Don't conflate all that shit. You saw the f'ing planes hit the twin towers. I can't account for both your lack of curiosity and your lack of education.
You know I take statins and Nexlizet. I will get the new vax. I'm 77. Think you'll make it that far with your reliance on junk science and conspiracy theory thinking driving your decisions?
The following is written well beyond your reading comprehension level but, TRY. Short take? Mass X acceleration = force; plus exploding fuel. How can such itty bitty light weight assault weapon rounds do so much damage? Get it?
The problem of the airplane wing cutting through the exterior columns of the World Trade Center is treated analytically. The exterior columns are thin-walled box beam made of high strength steel. The complex structure of the airplane is lumped into another box, but it has been found that the equivalent thickness of the box is an order of magnitude larger than the column thickness.
The problem can be then modeled as an impact of a rigid mass traveling with the velocity of 240 m/s into a hollow box-like vertical member. The deformation and failure process is very local and is broken into three phases: shearing of the impacting flange; tearing of side webs; and tensile fracture of the rear flange.
Using the exact dynamic solution in the membrane deformation mode, the critical impact velocity to fracture the impacted flange was calculated to be 155 m/s for both flat and round impacting mass. Therefore, the wing would easily cut through the outer column. It was also found that the energy absorbed by plastic deformation and fracture of the ill-fated column is only 6.7% of the initial kinetic energy of the wing.
Introduction
The September 11th attack demonstrated the vulnerability of tall steel buildings to the impact of a fast moving airplane. Millions of terrified spectators around the world watched as the Boeing 767 moving with a cruising speed of (500 mph) hit the exterior wall of the World Trade Center (WTC), cut through it, and disappeared in the smoky cavity, Fig. 1, Ref. [1].
To the casual observer, it would appear that the facade of the Twin Towers did not offer any resistance at all, and that the plane's wings and fuselage sliced through the exterior columns as if they were made of cardboard. This casual observation is confirmed by comparing the shape of the hole driven into the exterior walls with the outline of the plane.
One can clearly see the position of the fuselage, two engines, and above all two symmetric narrow slots cut by the wings. A slightly larger opening was caused by the falling floor, which dragged the sections of the exterior columns inside the building. How was it possible that the relatively weak, light and airy airframe damaged the apparently heavy lattice of high strength steel columns? The devastating result of this encounter came as a surprise to the engineering and scientific community or at least to the present authors.
The objective of this research is not only to unravel the mystery behind this interactive failure but even more importantly to develop a general two-dimensional dynamic model of ductile fracture and break up of two beam-like structures of comparable strength hitting each other with high velocity. Such an undertaking will also be helpful in explaining subsequent stages of the impacts in which fragments of the airframe plowed through the truss-like floor of the WTC Towers and hit the core structure.
The airplane wing is a complex structure composed of open section beams, ribs, and skin reinforced by stringers. Upon impact by smaller objects such as hail, birds, etc. the leading edge of the airfoil will clearly be dented and the degree of damage will depend on the size and speed of the aircraft. The process of interactive failure of two deformable and fracturing bodies is very complex and could only be solved by means of numerical methods.
However, it was observed that if all structural members of the wing are lumped together and smeared into a box beam of equivalent mass, its thickness becomes over 100 mm which is ten times larger than the 9.5 mm thickness of the hollow external column of the Twin Towers.
Therefore, in the first approximation, the impacting segment of the wing is treated as a rigid mass. The failure process of the exterior column is divided into three phases: instantaneous cutting through the front flange; tearing of side webs; and finally, tensile fracture of the rear flange.
The impact problem is dominated by the local inertia of the box column so that plastic deformation and fracture are restricted to the immediate vicinity of the stricken part of the column. Each stage of the failure process is analyzed in the paper using the rigorous calculation method while still retaining the simplicity of the closed-form solutions.
It is recognized that the fuel in the wing tanks will greatly increase the mass per unit length of the wings and add to their devastating power. High velocity impact of fuel-filled tanks into deformable structures constitutes a challenging problem by itself and will be addressed in future research.
To the best of the author's knowledge, the problem of a thin-walled box beam subjected to high velocity impact of a rigid mass was not considered in the open literature. However, there are numerous theoretical and experimental studies dealing with projectile impact on thin plates.
For a comprehensive review of the mechanics and physics of projectile impact, the reader is referred to the articles by Corbett et al. [2] and Goldsmith [3]. Hoo Fatt and Wierzbicki [4] showed that for relatively thin plates, where response is dominated by the membrane action, the critical impact velocity for penetration calculated on the basis of tensile necking or shear plugging was similar.
Jones et al. [5] demonstrated through a thorough theoretical analysis that the energy absorbed by plastic deformation is dominated by the membrane response for thin plates (relative to the projectile radius). The contribution of shear increases with the plate thickness for lighter projectiles. This result was independently confirmed by Hoo Fatt et al. [6].
