Patent Publication Number: US-2023145105-A1

Title: Metal beam with asymmetrical section and damage warning function

Description:
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 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 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 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 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.  2   a    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.  2   b    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 body section has identical widths and different thicknesses on two sides of the neutral axis. 
         FIG.  3   a    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.  3   b    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.  4   a    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.  4   b    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 according to the actual specifications, but only for illustration. 
         FIG.  4   c    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.  6   a    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.  6   b    is a bending moment diagram of the metal beam of  FIG.  6   a    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 illustrated based on a proportion for explanation but not subject to the actual component proportion. 
     Referring to  FIG.  1    to  FIG.  6   b   , 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 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.  2   a    to  FIG.  3   b   ), and the cross-sectional shape of the main body 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.  2   a    to  FIG.  2   b   ), wherein the thicker side is the pressure zone at the place of the maximum bending moment and has a 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.  3   a    to  FIG.  3   b   ). 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*7t*11T (as shown by  FIG.  4   a   , 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.  4   b   ), with the specification of the main body section being H400L*200W*7t*12T1/10T2 (T1 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.  4   c   ), with the specification of the main body section being H400L*200W*7t*5T1/7T2. 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: 
     
       
         
          TABLE 1
           
               
               
               
               
               
               
               
             
               
                 Model 
                 Section steel type (mm) 
                 Sectional Area(cm 2 ) 
                 Unit Weight kgf/m 
                 Moment of Inertia I x (cm 4 ) 
                 Section Modulus S x (cm 3 ) 
                 S x  Ratio 
               
             
            
               
                 1 
                 H400 L *200 W *7 t *11 T 
                 70.46 
                 56.1 
                 19800 
                 990 
                 100% 
               
               
                 2 
                 H400 L ∗200 W ∗7 t *12T1/10T2 
                 19710 
                 1039/937 
                 105%/95% 
               
               
                 3 
                 H400 L *200 W ∗7 t ∗15T1/7T2 
                 18361 
                 1158/761 
                 117%/77% 
               
            
           
         
       
     
     As shown in Table 1, regarding models 1, 2, and 3, the cross-sectional area thereof are all 70.46 cm 2 , and the unit weight are all 56.1 kgf/m. The section modulus (Sx) of model 1 is 990 cm 3 , 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 cm 3 , 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 cm 3 , 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   side (pressure zone) having the thickness of 15 mm is increased to 1158 cm 3 , 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 cm 3 , 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 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.  6   a   , 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.  6   b   , both M A  and M B  are presented as negative bending moments, and M max  is presented as positive bending moment. 
     
       
         
           
             
               M 
               A 
             
             
               
                 =M 
               
               B 
             
             
               
                 =2M 
               
               
                 m 
                   
                 a 
                   
                 x 
               
             
             = 
             
               
                 ω 
                 
                   1 
                   2 
                 
               
               
                 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 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  10  is increased, thus improving the load bearing capacity thereof, causing the pressure zone to exceed the elastic limit 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   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 kgf/m. 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 kgf/m 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, σ represents the maximum stress of the section; fy represents the yield stress of the metal material, which is hypothetically 2500 kgf/cm 2 ; S pressure  and S tension  represent the section moduli of the pressure zone and tension zone, which are same in Tables 3, 4, and 5 below.) 
     
       
         
          TABLE 2
           
               
               
               
             
               
                 Section modulus and stress 
                 Combination of main body and 
               
               
                 ratio σ/fy 
                 floor deck having original section 
               
               
                 support section 
                 span section 
               
             
            
               
                 Section modulus S pressure 
 
                 1063 
                 3222 
               
               
                 Section modulus S tension 
 
                 1197 
                 1533 
               
               
                 Stress ratio of pressure zone 
                 -1.034 
                 0.171 
               
               
                 Stress ratio of tension zone 
                 -0.919 
                 0.359 
               
            
           
         
       
     
     Still in an application over limit with the uniformly distributed load increased to 3300 kgf/m, the main body section of the main body  10  is replaced by the specifications of H400L*200W*7t*14T1/8T2 in an asymmetrical section arrangement. In such case, as shown in  FIGS.  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 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. 
     
       
         
          TABLE 3
           
               
               
               
             
               
                 Section modulus and stress ratio σ/fy 
                 Combination of main body and floor deck having asymmetric section 
               
               
                 Support section 
                 Span section 
               
             
            
               
                 Section modulus S pressure 
 
                 1224 
                 2640 
               
               
                 Section modulus S tension 
 
                 1021 
                 1625 
               
               
                 Stress ratio of pressure zone 
                 -0.899 
                 0.208 
               
               
                 Stress ratio of tension zone 
                 -1.078 
                 0.338 
               
            
           
         
       
     
     Alternatively, in an application without going over limit with the uniformly distributed load being 2750 kgf/m, 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: 
     
       
         
          TABLE 4
           
               
               
               
             
               
                 Section modulus and stress ratio σ/fy 
                 Main body having original section with floor deck contribution ignored 
               
               
                 Support section 
                 Span section 
               
             
            
               
                 Stress ratio of pressure zone 
                 -0.921 
                 0.460 
               
               
                 Stress ratio of tension zone 
                 -0.921 
                 0.460 
               
            
           
         
       
     
     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 main body section of the main body  10  can be reduced to the specifications of H380L*190W*7t*14T1/8T2 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. 
     
       
         
          TABLE 5
           
               
               
               
             
               
                 Section modulus and stress 
                 Combination of main body and 
               
               
                 ratio σ/fy 
                 floor deck having asymmetric section 
               
               
                 Support section 
                 Span section 
               
             
            
               
                 Section modulus S pressure 
 
                 1109 
                 2567 
               
               
                 Section modulus S tension 
 
                 935 
                 1507 
               
               
                 Stress ratio of pressure zone 
                 -0.830 
                 0.179 
               
               
                 Stress ratio of tension zone 
                 -0.984 
                 0.305 
               
            
           
         
       
     
     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 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 and/or 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, 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.