EP3851605A2

EP3851605A2 - Truss for mixed steel-concrete truss systems with optimized upper stringer

Info

Publication number: EP3851605A2
Application number: EP20216330.9A
Authority: EP
Inventors: Giovanni Vitone; Andrea Rizzi; Vito Rizzi
Original assignee: Individual
Current assignee: InfoMtr Srl
Priority date: 2019-12-23
Filing date: 2020-12-22
Publication date: 2021-07-21
Anticipated expiration: 2040-12-22
Also published as: IT201900025252A1; EP3851605B8; EP3851605B1; EP3851605A3

Abstract

Truss (100) comprising
- at least a lower stringer (111),
- at least an upper continuous stringer (110) with length equal to the whole length of the truss,
- a plurality of cores (112) connecting said lower (111) and upper stringers, said cores (112) being connected to the upper stringers at well defined geometrical intervals, with a constant pitch (p) along the development of the truss,
characterized in that it comprises further, at the two ends of its own longitudinal development, additional upper stringers (114), integrally connected to said cores (112), the length of said additional upper stringers (114) being equal to a multiple of said pitch (p) and lower than the length of said truss.

Description

The present invention relates to a lattice for mixed steel-concrete truss systems, in which the arrangement and the section of cores and upper stringers are optimized in order to reduce, the structural resistance being equal, the quantity of steel used, costs and the truss weight.

Technical field

Mixed steel-concrete trusses are made up of steel prefabricated lattices incorporated in concrete castings realized in the building yard. An example of a mixed truss, commonly used at the state of the art is shown in figure 1, where it is possible to observe a metal truss (1) supported on its supports (2), in the completing step with the other elements (3) of the floor which will be incorporated in the next concrete casting.
The truss (1) comprises upper stringers (10) and a lower stringer (11) connected by cores (12) arranged in regular geometrical way.
As it can be observed from figure 1, the upper stringers are realized by solid cross-section steel profiles of metal carpentry (typically round or square bars) running continuously from one end to the other one of the truss.
Although in figure 1 a truss (1) is shown, where the lower stringer (11) is made up of a steel lower bottom, three kinds of trusses are substantially known at the state of the art:

self-supporting truss with steel lower bottom (as the one shown in figure 1);
self-supporting truss with lower bottom in reinforced concrete, pre-casted in the facility;
truss with no lower bottom, to be shuttered and propped in the building yard for the next concrete casting.

For all the three above listed kinds, at the state of the art only one constructive morphology is known:

upper stringers (10), always made up of circular or square shaped, solid cross-section steel bars,
lower stringers (11), which, according to the kind, are realized with bars as the upper stringers, or by always in steel large plates,
cores (12) connecting the upper (10) and lower stringers (11), realized with circular or square shaped, solid cross-section steel bars.

The self-supporting trusses are those configured to resist, with no need of props, to loads acting on the same in step 1, the step 1 being the structure realization step, during which there occur loads due to the dead load of the truss itself, of the other elements of the floor and of the concrete casting, and during which the resistance properties of concrete are not to be relied on, since it is not solidified, or however, has not reached its own definitive resistance features yet.
As it is known, upper and lower stringers absorb the bending stress, while cores absorb the cutting stress.
Document EP0339018 describes a truss for realizing floors in partially prefabricated reinforced concrete. The truss according to EP0339018 comprises a lower stringer incorporated in the concrete prefabricated portion and connected to the upper stringer by welded diagonal profiles. In order to reduce the number of supports during mounting, the truss is provided in its own central region with a reinforcement made up of an additional upper stringer, which increases its resistance with respect to the side regions of the truss.
So, by reading the document it is clear that the truss according to EP0339018 is not self-supporting, and that in such document it is recommended to reinforce the central portion of the truss and not its ends.
In the document EP2048301 , it is described a method for joining two distinct trusses by means of a reinforcement welded to the upper and lower stringers. Therefore, the thus formed truss, as the truss described in EP0339018 , is reinforced in its central portion.
This document relates lattices for reinforced concrete elements, used for realizing floors, and does not describe supporting truss. So, the additional upper stringer has only the function of connecting element of two distinct lattices to be joined and it is used also for the lower stringers with the same function.

