruble this YEAR, Nezhdanov A.K. Way of improving bearing capacity of cylindrical pipe bending. Patent of Russia №2304479. Bull. No. 23. Published 20.08.2007. Oval

17. Nezhdanov K.K., Nezhdanov A.K., Kunickis P. Way exclude the possibility of collapse of steel structures frame from a fire in the Patent RU №2411330. C1. Application No. 2009 117090/03. 04.05.2009. IPC EV 1/94 (2006.01). Published on 10.02.2011.

The way to increase the survivability of steel trusses with ascending compressed reference and intermediate braces, struts and downstream stretched braces, namely, that the upper and lower zones of the farm are from revostock I-beam profile, in the most stressed zone in the Council of Europe is one of the top flight zone is converted into a tubular closed by welding laterally to ranocchiocciola h-profile guard leaves, all compressed elements of the lattice in the farm are of oval tubes with respect to a larger size to a smaller, equal to three, focusing a large dimension perpendicular to the plane of the farm, and in the plane of the farm raskrepljajut compressed struts two sprengerae, this reduces their flexibility in three times and significantly increase their carrying capacity (sustainability), after mounting the farm in the design position, attach the hoses beenprovided to the taps closed tubular farm, pump in the cavity elements fine expanding the concrete to produce trubobetonnykh items after setting of concrete, improve the survivability of all steel trusses 1.5...1.6 times exclude the possibility of a sudden loss of stability each of fortified compressed braces and interpret the work of the whole structure of the farm from dangerous stage according to the first final state in a more favourable second limit state.



 

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