Note: Descriptions are shown in the official language in which they were submitted.
CA 03157684 2022-04-11
METAL BEAM WITH ASYMMETRICAL SECTION
AND DAMAGE WARNING FUNCTION
BACKGROUND OF THE INVENTION
1. Field of the Invention:
The present invention relates to beam structures, and
more particularly, to a metal beam with asymmetrical section
and damage warning function.
2. Description of the Related Art:
Current practice of selecting metal beams and columns in
the industry has at least the following disadvantages:
1. Regarding the reinforced concrete deck (RC DECK), it
has a considerable influence on the section modulus of the steel
body. In terms of a symmetrical section, when the pressure
zone and tension zone are subjected to the bending moment and
axial pressure to reach the critical load, the pressure zone is
the first to yield. However, the industry usually ignores the
influence of reinforced concrete decks on the section modulus
of the steel body. As a result, the section modulus of the
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tension zone at the end of the beam column is greater than that
of the pressure zone and/or the pressure zone suffers a critical
damage unexpectedly.
2. In addition, the industry also currently ignores the beam
axial force (the pressure generated by the beam structure under
a load). As for a steel beam with two fixed ends, a so-called
axial pressure will be generated when it is loaded. As a result,
the pressure zone would reach the elastic limit first
unexpectedly.
3. Furthermore, regarding a cantilever steel beam with
reinforced concrete deck, due to the combination of the deck
and the beam, the section modulus of the tension zone would be
greater than the section modulus of the pressure zone.
However, the current practice of selecting metal beams and
columns in the industry, including ignoring the influence of
reinforced concrete floor deck on the section modulus of the
steel body, ignoring the beam axial force, and the situation of
the section modulus of the tension zone being greater than the
section modulus of the pressure zone due to the combination of
the deck and the beam, possibly make the pressure zone of the
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beam reach the elastic limit and yield before the tension zone,
causing a compressive shear damage to instantaneously occur,
leading to serious consequences.
Therefore, the improvement by the present invention aims
at solving and correcting the above-mentioned problems and
disadvantages of conventional beam structure.
SUMMARY OF THE INVENTION
To improve the issues above, the present invention
provides a metal beam with asymmetrical section and damage
warning function. With an asymmetrical section arrangement
for the section of the main body, the tension zone reaches the
elastic limit and yield to enter a plastic deformation before the
pressure zone, whereby the plastic deformation of the tension
zone provides a warning about possibly occurring compressive
shear damage of the pressure zone.
An embodiment of the present invention provides a metal
beam with asymmetrical section and damage warning function,
whose main body comprises a main body section. The
cross-sectional shape of the main body section defines a
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neutral axis. The main body section defines a pressure zone and
a tension zone when subjected to a pure bending moment load.
Each point of the main body is arranged in a linear relationship
with respect to the neutral axis within the elastic range, and the
cross-sectional shape of the main body section is on both sides
of the neutral axis in an asymmetrical arrangement. The
pressure zone of the main body section at the maximum bending
moment of the main body has a section modulus greater than
the section modulus of the tension zone. Before the pressure
zone bears a stress reaching the elastic limit to yield, the
tension zone has a stress exceeding the elastic limit first and
yield first, so that the plastic deformation of the yielding
tension zone serves as a warning about the possibly occurring
compressive shear damage of the pressure zone.
Therefore, because the shape of the main body section of
the present invention is designed to be asymmetrically
arrangement on both sides of the defined neutral axis, the
section modulus of the pressure zone of the main body section
at the maximum bending moment of the main body is greater
than the section modulus of the tension zone. Thus, when the
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main body bears a load, the tension zone has reached the elastic
limit to yield and begins to enter the plastic deformation,
whereby the tension zone entering the plastic deformation stage
provides a warning before the pressure zone undergoes a
compressive shear damage, earning time for emergency
treatments such as evacuation of personnel or structural
reinforcement.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a schematic view illustrating the support and
uniformly distributed load of a metal beam in accordance with
an embodiment of the present invention.
