Bending collapse of thin-walled beams with ultralight filler

结构力学（structural mechanics）Structural mechanics is a branch of solid mechanics, which mainly studies the laws of force and force transfer of engineering structures, and how to optimize the structure. The so-called engineering structure refers to the system that can bear and transfer the external load, including the rod, plate, shell and their combinations, such as aircraft fuselage and wing, bridge, roof truss and load-bearing wall.The task is to study structural mechanics in engineering structure under external load stress, strain and displacement law; analysis of different forms and different materials of engineering structure, analysis method and calculation formula for engineering design; engineering structure subjected to external forces and transfer; research and development of new engineering structure.The natural structure observed in nature, such as roots, stems and leaves of plants, animal bones, egg shell, can find their strength and stiffness related not only to material, but also closely related with their shape, many engineering structures are natural structures created out of inspiration. The structure design should not only consider the strength and stiffness of the structure, but also to do material saving and light weight. The weight is particularly important for some projects, such as aircraft weight can make the aircraft flight range, rising quickly, high speed and low energy consumption.A brief history of structural mechanicsHumans began to manufacture all kinds of artifacts in ancienttimes, such as houses, boats and bow, musical instruments, these are simple structure. With the progress of society, people for structural design patterns and the strength and stiffness of the structure has been gradually recognized, and accumulated experience, which is reflected in the brilliant achievements of ancient buildings, such as Egypt, Pyramid, China the Great Wall, Zhaozhou Anji bridge, Beijing the Imperial Palace. Despite the presence of mechanics in these structures in knowledge, but did not form a discipline.As far as the basic principles and methods are concerned, structural mechanics is developed simultaneously with theoretical mechanics and material mechanics. Therefore, structural mechanics is integrated with theoretical mechanics and material mechanics in the initial stage of development. By the early nineteenth Century, due to the development of industry, people began to design a variety of large-scale engineering structures, the design of these structures should be more accurate analysis and calculation. Therefore, the analysis theory and analysis method of engineering structure began to be independent. By the middle of the nineteenth Century, structural mechanics began to become an independent discipline.Many computational theories and methods of structural mechanics appeared in the nineteenth Century. At France in 1826 proposed a normal method for solving statically indeterminate structure problems. From 1830s onwards, due to the bridge by train, not only need to consider the bridge under static load problems, must also be considered to withstand the dynamic load, because the bridge span increases, the metal truss structure.In the decades since 1847, scholars have studied the force analysis of statically determinate truss structures by means of graphic method and analytic method, which laid the foundation of truss theory. In 1864, Maxwell established the unit load method and the displacement reciprocal theorem, and calculated the displacement of the truss by the unit load method. Thus, scholars finally got the method to understand the statically indeterminate problem.After the establishment of the basic theory, the new structure and its corresponding theory have been continuously developed while solving the problems of the original structure. From the late nineteenth Century to the early twentieth Century, scholars carried out a lot of mechanical research on the ship structure, and studied the dynamic theory of the beam under the moving load, as well as the problems of free vibration and forced vibration.In the early twentieth Century, the development of Aeronautical Engineering promoted the stress and deformation analysis of thin-walled structures and stiffened plates and shells, and studied the stability problems. At the same time, bridges and buildings started to use a large number of reinforced concrete materials, this requires scientists to study systematically the steel structure, the displacement method was founded in Germany in 1914 of the Dixon, for solving the problem of rigid frame and continuous beam etc.. Later, in the 20~30 century, some simple calculation methods were put forward for the complex statically indeterminate bar structures, so that the general designers could master and use them.By 1920s, people have put forward the idea of honeycomb sandwich structure. According to the concept of limit state of structure, scholars have come up with a new design and calculation theory for beams, plates and frames on elastic foundations. The mechanical problems of structures subjected to various dynamic loads (especially the action of earthquakes) have been studied in many aspects, such as experiment and theory. With the development of structural mechanics, fatigue problems, fracture problems and composite structure problems have entered the field of structural mechanics.In the middle of the twentieth Century, the advent of electronic computers and finite element methods made it possible to make complex calculations of large structures, thus bringing the level of research and application of structural mechanics to a new level.The discipline system of structural mechanicsThe general structural mechanics according to the different nature and its research object is the static structure, structural dynamics, theory, structure, fracture and fatigue theory of rod structure theory, theory of thin-walled structure and overall structure theory etc..Structural statics is the first branch of structural mechanics. It mainly studies the elastic-plastic deformation and stress state of engineering structures under static loads, and the structural optimization problems. Static load refers to the load that does not change with time, the load that changesslowly, and also can be regarded as static load approximately. Structural statics is the basis of other branches of structural mechanics.Structural dynamics is a branch of study on the response and performance of engineering structures under dynamic loads. Dynamic load refers to the load that changes with time. Under dynamic load, the stress, strain and displacement in the structure must be the function of time. Because of the time factor, the research content of structural dynamics is generally more complex than that of structural statics.The theory of structural stability is the branch of study on the stability of Engineering structures. Slender and thin structures are widely used in modern engineering, such as thin rods, thin plates and thin shells. When they are compressed, they will lose stability (wrinkling or buckling) when the internal stress is less than the yield limit, that is to say, the structure produces too large deformation, thus reducing and even completely losing the bearing capacity. Large deformation also affects other requirements of structural design, such as aerodynamic performance of aircraft. The most important content of structural stability theory is to determine the critical buckling load of structures.Structural fracture and fatigue theory is the study of engineering structures are inevitable because of internal crack, crack under external load expansion caused by fracture, caused by fatigue failure would be expanded subject in smaller amplitude under alternating load. Now, the research history of fracture and fatigue is not long and imperfect, but the theoryof fracture and fatigue is developing very fast.In structural mechanics, theoretical and experimental studies on various engineering structures, based on the research object also formed some research fields, which are the main truss structure theory, the theory of thin-walled structures and the overall structure of the theory of three categories. The whole structure is made of raw materials, machined by mechanical milling or by chemical etching. It is especially suitable for some boundary conditions and is often used as variable thickness structure. With the development of science and technology, many new structures emerge, such as sandwich structure and composite structure appearing in the middle of twentieth Century.The research methods of structural mechanics mainly include three kinds of analysis, experimental research, theoretical analysis and calculation of Engineering structure. In the structural design and research, these three aspects are often alternate and complement each other.The use analysis is in the structure use process, carries on the analysis, the comparison and the summary to the structure appears, this is easy and reliable one kind of research method. The use analysis plays an important role in the evaluation and improvement of structure. The newly designed structures also need to be used to test the performance.The experimental research can provide an important basis for the identification of structure, which is also the main means to test and develop the theory and calculation method ofstructural mechanics. The experimental research can be divided into three types: model experiment, real structural component experiment and real structure experiment. For example,Aircraft ground failure test, flight test and vehicle collision test, etc..The mechanical structure usually takes more manpower, material and financial resources, so only to a limited degree, especially in the early stages of the structural design, generally rely on theoretical analysis and calculation of the structural components.In the field of solid mechanics, provides the basic knowledge necessary for the development of material mechanics, structural mechanics, elastic mechanics and plastic mechanics is the theoretical basis of structural mechanics, structural mechanics is also combined with other physical disciplines form many interdisciplinary, such as fluid elastic force etc..Structural mechanics is an ancient discipline, and it is also a rapidly developing subject. A large number of new engineering materials and new engineering structures have provided new research contents and new requirements for structural mechanics. The development of computer provides a powerful computational tool for structural mechanics. On the other hand, structural mechanics also plays an important role in the development of mathematics and other subjects. The emergence and development of the finite element method is closely related to the study of structural mechanics.。