A comprehensive study on plastic response and fracture of beams loaded by a falling mass was undertaken by Jones and his co-workers [7], [8], [9], [10], [11]. They showed that thin beams fail by a combination of tensile necking and through thickness plugging. Based on extensive testing, a stress-based failure condition was established involving shear and membrane forces and bending moments [12]. Since most of the tests were performed in a drop tower facility with relatively large masses and slow impact speeds, the obtained results apply to a lower end of impact velocity spectrum up to 20M/s.
Hoo Fatt and Wierzbicki [13] developed a theory of high velocity impact into free–free plastic beams and a beam supported by a plastic foundation. An interesting feature of this approach was a dual formulation that led to identical results. First, a local dynamic approach was taken leading to the wave equation with suitable boundary and initial conditions. Then, the same problem was formulated and solved using the principle of conservation of linear momentum.
In both cases a characteristic velocity of propagation of lateral disturbances was identified which can serve as a convenient reference value for quantification of impact velocities. The above theory can also predict the onset of fracture with relatively simple calculations. This theory was found to be particularly well suited for solving a difficult problem of a mass impact into a box beam that involves a complex interactive failure pattern. A similar problem was solved in a very rigorous way in Ref. [14] using a plastic wave propagation theory.
Section snippets
Wings
The operation weight of the Boeing 767 is taken to be M=120 tons [1]. It is further assumed that the engine and wings contribute 25% each of the aircraft mass. Wings of modern transport aircraft are quite complicated structures consisting of open section beams, ribs, and a skin reinforced by stringers. Together they form a very stiff and strong box-type section. Determination of the strength of the wing relative to the strength of the building structure will require a detailed finite element
Impact of a rigid mass into a box column
The deformation pattern of a box column hit by a rigid object moving with Vo= 240m/s is very localized due to the inertia and involves denting and stretching of the impacted flange and folding and tearing of the webs.
The failure mode without and with fracture option was calculated by means of ABAQUS/explicit by Zheng and Wierzbicki [18], Fig. 4. At the critical velocity the fracture initiates. It will be calculated in subsequent sections. On increasing the impact velocity tensile and/or shear
Conclusions
In this paper, we have analyzed the sequential failure of a typical exterior column of the World Trade Center Towers subjected to the impact of the airplane wing traveling at 240 m/s. It was found that the fracture process started immediately and continued as plate tearing on the side webs to be completed as tensile/shear fracture on the rear flange. In each stage, the resisting forces arising from plastic deformation and fracture were calculated and the time history of the velocity of the... https://www.sciencedirect.com/science/article...3X02001069
You know I take statins and Nexlizet. I will get the new vax. I'm 77. Think you'll make it that far with your reliance on junk science and conspiracy theory thinking driving your decisions?
The following is written well beyond your reading comprehension level but, TRY. Short take? Mass X acceleration = force; plus exploding fuel. How can such itty bitty light weight assault weapon rounds do so much damage? Get it?
The problem of the airplane wing cutting through the exterior columns of the World Trade Center is treated analytically. The exterior columns are thin-walled box beam made of high strength steel. The complex structure of the airplane is lumped into another box, but it has been found that the equivalent thickness of the box is an order of magnitude larger than the column thickness.
The problem can be then modeled as an impact of a rigid mass traveling with the velocity of 240 m/s into a hollow box-like vertical member. The deformation and failure process is very local and is broken into three phases: shearing of the impacting flange; tearing of side webs; and tensile fracture of the rear flange.
Using the exact dynamic solution in the membrane deformation mode, the critical impact velocity to fracture the impacted flange was calculated to be 155 m/s for both flat and round impacting mass. Therefore, the wing would easily cut through the outer column. It was also found that the energy absorbed by plastic deformation and fracture of the ill-fated column is only 6.7% of the initial kinetic energy of the wing.
Introduction
The September 11th attack demonstrated the vulnerability of tall steel buildings to the impact of a fast moving airplane. Millions of terrified spectators around the world watched as the Boeing 767 moving with a cruising speed of (500 mph) hit the exterior wall of the World Trade Center (WTC), cut through it, and disappeared in the smoky cavity, Fig. 1, Ref. [1].
To the casual observer, it would appear that the facade of the Twin Towers did not offer any resistance at all, and that the plane's wings and fuselage sliced through the exterior columns as if they were made of cardboard. This casual observation is confirmed by comparing the shape of the hole driven into the exterior walls with the outline of the plane.
One can clearly see the position of the fuselage, two engines, and above all two symmetric narrow slots cut by the wings. A slightly larger opening was caused by the falling floor, which dragged the sections of the exterior columns inside the building. How was it possible that the relatively weak, light and airy airframe damaged the apparently heavy lattice of high strength steel columns? The devastating result of this encounter came as a surprise to the engineering and scientific community or at least to the present authors.