Fig. 2a is a schematic view of the H-shaped metal beam
with asymmetric main body section in accordance with an
embodiment of the present invention, wherein the main body
section has identical widths and different thicknesses on two
sides of the neutral axis.
Fig. 2b is a schematic view of the quadrangularly-shaped
metal beam with asymmetric main body section in accordance
with an embodiment of the present invention, wherein the main
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body section has identical widths and different thicknesses on
two sides of the neutral axis.
Fig. 3a is another schematic view of the H-shaped metal
beam with asymmetric main body section in accordance with an
embodiment of the present invention, wherein the main body
section has identical thicknesses and different widths on two
sides of the neutral axis.
Fig. 3b is another schematic view of the
quadrangularly-shaped metal beam with asymmetric main body
section in accordance with an embodiment of the present
invention, wherein the main body section has identical
thicknesses and different widths on two sides of the neutral
axis.
Fig. 4a is a sectional view of a conventional H-shaped
metal beam with a symmetrical main body section, wherein the
scale is not according to the actual specifications, but only for
illustration.
Fig. 4b is a sectional view of an H-shaped metal beam with
an asymmetrical main body section in accordance with an
embodiment of the present invention, wherein the scale is not
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according to the actual specifications, but only for illustration.
Fig. 4c is another sectional view of an H-shaped metal
beam with an asymmetrical main body section in accordance
with an embodiment of the present invention, wherein the scale
is not according to the actual specifications, but only for
illustration.
Fig. 5 is a schematic view of a conventional H-shaped
metal beam with a symmetrical section combined with a floor
deck.
Fig. 6a is a schematic view illustrating the support and
uniformly distributed load of another metal beam in accordance
with an embodiment of the present invention.
Fig. 6b is a bending moment diagram of the metal beam of
Fig. 6a bearing uniformly distributed load.
DETAILED DESCRIPTION OF THE INVENTION
The aforementioned and further advantages and features
of the present invention will be understood by reference to
the description of the preferred embodiment in conjunction
with the accompanying drawings where the components are
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illustrated based on a proportion for explanation but not
subject to the actual component proportion.
Referring to Fig. 1 to Fig. 6b, the present invention
provides a metal beam with asymmetrical section and damage
warning function, as shown by Fig. 1, comprising a main
body 10. The main body 10 in the embodiment is a transverse
beam, which has a plurality of supports 20 for bearing a load
and generates a plurality of regions with positive and
negative bending moments.
The main body 10 described in the present invention
comprises a main body section, whose cross-sectional shape
is asymmetrically arranged on two sides of a defined neutral
axis NA, so as to for an asymmetrical section. This main
body section defines a pressure zone and a tension zone when
subjected to a pure bending moment load. Each point of the
main body is arranged in a linear relationship with respect to
the neutral axis NA within the elastic range. The pressure
zone of the main body section at the maximum bending
moment of the main body 10 has a section modulus greater
than the section modulus of the tension zone. Before the
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pressure zone bears a stress reaching the elastic limit to
yield, the tension zone has a stress exceeding the elastic
limit first and yield first, so that the tension zone entering
the plastic deformation stage provides a warning about a
possible compressive shear damage of the pressure zone after
the tension reaches the elastic limit and deforms. The elastic
limit refers to the critical limit of the bearable stress (both
tension and pressure) of the metal beams and columns before
yielding. In other words, when the stress exceeds the elastic
limit, the metal beams and columns begin to yield and enter a
plastic deformation.
The main body 10 is preferably an H-shaped steel beam
or a quadrangularly-shaped steel beam (as shown in Fig. 2a
to Fig. 3b), and the cross-sectional shape of the main body
I 5 section is asymmetrical one two sides of the neutral axis NA.
In an embodiment, the widths of the main body section one
the two sides are the same, but the thicknesses thereof are
thicker on one side and thinner on the other side (as shown in
Fig. 2a to Fig. 2b), wherein the thicker side is the pressure
zone at the place of the maximum bending moment and has a
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larger section modulus; and the thinner side is the tension
zone at the place of the maximum bending moment and has a
smaller section modulus. The main body 10 of the present
invention is not limited to having the aforementioned
differences in thickness. For example, in another
embodiment, the main body section thicknesses of the main
body on two sides are same, but the widths thereof are wider
on one side and narrower on the other side (as shown in Fig.