Structural behavior in step 1 and step 2

The laying of the kind to be shuttered and propped is similar to the traditional reinforced concrete trusses: the reinforcement is arranged on the formwork suitably supported by provisional structures, the concrete casting is realized and when it is cured the supports and the formworks are eliminated. So, the truss begins its working life with all the loads acting on the same; hence, it has only one life step.
The laying of the self-supporting trusses kinds instead consists of two different steps, called step 1 and step 2 respectively, to which different static models and structural behaviors correspond.
During step 1, the metal lattices are positioned on the pillars and then they are charged with the floors and the completing concrete casting. In this step, accidental loads are to be added to the cited ones.
When the concrete has developed the project mechanic properties, the step 2 begins, during which the resistant structure is made up of the lattice in pre-stressed steel and of the concrete, with acting loads typical of the working step.

Technical problem

In the light of the just described morphological features, it can be observed that for all the trusses kinds, whether self-supporting or self-supporting, the current constructing models have two problems:

1. the cores (12) are uniform for all the truss development, both in the cross-section of the profiles, which make up it, and in the arrangement of the same;
2. the upper stringers (10) are realized with bars running from one end to the other one of the truss, and so they are uniformly consistent along all the development of the truss (1).

In step 1 (relating to the structure realization), in which the structural model is the one of a metal truss simply supported at ends, the sole steel lattice has to resist to all the loads acting on the same and it has to be realized necessarily uniform along its whole development.
In step 2 (structure working), the concrete casting is solidified, and the truss is integral to the contiguous supporting structures (trusses and pillars). Therefore, the structural model is the one of a mixed steel-concrete truss, with hyperstatic scheme (frame or contiguous truss), subjected to second step incremental loads, both permanent and accidental, with the reinforcements pre-stressed by the actions in step 1.
The truss to be propped in the building yard (not self-supporting), once it is freed from the provisional structures, has the same structural scheme in step 2, with the difference that in this case the truss is subjected to all the loads acting on itself and the reinforcements are not pre-stressed by the loads of step 1 (during the realization step the not self-supporting truss is not stressed, the stresses being absorbed by the props).
For both the kinds of trusses, as yet said, the current constructing practice uses both for the core and for the upper stringers a uniform reinforcement for the whole development of the truss.
In particular, in the current constructing mode both the core dimensioning and the upper stringers dimensioning occur according to the maximum incremental stress of step 2 (or according to the total stress in case of not self-supporting trusses), with cutting (for the cores) and negative bending moment (for the upper stringers) respectively.
It is clear that dimensioning the whole truss with respect to the stress acting on the most stressed section (supporting section) leads to a substantial over-dimensioning of the less stressed areas.
In fact, in ordinary conditions the acting load is distributed uniformly, however the core reinforcements in the middle are the same as the end sections, even though they are subjected to lower stresses.
Similarly, the upper stringers are dimensioned for the negative maximum moment at the supports and have the same section also in the middle where the bending moment, having positive sign, engages the lower stringers more.

Aim of the invention

Therefore, aim of the present invention is to provide a mixed truss, which overcomes the limits linked to the embodiments known at the state of the art. In particular, the present invention provides a mixed truss provided with upper stringers with different cross-section along its own longitudinal development. According to another aim, the present invention provides a mixed truss provided with upper stringers and cores with different cross-section along its own longitudinal development.
More generally, the present invention provides a mixed truss with optimized reinforcement, which allows to avoid the over-dimensioning of the steel portions in the less stressed areas, thus optimizing the quantity of steel used, with equal project dimensions and load, and as a consequence, the costs and the weight of the truss.

Brief description of the invention

The invention reaches the prefixed aims since it is a truss (100) comprising at least a lower stringer (111), at least an upper continuous stringer (110) with length equal to the whole length of the truss, a plurality of cores (112) connecting said lower (111) and upper stringers, said cores (112) being connected to the upper stringers at well defined geometrical intervals with a constant pitch (p) along the development of the truss, characterized in that it comprises further, at the two ends of its own longitudinal development, additional upper stringers (114), integrally connected to said cores (112), the length of said additional upper stringers (114) being equal to a multiple of said pitch (p).