建筑设计外文翻译文献(文档含中英文对照即英文原文和中文翻译)外文：Structural Design of Reinforced Concrete Sloping Roof Abstract: This paper point out common mistakes and problems in actual engineering design according immediately poured reinforced concrete sloping roof especially common residential structure.It brings out layout and design concept use folded plate and arch shell structure in order to reduction or elimination beam and column Layout to reduce costs and expand use function for user of garret . The paper also discussed the need to open the roof holes, windows, and with other design with complex forms . The corresponding simple approximate calculation method and the structure treatment also described in this paper.Keywords : sloping roof;folded plate; along plane load;vertical plane load1. IntroductionIn recent years, reinforced concrete slope of the roof has been very common seen, the correct method of it’s design need establish urgently It’s target is to abolish or reduce the roof beams and columns, to obtain big room and make the roof plate "clean ". This not only benefits tructure specialty itself but also to the design of the building professionals to develop new field, and ultimately to allow users, property developers benefited,and so it has far-reaching significance.In the common practice engineering practice, a designer in the calculation of the mechanical model often referred sloping roof as vertical sloping roof under the projection plane Beam, or take level ridge, ramps ridge contour as a framework and increase unnecessary beam and tilt column . In fact ,the stress is similar between General square planar housing, double slope, multi-slope roof and arch, shell.Ping and oblique ridge are folded plate like “A”, whether layout beams and columns, its ridge line of the deformation pattern is different from the framework fundamentally. All these method will make the difference between calculation results and real internal structure force. During the construction process, housing backbone, plate bias department template has complex shapes, multi-angle bars overlap, installation and casting is very difficult. These projects are common in construction and is a typical superfluous. Some scholars use the elastic shell theory to analyze folded plate roof、internal force and deformation, reveals the vertical loads law of surrounding the base is neither level rise nor the vertical displacement which to some extent reflects the humps and shell’s features .But assume that boundary conditions which is very different from general engineering actual situation and covered the eaves of a vertical cross-settlement and bottom edge under the fundamental characteristics of rally, so it is not for general engineering design .2. Outlines of MethodsFor most frequently span, the way to cancel the backbone of housing, didn’t add axillary often. But in the periphery under the eaves to the framework need established grid-beam or beams over windows. For long rectangular planar multi-room, multi-column, building professionals in a horizontal layout of the partition wall between each pair of columns and the direction set deep into the same thickness width have possession of a gathering of the rafah beam profiles . Pull beam above has a two-slope roof plate affixed sloping beams expect smaller span. For residential,if it has no needs according construction professional, we will be able to achieve within the household no ceiling beams exposed, see figure 1. Similar lattice theory, this approach emphasizes the use of axial force component effe ct, But is different with the truss because it’s load distribution along the bar not only single but also along the axis of the plate. Generally each plate has force characteristics of folded plate, for bear gravity at the roof, wind, earthquake loads, caused the plate along with the internal force components, each plate is equivalent to strengthen the thin flange beams .Among vertical bearing , it is thin-walled beams anti-edge horizontal component to balance Wang thrust formed by arch shell effect. When plates bear the the vertical component load, each plate is equivalent to a solid edge embedded multilateral bearing plates .The design feature of this method is establish and perfect the sloping roof of the arch, folded plate system Consciously, at top of the roof, using a minimal level of rafah balance beam ramp at the level of thrust.It’s calculation methods can be divided into hand algorithm and computer paper, this paper focus on the hand algorithm.Hand algorithm take the single-slope plate of sloping roof plate as slider , through approximate overall analysis, Simplified boundary conditions of determine plate,solving load effect along level and vertical plane, Internal forces of various linear superposition under the condition of assumption of normal straight, testing stability and integrated reinforcement. The method pursuit of operational, use general engineer familiar calculation steps to address more complex issues.This method is suitable for the framework structure, little modifications also apply to masonrystructure or Frame-wall structure. General arch structure have good anti-seismic performance, if designed properly, the sloping roof will also do so. In this paper the pseudo-static is used to analysis earthquake effects.3. Analysis and Design for Along Plane Effect of LoadsFirst regard to cross profile of figure 1,we analysis equal width rectangular parts of long trapezoidal panels 1、2. as for approximate calculation,it is take plane loads along plane as a constant just like four rectangular plate can be simplified to one-way slab,we take along to long unit width narrow structure as analysis object ,take hinged arch model shown in figure 2.图2a图3a图2b图3b图2c图3cIn Figure 2 the right supports vertical linkage representatives roof beams supporting role, ramps connecting rod on behalf of the board itself thin beam reaction effect which is virtual and approximate equivalent. We would like to calculate two anti-bearing.Because the total pressure of physical project through two plate roof beams and transfer to the ends column, So Anti two numerical difference can be seen as two plates bear along with the plane load and roof beams bear the vertical load pressure. Two Anti power link expressions in Various conditions were given as follows, because the model take units width,so the results is line averageload distribution except it has Focus quality in house.They are bouth represent by N , English leftover subscript s, b, represent the plane along the roof panels and vertical role in the roof beam, g, w, e,represent gravity, air pressure and the level of earthquake separately. d, c, represent distribution of concentrated load or effect separately, In the formula h is thicness of every plate,g is gravitation acceleration, a is roof for the horizontal seismic acceleration value formula, Wk represent the standard value Pressure.m with number footnotesrepresent every numbered ramp the quality distribution per unit area ,m with english footnotes represent