3a to Fig. 3b). In such case, the wider side is the pressure
zone with a larger section modulus, and the narrower side is
the tension zone with a smaller section modulus.
For example, an H-shaped metal steel beam is provided
in a symmetrical arranged on two sides of the central axis NA,
with the specification of the main body section being
H400L*200W*7011T (as shown by Fig. 4a, wherein L is
height; W is width; t is web thickness; T is upper and lower
flange thickness). Also, an H-shaped metal steel beam is
provided in an asymmetrical arranged on two sides of the
central axis NA (as shown by Fig. 4b), with the specification
of the main body section being H400L*200W*7t*12T1/10T2
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(Ti is the pressure zone at the place of the maximum bending
moment; T2 is the tension zone at the place of the maximum
bending moment). Also, still another H-shaped metal steel
beam is provided in an asymmetrical arranged on two sides
of the central axis NA (as shown by Fig. 4c), with the
specification of the main body section being
H400L*200W*7t*15T1/7T2. Regarding these three H-shaped
metal steel beams, the sectional area, unit weight, moment of
inertia Ix, section modulus Sx, and the ratio of section
modulus Sx thereof are shown in Table 1 below:
Unit Moment of Section
Section steel type Sectional
Model Modulus
(mm) Area(cm2) Weight Inertia
kgf/m lx(cm4)
Sx(cm3) Sx Ratio
H400 L *200 W *7 t
1 19800 990
*111 100%
H400 L *200 W *7 t
2 70.46 56.1 19710 1039/937
*12T1/10T2 105%/95%
H400 L *200 W *7 t
3 18361 1158/761 117%/77%
*15T1/7T2
Table 1
As shown in Table 1, regarding models 1, 2, and 3, the
cross-sectional area thereof are all 70.46 cm, and the unit
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weight are all 56.1 kgfim. The section modulus (Sx) of model
1 is 990 cm3, and the ratio is set as 100%. Comparing model
2, under the condition that the sectional area and unit weight
remain unchanged, only the thickness of the upper and lower
flanges 11 are modified according to the specifications of the
main body section, so as to be asymmetrical on two sides of
the neutral axis NA, wherein the upper and lower flanges
thicknesses are modified into 10 mm and 12 mm, respectively.
In the case, the section modulus of model 2 on the flange 11
side (pressure zone) having the thickness of 12 mm is
increased to 1039 cm3, which is 5% higher than that of model
1. Meanwhile, the section modulus on the flange 11 side
(tension zone) having thickness of 10 mm is reduced to 937
cm3, which is 5% less than that of the model 1. Comparing
the model 3, the thicknesses of the upper and lower flanges
11 are modified according to the specifications of the main
body, so as to be asymmetrical on two sides of the neutral
axis NA. That is, the thicknesses of the upper and lower
flanges 11 are changed to 7 mm and 15 mm, respectively. In
such case, the section modulus of model 3 on the flange 11
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side (pressure zone) having the thickness of 15 mm is
increased to 1158 cm3, which is 17% higher than that of
model 1. Meanwhile, the section modulus on the flange 11
side (tension zone) having thickness of 7 mm is reduced to
761 cm3, which is 23% less than that of the model 1. It can be
seen that when such main body section is used for structures
with fixed loading direction at critical points (such as
construction beams and side columns), the load-bearing
capacity on the side with a relatively large section modulus
can be improved. Meanwhile, the other side with a relatively
smaller section modulus, if in a tension status, will yield and
undergoes deformation damage after exceeding the elastic
limit, thereby providing a warning of compressive shear
damage.