Detailed description of the invention

The invention will be described in detail in the following with reference to the appended figures 1 to 8.
In figure 1, it is shown an embodiment known at the state of the art of a mixed truss; in figures 2 and 3 there are shown embodiments, the one known at the state of the art and the other one according to the invention, respectively, of a mixed truss with steel lower stringer; in figures 4 and 5 there are shown embodiments, the one known at the state of the art and the other one according to the invention, respectively, of a mixed truss with lower stringer in prefabricated concrete; in figures 6 and 7 there are shown embodiments, the one known at the state of the art and the other one according to the invention, respectively, of a mixed not self-supporting truss; in figure 8 it is shown a side view of a preferred embodiment of the truss according to the invention.
As it is shown in the example of figure 3, the truss (100) according to the invention comprises a lower stringer (111), some upper stringers (110) and some cores (112) connecting said lower (111) and upper stringers. Said cores (112) are connected to their upper stringers at well defined geometrical intervals. According to a first embodiment, said cores are connected to said upper stringers with a constant pitch (p) along the development of the truss.
In the example of figure, the lower stringer (111) is a metal bottom, and it is made up of a large plate and possible additional round or square iron pieces, welded to said plate; the upper stringers (110) are realized as round or square cross-sectioned steel bars and the cores (112) are connecting means realized with round or square cross-sectioned steel bars and welded both to the upper stringers (110) and the lower plate (111).
The truss (100) is characterized in that it comprises additional upper stringers (114) integrally connected (i.e. welded) to said cores (112) and positioned as the upper stringers (110). The additional upper stringers (114) are arranged under the continuous upper stringers (110) and in order to function properly they are to be welded to the cores (112), as it is done also with the continuous upper stringers (110).
Therefore, conveniently the length of the additional upper stringers (114), calculated as described in detail in the following, will be approximated to a multiple of the pitch (p) of the cores (112), in addition to a little upwards approximation.
From the figures, it is also clear the positioning of the upper stringers at the two ends of the truss longitudinal development.
It is to be specified, as it is also known at the state of the art, that the truss (100) according to the invention comprises also horizontal terminals (115) and oblique terminals (116) realized with round or square cross-sectioned steel bars.
Even if it is to be referred to the specific paragraph for the description of the modes of structural calculation of the truss according to the invention, it is said that the presence of the additional upper stringers (114) allows to dimension the continuous stringers (110) with a lower resistant cross-section, and this possibility is the great advantage, also economical, with respect to the embodiments known at the state of the art.
Other embodiments of the truss according to the invention are shown in figures 5 and 7, with a fast comparison with the embodiments known at the state of the art shown in figures 4 and 6.
In figure 5, it is shown a truss (300) whose lower stringer (311) is made up of a floor in concrete reinforced with suitable steel reinforcements. The cores (312) and the additional upper (314) and continuous stringers (310) are realized according to the same just described logic.
In figure 7, it is shown a truss (400) of the not self-supporting kind, in which the lower stringer (411) is realized by means of round or square cross-sectioned steel bars, while also in this case the cores (412) and the additional upper (414) and continuous stringers (410) are realized according to the same just described logic.

Upper stringers dimensioning

With reference to the dimensioning of the continuous upper (110) and additional stringers (114), the dimensioning method which can be adopted is the following.

a. the continuous upper stringers (110) are dimensioned as a function of the positive maximum moment in the middle of the truss, and have constant cross-section on the whole longitudinal development of the truss (100);
b. the cross-section of the additional upper stringers (114) is dimensioned to complete the cross-section of the continuous upper stringers (110), as a function of the maximum negative value of the bending moment acting in the end section;
c. the length of the additional upper stringers (114) is calculated as the distance between the end of the truss and the section of the truss in which the cross-section of the continuous upper stringers (110) alone is sufficient to absorb the negative bending moment.
d. the length of the additional upper stringers (114) calculated in point c. is modified, upwards, up to become equal to a multiple of the pitch (p) with which the cores (112) are connected to the upper stringers.

It is to be specified that in point b. with "to complete" it is intended that the resistant cross-section which has to absorb the maximum moment acting in the ends of the truss (100) is the sum of the cross-section of the continuous stringers (110) and the additional stringers (114).
It is also to be specified, in case of self-supporting truss, that the final reinforcement cannot be lower than the one required to satisfy the acting loads in steps 1, and so, the just described process will begin from the reinforcement calculated to resist to the loads of step 1, and in the tests for the loads of step 2 it will be possible to increase the cross-section of the continuous stringers (110).
It is convenient to precise that this technical optimization solution of the upper stringers cross-section is not limited to the hypothesis of uniformly distributed loads, and it can be adopted for any kind of loads acting on the truss.