quality of per location.as to two symmetrical slopes, the formula can be more concise.Figure 2a represent situation of vertical gravity load ,these formulas as follows:()()'''111100110cos cos 38cos cos cos cos L AL L m L AL N l h l h l m ωαβμααββ-=++ ()()()()'10000000101'100000cos cos 2cos cos 8sin cos 8sin cos cos 8sin cos cos cos l l l l l h m m s h N l l h h l h l μαβωααηαβωμβββαββααβ++-=--++()()()()101101110100001012111cos 2cos cos 2L L L L L L L m LL L L mLL L L L L L N h B hL hL LIμξβαβ⎡⎤⎛⎫⎛⎫⎛⎫--+-+--+⎢⎥ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎣⎦=++()()()()()001001110011200101021000110111121cos sin 2sin 2sin cos cos A L h L m LL L L mL L m a L L L L h h L m l m N L L L Ah L L k B h L h L δδββββαβ⎛⎫⎛⎫⎡⎤⎛⎫-+-+--+ ⎪ ⎪ ⎪⎢⎥+⎝⎭⎝⎭⎝⎭⎣⎦=+---++Figure 2b represent situation of bear wind load, these formulas as follows:()()222211122111cos cos cos 8cos cos cos cos wkL h L L S li N a L h h b ωαωββαβα-=++ ()()()()22222001111222212110cos cos cos 11cos cos cos cos sin 5cos sin cos cos sin cos k K L h l w L w w h w h m L N l l AL h L a h L αωαβαβλαβααββββαββ⎡⎤-⎡⎤+⎢⎥=+++-+⎢⎥++⎢⎥⎣⎦⎣⎦Figure 2c represent situation of role of level earthquake, these formulas as follows:()()2222210011022001sin cos sin cos 3sin cos cos cos cos cos a a L h l L L N L h l hl αμβαωαβωβδαβαβδβ+=--+ ()()()()222221011120322222102101sin cos sin cos sin sin sin 3cos 2ln cos 5ln cos cos cos cos a l h m l m L m m m N n s l l l g h l h l δβααβαββββαβαβαβ++=++++ ()()()0010011012110121000111sin cos 2cos 2cos cos cos a a L L m L L L n L L L L L nh L N L l h l h l ββαβαβ⎡⎤⎛⎫⎛⎫-+-+⎢⎥ ⎪ ⎪⎝⎭⎝⎭⎢⎥=+⎢⎥+⎢⎥⎢⎥⎣⎦ ()00000201sin 2cos a a L m L L L h L l θβα⎡⎤⎛⎫-+-⎢⎥ ⎪⎝⎭⎣⎦+()()()2000010121001sin sin cos sin cos sin cos cos 2sin cos a e L m L L L h L m m N l l h βααβαββαβββ⎡⎤⎛⎫-+-⎢⎥ ⎪+⎝⎭⎣⎦=-+ ()()()001001001221111221001sin 1sin cos 2cos 2cos cos cos sin a a L L L L L L m L L L L L h L h l L h l h ωαββαβαββ⎡⎤⎛⎫⎛⎫-+-+⎢⎥ ⎪ ⎪⎝⎭⎝⎭⎢⎥-+⎢⎥+⎢⎥⎢⎥⎣⎦ When vertical seismic calculation required by Seismic Design ParametersIt’s calculate formula generally similar as formula 1 to 4 which only need take gravity g asvertical seismic acceleration a. Above formulas apply to right bearings in figure 2 and also to left when exchange data of two plate.As end triangle of Multi-slope roof ,for simplify and approximate calculation need, we assume two lines distribution load only produced by roof board of several load, effect.now II-II cross-section from figure is took to analysis Long trapezoidal plate two’s end triangle, assuming the structure symmetry approximately, take half of structure to establish model (figure 3). Because linked with the end triangular plate-3 plane has great lateral stiffness ,therefore assume the model leftist stronghold along the central component around which can not be shifted direction. Central Plate vertical stiffness small, in general gravity load of roughly symmetric midpoint only next movement happened possible, Therefore, the model used parallel two-link connection. Wind loading, and the general role of the earthquake in two slope was roughly antisymmetric,so plate model in the central use fixed hinge bearings which allow rotation and transtlateral force to plate 3near the plate beam. Under plate two triangular area is eaves of vertical beams and plates itself along with plane load distribution is functionshown in Figure 1 take the variable x as an argument,assume the distance from position of section II to end part is x 0s so the slope level length is y 0=x 0L 2/L 3,formula 11 to 14 is the value of Vertical triangle of gravity along the x direction arbitrary location of the two load distribution ,where h 3 is Slitting vertical thickness of plate 3.()22001cos 212cos e a a mkxL h x N L sh v l x ββ⎡⎤=-⎢⎥+-⎢⎥⎣⎦ ()211121001sin cos 212cos m kvL h x N l xh x L V βββ⎡⎤=+⎢⎥+-⎢⎥⎣⎦ ()22000002221100max 1123cos L La h L L L L N VL h h l a V L L αγβ⎡⎤⎛⎫=---⎢⎥ ⎪+-⎢⎥⎝⎭⎣⎦ ()22201000112222201001ln 23cos a L L h l L L L n V s xl h v h L x x l L ββ⎡⎤⎛⎫=+-⎢⎥ ⎪+-⎢⎥⎝⎭⎣⎦ As wind load and earthquake effect, sketch could use approximate figure 3b 、3c and use method of structural mechanics to solve But the process is cumbersome and reasonable extent is limited .the wind and earthquake effect is not important compare with the load effect. Moreover,the triangle area is small As approximate calculation, such direct-use rectangular plate slope calculation is more convenient and not obvious waste. The method of solve two load distribution of plate three is same as the solution of Long trapezoidal plate area just make the change of x and y、L2 and L3 in figure 1.The actual profile is part III-III shown in figure 1A B C图4a图4b BDFigure 4 is vertical launch plan and bear load portfolio value of roof ramp shown in Figure 1 to analysis inclined plate and the internal forces of the anti-bearing column . in the figure hypotenuse is oblique roof equal to strengthen frame, Similar wind ramp truss rod and the next edge portfolio, could form the dark truss system ,while long rectangular plate can be seen as part of thin-walled beams, which could also be seen as truss. Therefore, we called roof boarding the plane formed a "thin-walled beam-truss" system, in concrete theory, between the truss and the b eam have no natural divide . it’s no need hand count accurate internal forces and bearing force to such a joint system, Because on the one hand span more, big bending stiffness structure sensitive to the bearing uneven subsidence and have to stay safe reserves; on the other hand it has high cross-section, by increasing reinforced to increase capacity on the cost impact is not significant. Specific algorithm is: Single-ramp calculate by simple cradle, Multi-Span ramp’s bending moment, shear, and supporting anti-edge use the calculate value by the possible maximum numerical control methods, Moment is calculate by simple cradle two sides of supports middle Shear, negative moment and support force calculate according to bearing this continuous, two-hinged, about two span take the largest one. Pin-Pin bearing shear force that is supported by the inter-simple calculate according to simple cradle. But in this method the location of the various internal force’s safety level is uneven expansion, appropriate adjustmen t should be made is late calculation. No mater f the triangular or rectangular part of plate, Thin-plane bending rebar can get by method of moment right boards from the bottom point for the moment distance whichassigned to the eaves or roof. The author believe it has no necessary control number of reinforcement according to smallest beams reinforced rate. On the rim of triangle equivalent to ramp strut can shear entirety. when consider the end is weak can properly reinforced its roof beam below the reinforcement. If shear required stirrup in the rectangular part of thin-walled, should superposition to the beam, generally it’s no need to intentionally imaginary abdominal strengthening reinforcement at rod position.4. Calculation and Design of Pull Beam and Roof BeamsBy column in figure 1 marked calculated value of supporting force