Regarding the main body 10 shown in Fig. 1, when a
floor deck D is laid on the upper flange 11 and fixed with
shear stud 30, if the shear stud 30 has sufficient density and
strength, the floor deck D is combined with the main body 10
through the shear stud 30 to form a T-shaped integral beam
(as shown by Fig. 5). At this time, the span section between
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the main body 10 and the support 40 is presented as a
positive bending moment, with the pressure zone on the
upper side and the tension zone on the lower side. Because
the upper flange 11 is constrained by the floor deck D, the
section modulus of the pressure zone increases, thereby
improving the carrying capacity thereof. According to the
structural mode, the bending moment relationship can be
expressed in accordance with mechanics of material (as
shown in formula 1), and as shown in Fig. 6a, the supports 40
(also presented by end points A and B) on two sides and the
middle point of the span are critical points (end points A and
B are characteristic critical points). Also, as shown in Fig.
6b, both MA and MB are presented as negative bending
moments, and M. is presented as positive bending moment.
4,40 t2
Formula 1: MA=MB-21Arnax--
12
However, the main body 10 is presented as a negative
bending moment at the support 40, with the tension zone on
the upper side and the pressure zone on the lower side. The
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upper flange 11 is also constrained by the floor deck D,
which in turn causes the section modulus of the tension zone
to increase, thereby improving the bearing capacity thereof.
As a result, the pressure zone at the support 40 first exceeds
the elastic limit instead and breaks. Accordingly, it is known
that when the main body 10 is combined with the floor deck
D, the section modulus of the tension zone of the main body
is increased, thus improving the load bearing capacity
thereof, causing the pressure zone to exceed the elastic limit
10 first and may instantaneously undergo a compressive shear
damage. This can greatly affect the design safety of the floor
structure. However, according to the structural analysis and
design method commonly used in the current construction
industry, the combination of the floor with the main body 10
is regarded as non-contributing and therefore ignored. So,
when used over limit, it may cause the risk of instantaneous
damage of the pressure zone.
For example, a main body 10 has the aforementioned
supports 40 at only two ends thereof, with the span between
the two supports 40 being a span section, and the support 40
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section being a support section. The main body section of the
body 10 has the aforementioned specifications of
H400L*200W*7t*11T, and the uniformly distributed load of
the main body 10 is 3000 kgfim. Also, the upper flange 11 of
the main body 10 is laid with a floor deck D which is fixed
by shear stud 30. In such case, if the uniformly distributed
load is increased to 3300 kgfim in an application over limit,
as shown in Table 2, the section modulus of the tension zone
of the support section increases, so that the load bearing
capacity is improved, which results in that the stress ratio is
prevented from exceeding the elastic limit. Instead, the
stress ratio of the pressure zone of the support section
exceeds the elastic limit to be broken. (In Table 2, a
represents the maximum stress of the section; fy represents
the yield stress of the metal material, which is hypothetically
2500 kgficm2; SpreSSurc and S1en8lon represent the section
moduli of the pressure zone and tension zone, which are same
in Tables 3, 4, and 5 below.)
Section modulus and stress Combination
of main body and
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ratio affy floor
deck having original section
Support
Span section
section
Section modulus Spressure 1063 3222
Section modulus Slension 1197 1533
Stress ratio of pressure zone -1.034 0.171
Stress ratio of tension zone -0,919 0.359
Table 2
Still in an application over limit with the uniformly
distributed load increased to 3300 kgfirm, the main body
section of the main body 10 is replaced by the specifications
of H400L*200W*701411/812 in an asymmetrical section
arrangement. In such case, as shown in Fig. 3, although the
load bearing capacity of the tension zone of the support
section is improved due to the increased section modulus, the
cross-sectional shape of the main body section of the main
body 10 is asymmetrical arranged on two sides of the neutral
axis NA. Therefore, for the main body 10 combined with the
floor deck D, the section modulus of the pressure zone is still
greater than the section modulus of the tension zone, so that
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the stress ratio of the pressure zone of the support section is
prevented from exceeding the elastic limit in an over limit
application; instead, the stress ratio of the tension zone of
the support section exceeds the elastic limit first and yields
to under a plastic deformation damage, thereby still
providing a warning about a possibly occurring unexpected
instantaneous compressive shear damage of the pressure
zone.