Cores dimensioning

It is to be described now a morphology of the cores arrangement, as well as of the calculation of the cross-sections of the same which can be used, according to the present invention, for each kind of just described trusses.
The trusses are generally subjected to uniformly distributed loads: this loading scheme generates at the ends of the truss the maximum value of cutting stress, a stress with tends to be nullified at the middle. As a consequence, since the cores are arranged with a regular geometry along the whole truss longitudinal development, the dimensioning of the same with respect to the maximum stress acting at the ends determines an over-dimensioning of the cores arranged in the central portion of the truss, which can be conveniently realized with lower cross-sectioned profiles.
In order to obviate this phenomenon, with reference to figure 8, according to another embodiment, the truss according to the invention (200) is subdivided along its own longitudinal development in three distinct areas (201, 202, 203), in which the truss cutting reinforcement is dimensioned differentially. In particular, the different dimensioning relates to the dimension of the bars making up the cores, while the pitch and the bar kind are constant. As it is shown in figure 8, said end areas (201, 203) are arranged at the ends of the truss and are of the same length, thus resulting symmetrical with respect to the centre.
Specifically, the cores (215) of the two end areas (201, 202) have a greater cross-section than the cores (212) of the central area.
The dimensioning of the end cores (215) is carried out as a function of the maximum cutting stress at the truss supports, as it occurs commonly for all the cores of the truss.
On the contrary, the cores (212) of the middle area (202) are dimensioned as a function of a reduced cutting stress, and in particular as a function of the greater value of the cutting stress determined in the passage points from the central area (202) to one of the end areas (201, 203).
Steel saving quantification compared to the traditional solution
As a way of sole and not limiting example of the aims of the invention, in the following it is described a comparison relating to a real case of a building construction, between a truss realized according to what known at the state of the art and what provided by the present invention.
The truss, object of the study, is a metal self-supporting truss with lower bottom in steel with cross-section 60 x 60 cm. It is arranged on the ground floor between two pillars, with net length of 9,10 m, and supports two floor fields arranged one at its right and one at its left of average net length of 5,80 m. The loads acting on the floors are 1275 daN/m² totally.

In the following it is reported the dimensioning of the reinforcements of the truss in the two morphologies, as obtained by the dedicated calculating software:

	Traditional embodimet			Embodiment according to the invention
	Number	Lenght	Cross-section	Number	Lenght	Cross-section
Continuous upper stringers	3	9,10 m	φ34	3	9,10 m	φ32
Additional upper stringers	-----	-----	-----	1	1,03 m for end	φ18
cores
	2	22,47 m	φ36	2	11,74 m / 10,73 m	φ36/φ30

Therefore, by developing the weights of the single steel elements and by comparing them for the two morphologies, the traditional and innovative ones, by quantifying, for the example truss, steel saving is obtained with the proposed model.

Element Weight [Kg] Percentage difference

Proposed model Traditional model Difference

Cores 306,8 359,1 -52,3 -15%

Continuous + additional upper stringers 176,5 194,6 -18,1 -9%

Proposed model mathematical development

The present invention provides also a computer program configurated to carry out the just described calculating method for the optimization of the cross-section of the cores and stringers in mixed trusses, as well as calculating electronic means on which such computer program is loaded.
In particular, the computer program according to the invention is configured to acquire in input the information relating to the geometry and the application of the truss (constructive kind of the truss, length of the truss, acting load) and so to dimension the upper stringers according to the following method:

a. the continuous upper stringers (110) are dimensioned as a function of the positive maximum moment in the middle of the truss, and have constant cross-section on the whole longitudinal development of the truss (100);
b. the cross-section of the additional upper stringers (114) is dimensioned to complete the cross-section of the continuous upper stringers (110), as a function of the maximum negative value of the bending moment acting in the end section;
c. the length of the additional upper stringers (114) is calculated as the distance between the end of the truss and the section of the truss in which the cross-section of the continuous upper stringers (110) alone is sufficient to absorb the negative bending moment.
d. the length of the additional upper stringers (114) calculated in point c. is modified, upwards, up to become equal to a multiple of the pitch (p) with which the cores (112) are connected to the upper stringers.
e. testing the technical-economical convenience of the application of additional upper stringers, and in particular testing that:
1. i. the length of the additional upper stringers is lower than three times the dimension of the height of the cross-section of the same truss;
2. ii. the dimension of the cross-section of the bar of the additional upper stringer is lower than the double of the dimension of the cross-section of the bar of the continuous upper stringer.
f. In case the two conditions at point e.i) and e.ii) are tested, providing as output the geometrical features of the truss according to the present invention; in case the two conditions at points e.i) and e.ii) are not tested, providing as output the indication that it is convenient from a technical-economical point of view to realize the truss according to the traditional geometries.