and their level of vertical component, horizontal component of the total force multiplied by the cosine of angle. Take column A as example, the first footnotes in R A2 is column number, the first footnotes represent the force generated by the panel two. Their horizontal component balanced by triangle three under the eaves of beams. horizontal component of intermediate support reaction is balanced by the two-level pull beam in deep direction. Then pull beam and above the sloping beams constitutes steel Arch. Because of the existence of antisymmetric load, bilateral role in the anti-power-level components may be inconsistent and pull beam should take the average lag. consider the support impact of uneven settlement, the level pull beam design should take bigger value.Roof beams general under four internal forces: First of the above is levels Rally, The second is axial force generated when oblique roofing in the flange plate plane bending. The third is the vertical load to bear as the roof slab edge beams under bending moment, shear ,like board supported by multi-faceted, Actual force is smaller than bear calculated by one-way plate N b,Fourth is the effect of lateral framework of internal forces .it should linear superposition ,Composite Reinforced, in the situation of weight Load, span and the small dip, checking computations should be took for tension beams cracking, appropriate intensify the section, with fine steel, including the side beams of steel beams rafah terminal should take two meander anchorage,just like letter L With ng as 10d long bends, meander 135 degrees angle and put pull beam intersection with the vertical reinforcement column touting the Meander overcast horn.This paper take model in figure 1 as example, ignore tigers window , 4 sloping roof are 35 o angle, the length of roof slab dimensions are shown in figure 4. Plate unit area quality is 350kg/m2,Overhaul live load is 0.50 kN/m2, Pressure standard of windward side is 0.21 kN/m2, Leeward face is -0.45 kN/m2, Design value of roof horizontal seismic acceleration is 0.1g, Calculate the bearing capacity limit by standardizing, Considered separately with and without seismic load effect of the combination basic design value,we use combination of without earthquake force through compare，Load calculation and analysis results of every position shown in table 1:5. Analysis and Design for Roof of the Vertical Loads Under Sloping RoofSlabs as a Multilateral Support PlateFolded plate structure has character of “unified of borad and frame”: General intersection of each pair of ramps are for mutual support, both sides of the transition line’ plate can be counted dogleg small rotation and transmission, distribution Moment.Under load control which is the role of gravity the two sloping geometry load roughly symmetrical occasions, there is no corner at symmetry capital turning point, Approximate seen as the plate embedded solid edge.if take out a distance by plate of eaves, plate of inside ridge also formation to negative moment,and long roof slabs in the plate sloping beams department and neighbor plate linked together, these all can be approximated as embedded-plate edge to process.For antisymmetric load like horizontal seismic load,the Ping roof should be treated as shear,but it is not control load usually. Plate final design moment value is the status of various unfavorable combination of linear superposition, from the cross-sectional direction plate reinforced by the columns, Reference, balance the require of concrete deep beams of tectonic, upper plate for Moment of negative reinforcement should be reinforced at all or an entire cross-leader, as they also serve as a deep beam distribution lumbartendons or stirrup. plate in the bottom vertical with reinforcement eaves, Negative reinforcementin accordance with their respective calcualte requirements,and it is different after superpositionstirrups requirementBoth sides of "stirrup" in this situation cann’t linked at awnings edge follow shape “U”, can bebent to shape "L" follow upper and down direction,legnth of packs could equal to thickness ofplate.It should enhenced at the node of ramp at the intersection appropriately. It recommended thatuse swagger tectonic shown as in Figure 5 considing simple structure without axillary at thesituation of Cloudy angle without pull. To ensure all reinforced Installing accuracy, Few of therhombus with the supports and rebar stirrups could be added to formed positioning Skeleton atstrengthening reinforced department in the figure, Let two later installed sloping steel plate tie toits lashing,designers should use a three-dimensional geometric method to accurately calculate thediamond stirrups limb edge length and Forming a swagger construction plans6. Calculating and processing of open window and hole in sloping roofAssume the plate in figure 6 has a big hole whose wideth is b ,height is h 0 ,assuming that tungcenter along with the plane bending moment, shear, respectively are M and V through overall calculation, use vierendeel calculation method get about middle cave:1XO MM T τ= 2NR MM T τ=3113312h V V h h =+ 0XO NR M M M V h --= Where I 1、I 2 、I respectively represent upp er and down plate limb’s Section moment of inertia anddouble limbs section moment of inertia.while Edge Moment by hole is:1113I M V b M α=+ 2212I M V b M μ=+not very big by the hole, close to the neutral axis in most cases overall, under the no-hole design of the reinforced the opening hole after the plane can meet the demands by calculation,under the no-hole design of the reinforced the opening hole after the plane can meet the demands by calculation.General tiger win dow’s form prominent roof Facade which a hole had opened up and the other faces a concrete slab closed.when analysis of vertical slab roof slab surface loads ,compare with without windows and roof slabs hole window sheet increased load. profiles of window’s folded plate form make it reduce the bending stiffness compare with without hole roof board, But with the profile hole edge which parallel to the vertical plate is a partial increase in bending stiffness. In the absence of the vertical plate window subordinate legislation should have upturns beam to increase stiffness of the surrounding caves near.in this way i can temporarily ignore the plate stiffness variation acording to the actual load, size and boundary conditions by entities plate to calculate psitive and negative moment and further processing nodes.it should point out that theRoof ramp layout hole edge ideal location is near the plate-bending line, especially in the open side of the window because it was cut down byvertical transmission line of the moment. If the roof slab roof beams department no outward roof then the actual plate-bending force on the line near the roof beam reversed also true, Because of this architects should strive for when determine oosition of tiger position take appropriate care.When pin tung far away from line-bending window wall and roofing in the intersection must bear folded plate