Combination of main body and
floor deck having asymmetric
Section modulus and stress
section
ratio a/fy
Support
Span section
section
Section modulus Spressure 1224 2640
Section modulus Stension 1021 1625
Stress ratio of pressure zone -0.899 0.208
Stress ratio of tension zone -1.078 0.338
Table 3
Alternatively, in an application without going over limit
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with the uniformly distributed load being 2750 kgfim, while
the upper flange 11 of the main body 10 is also laid with a
floor deck D which is fixed by the shear stud 30, according to
commonly applied structural analysis in the current industry
(contribution of floor deck D ignored), the specifications
above RH400L*200W*7t*11T would be used, with the stress
ratio shown in Table 4:
Main body having original section
with floor deck contribution
Section modulus and stress
ignored
ratio a/fy
Support
Span section
section
Stress ratio of pressure zone -0.921 0.460
Stress ratio of tension zone -0.921 0.460
Table 4
Accordingly, under the same conditions, if the metal
beam with asymmetrical section of the present invention is
selected instead, plus the contribution of floor deck D in
accordance with the actual situation, the specifications of the
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main body section of the main body 10 can be reduced to the
specifications of H380L*190W*7t*1411/8T2 asymmetrical
section arrangement. As shown in Table 5, the stress ratio of
the pressure zone and the tension zone are both within the
elastic range (stress ratio 1). Also, when
there is a floor
deck D, the section modulus of the pressure zone is greater
than that of the tension zone, which still provides a higher
load bearing capacity. Even in the case of application over
limit, the stress ratio of the tension zone of the support
section would exceed the elastic limit first and yield to
undergo a plastic deformation damage. It can not only
provide a warning about possibly occurring instantaneous
compressive damage, but also reduce the unit weight due to
the reduction of specifications (the unit weight being
reduced by 6.4% compared to the specifications of
H400L*200W*7t*11T). Also, as long as the structural safety
prerequisite is met, the material cost of the main body 10 can
be reduced.
Section modulus and stress Combination
of main body and
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ratio cafy floor deck
having asymmetric
section
Support
Span section
section
Section modulus Spressure 1109 2567
Section modulus Stenston 935 1507
Stress ratio of pressure zone -0.830 0.179
Stress ratio of tension zone -0.984 0.305
Table 5
From the above description, the characteristics of the
present invention are clear as follows:
1. When the main body 10 of the present invention bears
a critical loading, because the shape of the main body section
of the present invention is designed to be asymmetrically
arrangement on both sides of the defined neutral axis, the
section modulus of the pressure zone of the main body
section at the maximum bending moment of the main body 10
is greater than the section modulus of the tension zone. Thus,
when the main body 10 bears a load, the tension zone has
reached the elastic limit to yield and begins to enter the
plastic deformation, thereby providing a warning before the
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pressure zone undergoes a compressive shear damage, thus
beneficial for earning time for emergency treatments such as
evacuation of personnel or structural reinforcement.
2. The current industry usually neglects the effects of
reinforced concrete floor deck on the modules of the steel
body or ignores the beam axial force (the pressure generated
by the beam structure under a load), which causes the issues
of the section modulus of the tension zone of the main beam
column end being greater than that of the pressure zone
andior the pressure zone undergoing critical damage first
unexpectedly, or the issue of a cantilever steel beam of a
floor deck D, due to the combination of the deck and the
beam, having a section modulus of the tension zone greater
than the section modulus of the pressure zone. Such issues
can be resolved by use of the main body section of the main
body 10 of the present invention, which is designed in an
asymmetrical arrangement, so as to correct abovementioned
improper construction practice.
3.The main body section of the main body 10 of the
present invention has an asymmetrical section design,
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wherein the tension zone, after reaching the elastic limit,
yields and begins to enter the plastic deformation, thereby
not only providing a warning before the pressure zone
undergoes a compressive shear damage, but also lowering the
unit weight with the reduction of main body section
specifications. Thus, as long as the structural safety
prerequisite is met, the material cost of the main body 10 can
be reduced.
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