Moreover, the computer program according to the invention is configured to acquire in input the information relating to the geometry and the application of the truss (constructing kind of the truss, length of the truss, acting load) and so to dimension the cores according to the following method:

a. subdividing the truss in three distinct areas (201, 202, 203), a central one (202) and two end areas (201, 203) arranged at the ends of the truss and of equal length, in which the cutting reinforcement of the truss has a different dimensioning.
b. carrying out the dimensioning of the cutting cores provided in said end areas as a function of the maximum cutting stress at the truss supports;
c. carrying out the dimensioning of the cores (212) of the middle area (202) as a function of the greater value of the cutting stress determined in the passage points from the central (202) to one of the end areas (201, 203).
d. testing the technical-economical convenience of the application of the cores with different cross-section, and in particular to test that:
1. i. the length of the truss is greater than four meters.
2. ii. the number of the cores with reduced cross-section is at least equal to 30% of the whole number of the cores.
e. In case the two conditions at point d.i) and d.ii) are tested, providing as output the geometrical features of the truss according to the present invention; in case the two conditions at points d.i) and d.ii) are not tested, providing as output the indication that it is convenient from a technical-economical point of view to realize the truss according to the traditional geometries.

Claims

Truss (100) comprising
- at least a lower stringer (111),

- at least an upper continuous stringer (110) with length equal to the whole length of the truss,

- a plurality of cores (112) connecting said lower (111) and upper stringers, said cores (112) being connected to the upper stringers at well defined geometrical intervals, with a constant pitch (p) along the development of the truss,
characterized in that it comprises further, at the two ends of its own longitudinal development, additional upper stringers (114), integrally connected to said cores (112), the length of said additional upper stringers (114) being equal to a multiple of said pitch (p) and lower than the length of said truss.
Truss according to claim 1, characterized in that said lower stringer (111) comprises a metal bottom made up of a large plate and possible round or square iron pieces, welded to said plate;
said at least one continuous upper stringer (110) is realized in round or square cross-sectioned steel bars,
and said cores (112) are connecting elements realized with round or square cross-sectioned steel bars and welded both to said at least one continuous upper stringer (110) and to said lower plate (111).
Truss according to claim 1, characterized in that said lower stringer (311) is made up of a floor in concrete reinforced with suitable steel reinforcements.
Truss according to claim 1, characterized in that said lower stringer (411) is realized by means of round or square cross-sectioned steel bars.
Truss according to any one of claims 1 to 4, characterized in that said truss is subdivided along its own longitudinal development in two end areas (201, 203) arranged at the ends of the truss and of equal length, and a central area (202), comprised between said two end areas, said cores (215) connecting said lower (111) and upper stringers in the two end areas (201, 202) having a cross-section greater than said cores (212) connecting said lower (111) and upper stringers in the central area of the said truss.
Method for dimensioning the continuous upper (110) and additional stringers (114) in a mixed truss according to any one of claims 1 to 5, comprising, after acquiring information relating to the geometry and the load conditions of said truss, the steps of:
a. dimensioning the cross-section of said continuous upper stringers (110) as a function of the positive maximum moment in the middle of the truss;

b. dimensioning the cross-section of the additional upper stringers (114) as a function of the maximum negative value of the bending moment acting in the end section;

c. calculating the length of the additional upper stringers (114) as the distance between the end of the truss and the section of the truss in which the cross-section of the continuous upper stringers (110) alone is sufficient to absorb the negative bending moment on said truss;

d. modifying upwards said length of the additional upper stringers (114) calculated in point c. so that it is equal to a multiple of said pitch (p) ;

e. testing that:
i. the length of the additional upper stringers is lower than three times the dimension of the height of the cross-section of the same truss;

ii. the dimension of the cross-section of the bar of the additional upper stringer is lower than the double of the dimension of the cross-section of the bar of the continuous upper stringer.

f. In case the two conditions at point e.i) and e.ii) are tested, providing as output the geometrical features of the truss calculated in points a) to d) ; in case the two conditions at points e.i) and e.ii) are not tested, providing as output the indication that it is convenient from a technical-economical point of view to realize the truss according to the traditional geometries.
Method for dimensioning the cores in a mixed truss according to any one of claims 1 to 5, comprising, after acquiring information relating to the geometry and the load conditions of said truss, the steps of:
a. subdividing said truss in three distinct areas (201, 202, 203), a central one (202) and two end areas (201, 203) arranged at the ends of the truss and of equal length;

b. carrying out the dimensioning of the cutting cores provided in said end areas as a function of the maximum cutting stress at the truss supports;

c. carrying out the dimensioning of the cores (212) of the middle area (202) as a function of the greater value of the cutting stress determined in the passage points from the central (202) to one of said end areas (201, 203).

d. testing that:
i. the length of the truss is greater than four meters,

ii. the number of the cores with reduced cross-section is at least equal to 30% of the whole number of the cores.

e. In case the two conditions at point d.i) and d.ii) are tested, providing as output the geometrical features of the truss calculated in points a) to c) ; in case the two conditions at points d.i) and d.ii) are not tested, providing as output the indication that it is convenient from a technical-economical point of view to realize the truss according to the traditional geometries.