and transmission moment, but compare with plate without hole its capacity is weaken surely,and it’s node turn into weak parts. To fill thy judgment and calculation errorstwo panels can be double reinforcement. When the hole is less than line-bending scope should increase negative reinforcement around to keep overall security plate bearing capacity. To ensure steel plate in place accuratly,also should use positioning stirrups and longitudinal reinforcement constitute skeleton similar as figure 5. Hoop end within vertical bars should be strengthen steel and end cave corner should be harvested more than one anchor length to make sure that bottom of the cave 4 tensile stress concentration.7. Stabilize Roof SlopeIn China's V-shaped folded plate structure design norms,the method prevent both sides of theflanges at local instability is limit its generous ratio,This requirement come from the use of isotropic plate buckling theory analysis. In research the flanges outside instability in critical state, the boundary conditions of winglets suppose as freedom outside, fixed interior, pre - and post-hinged on both sides,the situation plates subjected to the bending stress to solve width and height ratio corresponding with the critical pressure compressive stress. When the grade of concreteIs C30,the limit of width and height(b/t)ratio is 47, take 35 as stress non-normative value. Concrete elastic modulus and strength levels is not a linear relationship if use high-strength concrete other study should be taken. In the actual slope roof only a long row to the middle plate bearing plate outside may receive pressure. And here is just the pouringplate affixed roof sloping beams and horizontal pull beam cast together.Have no possible of rollover and foreign rising displacement. norms limited of folded plate span is 21m. roof below and the vertical column spacing generally much smaller it. And the board which into one with roof beams changed boundary conditions of plate, anti-great instability role also very big. For other locations ramp vertical compression edge May also set up the appropriate plate edge beams all these method will receive beyond the norms of redundant safety. Taking into account the plate shear plane, while the vertical direction of the load caused the exit plane effects, Therefore, the grasp of security of caution should cautious. This paper proposed ramp thickness not less than to the short span of 1 / 35 which also conform to design experience of generally confined SLABS, Concrete should graded between C25 and C35 while Steel should I or class II.puter Calculation Method of Local Sloping Roof Structure andOverall ICC of Overall StructureAny calculate software with inclined plate shell modules and the modules bar structural finite element can calculation of competent sloping roof. Shell element of each node have 3 membrane freedom and three panels freedom and can analysis the plane board and internal forces Of out-of-plane effects. However, the current prevalence of certain spatial structure finite element computer program which although have shell model but some are not inclined plate, some not right at the same plane, the stress state and foreign integrated reinforcement are not perfect. Withstructures becoming more diverse, complex and ramp space problems often encountered. Such software should expand its pre - and post-processing functions for conversion of shell element stiffness matrix and loading vector in the direction of freedom and further analysis of ramp space, the space of concrete against stress integrated reinforcement. In a fundamental sense manual method and the finite element method are interchangeable but the result may be very different. As long as layout roof component as this concept,then use the software to calculate can fast, precise, to achieve this goal of this paper.From the eaves to the roof elevation areas, the whole roof of anti-lateral stiffness lower than mutation, quality small than lower,this could not easy to simulate in calculation of whole housing. At the top construction of the seismic as higher-mode response which is also whiplash effect, the earthquake-lateral force may be abnormal and have effect on under layers. Therefore, in the partial hand count roof occasions when take ICC analysis to the overall structure, it proposed roof layer use model of tilt rod ramp support to reduce effect on the overall results distortion.If use software with function of space ramp handling and sloping roof modeling with shell element,all will be wrapped from top to bottom. Top results can be directly used and the distortion of the overall impact would cease to exist.10. Conclusion1）Concrete ramps, side beams in different directions superposition of internal forces, reinforced and ramp stability, the hole limits all to be do in-depth study related this research. Similar typical problems are top floor of structural transformation layer and box-type base box side wall all their research results can be used to adopt.It’s a important method do observation on project; finite element analysis ICC will be more economical, practical and popular. Currently existing completed sloping roof no matter the subjective designers use what kind of assumptions and analysis and whether reinforcement is reasonable as long as the overall structure of the objective reality, create a space folded plate and the arch system that their current work state can be used to summarize and draw upon.2）This structure forms make a new world of design concept of use the top floor and impact on people's living habits.The economic, social benefits it taked will gradually revealed,however it need interaction of architectural and structural professionals and People’s awareness andinformation and even real estate management policies and other support aspects.This method is hard for structure professional,some specific details have no norms to follow at present. This is the challenges sructure staff faced and also the happy exist.references[1]Francis D.K.Ching A Visual Dictionary of Architecture, International Thomson Publishing Inc. 1997.[2]Jiang Fengqing :internal forces of Simply supported two-way pack square plate, Civil Engineering Journal,1982(2)[3]Lai Mingyuan.Zhang Guxin:Deflection and internal forces of Simple peripheral portfolio folded plate roof, Civil Engineering Journal,1992(2)[4] ]Lai Mingyuan: Deflection and internal forces of Simple flattened four folded plate roof slope, Civil Engineering Journal, 1995(1)[5]Li Kaixi.Cui Jia:Local Stability About Yan Beam, Building Structures ,1996(1) [6]user manuals and technical conditions of Multi-storey high-rise building and the space finite element structural analysis and design software SATWE, PKPM CAD department of China Building Research Academy[7]Chen Xinghui.Lin Yuankun: Several calculation problems in the design of V-folded plate roof , Scientific publishing house,1985[8]current building structure norms, China Construction Industry Press,2002译文：钢筋混凝土坡屋顶的结构设计简介：本文对于现浇钢筋混凝土坡屋顶，尤其是常见的住宅结构，指出实际工程中常见的设计错误及问题。