The objective of this research is not only to unravel the mystery behind this interactive failure but even more importantly to develop a general two-dimensional dynamic model of ductile fracture and break up of two beam-like structures of comparable strength hitting each other with high velocity. Such an undertaking will also be helpful in explaining subsequent stages of the impacts in which fragments of the airframe plowed through the truss-like floor of the WTC Towers and hit the core structure.
The airplane wing is a complex structure composed of open section beams, ribs, and skin reinforced by stringers. Upon impact by smaller objects such as hail, birds, etc. the leading edge of the airfoil will clearly be dented and the degree of damage will depend on the size and speed of the aircraft. The process of interactive failure of two deformable and fracturing bodies is very complex and could only be solved by means of numerical methods.
However, it was observed that if all structural members of the wing are lumped together and smeared into a box beam of equivalent mass, its thickness becomes over 100 mm which is ten times larger than the 9.5 mm thickness of the hollow external column of the Twin Towers.
Therefore, in the first approximation, the impacting segment of the wing is treated as a rigid mass. The failure process of the exterior column is divided into three phases: instantaneous cutting through the front flange; tearing of side webs; and finally, tensile fracture of the rear flange.
The impact problem is dominated by the local inertia of the box column so that plastic deformation and fracture are restricted to the immediate vicinity of the stricken part of the column. Each stage of the failure process is analyzed in the paper using the rigorous calculation method while still retaining the simplicity of the closed-form solutions.
It is recognized that the fuel in the wing tanks will greatly increase the mass per unit length of the wings and add to their devastating power. High velocity impact of fuel-filled tanks into deformable structures constitutes a challenging problem by itself and will be addressed in future research.
To the best of the author's knowledge, the problem of a thin-walled box beam subjected to high velocity impact of a rigid mass was not considered in the open literature. However, there are numerous theoretical and experimental studies dealing with projectile impact on thin plates.
For a comprehensive review of the mechanics and physics of projectile impact, the reader is referred to the articles by Corbett et al. [2] and Goldsmith [3]. Hoo Fatt and Wierzbicki [4] showed that for relatively thin plates, where response is dominated by the membrane action, the critical impact velocity for penetration calculated on the basis of tensile necking or shear plugging was similar.
Jones et al. [5] demonstrated through a thorough theoretical analysis that the energy absorbed by plastic deformation is dominated by the membrane response for thin plates (relative to the projectile radius). The contribution of shear increases with the plate thickness for lighter projectiles. This result was independently confirmed by Hoo Fatt et al. [6].
A comprehensive study on plastic response and fracture of beams loaded by a falling mass was undertaken by Jones and his co-workers [7], [8], [9], [10], [11]. They showed that thin beams fail by a combination of tensile necking and through thickness plugging. Based on extensive testing, a stress-based failure condition was established involving shear and membrane forces and bending moments [12]. Since most of the tests were performed in a drop tower facility with relatively large masses and slow impact speeds, the obtained results apply to a lower end of impact velocity spectrum up to 20M/s.
Hoo Fatt and Wierzbicki [13] developed a theory of high velocity impact into free–free plastic beams and a beam supported by a plastic foundation. An interesting feature of this approach was a dual formulation that led to identical results. First, a local dynamic approach was taken leading to the wave equation with suitable boundary and initial conditions. Then, the same problem was formulated and solved using the principle of conservation of linear momentum.
In both cases a characteristic velocity of propagation of lateral disturbances was identified which can serve as a convenient reference value for quantification of impact velocities. The above theory can also predict the onset of fracture with relatively simple calculations. This theory was found to be particularly well suited for solving a difficult problem of a mass impact into a box beam that involves a complex interactive failure pattern. A similar problem was solved in a very rigorous way in Ref. [14] using a plastic wave propagation theory.
Section snippets
Wings
The operation weight of the Boeing 767 is taken to be M=120 tons [1]. It is further assumed that the engine and wings contribute 25% each of the aircraft mass. Wings of modern transport aircraft are quite complicated structures consisting of open section beams, ribs, and a skin reinforced by stringers. Together they form a very stiff and strong box-type section. Determination of the strength of the wing relative to the strength of the building structure will require a detailed finite element
Impact of a rigid mass into a box column
The deformation pattern of a box column hit by a rigid object moving with Vo= 240m/s is very localized due to the inertia and involves denting and stretching of the impacted flange and folding and tearing of the webs.
The failure mode without and with fracture option was calculated by means of ABAQUS/explicit by Zheng and Wierzbicki [18], Fig. 4. At the critical velocity the fracture initiates. It will be calculated in subsequent sections. On increasing the impact velocity tensile and/or shear
Conclusions
In this paper, we have analyzed the sequential failure of a typical exterior column of the World Trade Center Towers subjected to the impact of the airplane wing traveling at 240 m/s. It was found that the fracture process started immediately and continued as plate tearing on the side webs to be completed as tensile/shear fracture on the rear flange. In each stage, the resisting forces arising from plastic deformation and fracture were calculated and the time history of the velocity of the... https://www.sciencedirect.com/science/article...3X02001069
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