⼒学界公认的名著或经典教科书，都是⼤⽜们写的...
马赫《⼒学的⼀般批判发展史》
雅普诺夫《运动稳定性的⼀般问题》
庞加莱《天体⼒学新⽅法》
安德罗诺夫《振动理论》
普朗特《流体⼒学概论》
谢多夫《⼒学中的相似⽅法与量纲理论》
乐甫《弹性的数学理论教程》
阿佩尔《理论⼒学教程》
汤姆孙《流体⼒学教程》
瑞利《声学理论》
洛强斯基《理论⼒学教程》
普赫哥尔茨《理论⼒学教程》
科钦等《流体⼒学》
穆什海⾥什维⾥《数学弹性⼒学中的⼏个基本问题》
哥尔琴⽂塞尔《弹性薄壳理论》
诺沃⽇洛夫《⾮线性弹性⼒学》
萨博《⾼等⼯程⼒学》
马格努斯《⼯程⼒学基础》
阿诺尔德《经典⼒学中的数学⽅法》
铁摩⾟柯的《材料⼒学》、《⾼等材料⼒学》、《弹性理论》、《弹性稳定理论》、《板壳理
论》、《⼯程中的振动问题》
鹫津久⼀郎《弹性和塑性⼒学中的变分法》
鲍洛⾦《弹性体系的动⼒稳定性》
路尔叶《弹性理论》
Lamb, Hydrodynamics
Batchelor, An Introduction to Fluid Dynamics
Vlasov, Thin Walled Elastic Beams
Clough et al., Dynamics of Structures
Ghali, et al., Structural Analysis-A Unified Classical and Matrix Approach
来源：科学家⽹，王⽂的博客。

曲梁的应用及研究作者：孙皆宜来源：《科技风》2018年第16期摘要：随着工程建设的不断复杂，直梁已经无法满足实际需求，对曲梁的研究显得尤为必要，特别是在材料科学与工程方面，显得尤为必要。

本文通过研究国内外对曲梁的研究，并结合曲梁力学模型的理论研究，对刚度矩阵在曲梁的分析进行了探讨。

关键词：曲梁；梁平衡；刚度矩阵；有限单元法在无载荷的条件下，具有平面曲线轴的梁，通常称为曲梁。

现代结构工程中，尤其是在桥梁工程中，曲梁的应用非常广泛，在船舶工程和航天工业中也有着广泛的应用。

曲线梁样式多样，如连续曲梁、薄壁开口曲梁、复合曲梁、多曲梁等。

根据线性分为变曲率曲梁、圆弧和直线的组合曲梁等；按截面形式分为I型、槽型等。

从外观上来说，曲线梁桥造型独特，和周围的环境，可以带来美的视觉上的享受，满足人们的审美要求；从结构上来说、曲线梁桥能很好地适应地形、地物的限制要求，使交通规划更加科学合理，具有更好的承载能力。

近年来，随着科学技术的不断进步，特别是材料科学方面的进步，复合材料的大量出现，使得曲梁的应用空间得到了极大的扩展。

同时，随着交通和城市建设的进一步发展，高等级公路、铁路和城市立交枢纽的曲线桥逐渐增多。

曲线梁的分析方法也受到国内外许多学者的关注。

然而，由于曲梁原有曲率的存在，使得曲梁的力学性能非常复杂，研究较为困难，其中曲梁的稳定性是一个非常突出的问题，而且曲梁的屈曲理论远远小于直梁的屈曲理论。

许多学者对曲梁理论进行了研究，但结果却不尽相同。

一、国内外研究现状相对直梁的研究，曲梁的研究相对较晚，最早的研究可以追溯到十九世纪，S.Venant在1855和1856年用半逆解法分别求解柱体扭转和弯曲问题，对圆截面曲杆的扭转理论进行了研究。

曲梁这一理论直到二十世纪50年代才开始了更深入的研究，前苏联学者Vlasov[1]建立了经典的稳定性理论，曲梁在直梁平衡方程中，相应的曲率被替换，得到曲梁。

随后曲梁的研究，基本上都是基于Vlasov的理论展开的。

1施工概况笔者单位施工的某大桥，桥址区属黄土梁峁沟壑地貌，横跨侵蚀冲沟及黄土梁布设，冲沟沟道狭窄，呈“V ”型谷，桥址区地形起伏大，线路地面标高介于2120~2192m 之间，高差约72m 。

沟岸基岩裸露，坡面陡峻，自然坡度约35°~55°，坡面基本无植被。

大桥设计空心薄壁墩4个，其中左幅1个（2#墩墩高40m 断面尺寸为6m*2.5m ）、右幅3个（2#墩墩高50.5m 断面尺寸为6m*3.0m 、3#墩墩高41m 断面尺寸为6m*2.5m 、10#墩墩高40m 断面尺寸为6m*2.5m ），其中最大墩高50.5m ，盖梁采用贝雷梁支架法施工。

该大桥右幅2#盖梁尺寸较大，尺寸规格11.95m ×3.2m ×1.8m ；悬臂长2.25m ，悬臂高0.8m 。

盖梁构造图见图1。

2盖梁主要施工流程及施工工艺施工顺序为：施工准备→墩柱预埋爬锥清理→安装支撑体系→安装作业平台→铺设底模→钢筋绑扎→侧模安装、固定→盖梁混凝土浇筑→混凝土养护→侧模拆除→底模模拆除→混凝土养护。

2.1工艺流程图（图2）2.2主要的施工工艺施工准备：复测标高，凿浮浆，牢固联接好墩柱与盖梁。

安装盖梁支架：预埋好爬锥并量测各部位高程和位置，用高强螺栓将钢板与爬锥栓接紧固，用工字钢与钢板焊接好四组三角形托架，保证焊缝质量，安装千斤顶及贝雷片及连接杆；安装作业平台，承重梁安装固定完毕后进行分配梁I18工字钢安装，分配梁布置间距0.5m ，本项目共用32根；作业平台安装采用底模悬出的分配梁为主要受力支撑，在横梁上设置5cm 厚的满铺木板，并与分配梁进行牢固的捆绑。

平台四周满挂安全网和钢管防护栏防护，在安全爬梯位置预留通道。

铺设底模：测出各中心点和高程及设计中线和轴线，———————————————————————作者简介:王鹏旭（1990-），男，甘肃平凉人，工程师，本科，学士，研究方向为桥梁工程。

简历孙光永，男，1981年6月出生于重庆铜梁县。

2003年以优异的成绩毕业于湖南大学机械与运载工程学院机械设计制造及自动化专业；同年保送进湖南大学机械与运载工程学院车辆工程专业攻读硕士学位；2005年3月被湖南大学机械与运载工程学院车辆工程专业录取为提前攻读博士学位研究生；2008年9月公派澳大利亚悉尼大学航空与机械工程系进行为期两年的联合博士研究生培养。

曾获得“湖南大学优秀毕业生”，“湖南省优秀毕业生”，“熊晓鸽奖学金”，“湖南省自然科学优秀论文一等奖”等多种奖励及荣誉称号。

攻读博士学位期间参与了国家973、国家自然科学基金重点项目、国家自然科学基金杰出青年基金、跨世纪优秀人才计划等多项国家重大纵向课题的研究以及作为骨干成员参与了奇瑞S12车型的安全性设计和上汽通用五菱N300车型的安全性改进等产学研项目并取得了较好的应用成果。

发表SCI/EI收录论文30余篇，期中影响因子大于7的一篇，影响因子大于3的四篇，单篇引用次数超过20次的1篇。

已被聘为权威期刊《固体力学学报》和《Aust J Mech Eng》的评审专家。

现已成为中国力学学会和中国计算机学会学生会员。

参加了在韩国，澳大利亚等举办的国际学术会议。

1.张冠军，曹立波，官凤娇，孙光永，Yang King H. 基于汽车与行人碰撞载荷特点的下肢长骨建模. 力学学报（接收）（EI源刊）2.W. Xu, J.G. Zhu, Y.C. Zhang, Y.G. Guo, and G.Y. Sun. One novel equivalent circuit of a single-sided linear induction motorbased on winding function theory. IEEE Transactions on Industrial Electronics. (录用) (SCI, EI源刊)3.Fangyi Li, Guangyao Li, Guangyong Sun, Zhen Luo. Multidisciplinary optimization for multi-objective uncertainty designof thin walled beams. CMC: Computers, Materials, & Continua. (录用) (SCI, EI源刊)4.Shiwei Zhou, Wei Li, Y uhang Chen, Guangyong Sun, Qing Li. Topology Optimization for Negative PermeabilityMetamaterials Using Level Set Algorithm. Acta Materialia.(录用) (SCI, EI源刊)5.闫晓磊，钟志华，查云飞，莫旭辉，孙光永. 功能梯度材料飞轮转子优化设计研究. 机械工程学报（接收）（EI源刊）6.Guangyong Sun, Guangyao Li, Zhihui Gong, Guangqiang He, Qing Li. Radial Basis functional model for multiobjectivesheet metal forming optimization. Engineering Optimization. (录用) (SCI, EI源刊)7.Guangyong Sun, Guangyao Li, Shiwei Zhou, Hongzhou Li, Shujuan Hou, Qing Li. Vehicle crashworthiness design byusing multiobjective robust optimization. Structural and Multidisciplinary Optimization (录用) (SCI, EI源刊)8.J.H. Tian, X. Han, S.Y. Long, G.Y. Sun, Y. Cao, G.Q. Xie, W. Xu. An analysis of the transient heat conduction for plateswith the functionally graded material using the hybrid numerical method, CMES: Computer Modeling in Engineering & Sciences, 2010, 63(2): 101-116 (SCI, EI)9.Tammareddi S, Sun GY, Li Q. Computational design analysis for deployment of cardiovascular stents. IOP Conf. Series:Materials Science and Engineering 10 (2010) 01212310.Chaiy Rungsiyakull, Qing Li, Guangyong Sun, Wei Li, Michael V. Swain. Surface morphology optimization forosseointegration of coated implants. Biomaterials, 2010, 31(27): 7196-7204. (SCI, EI)11.孙光永，李光耀，钟志华. 多目标稳健优化设计方法在车身设计制造中的应用研究. 固体力学学报(录用) (EI源刊)12.Xu w, Zhu JG, Jin JX, Sun GY. Transient and dynamic performance study of a linear induction machine, Appliedsuperconductivity and electromagnetic, 2010, 1(1):82-88.13.Sun GY, Li GY, Zhou SW , Xu W, Li Q. Multifidelity Optimization for Sheet Metal Forming Process, Structural andMultidisciplinary Optimization (录用) (SCI, EI源刊)14.Yong Zhang, Guangyong Sun, Guangyao Li, Qing Li，Identification of material parameters for high strength steel underimpact loading, Adv Sci Lett. (录用) (SCI源刊)15.Guangyong Sun, Guangyao Li, Michael Stone, Qing Li. A two-stage multi-fidelity optimization procedure forhoneycomb-type cellular materials, Computational Materials Science, 2010, 49(3):500-511. (SCI, EI)16.T. Hu, C. S. Wen, G. Y. Sun, S. L. Wu, C. L. Chu, Z. W. Wu, G. Y. Li, J. Lu, K. W. K. Yeung, and P. K. Chu, WearResistance of NiTi Alloy after Surface Mechanical Attrition Treatmentﾔ, Surface and Coatings Technology, 2010, 205:506-510. (SCI, EI).17.王建华, 李光耀, 李胜, 孙光永, 伍广. 基于GPU的冲压成形快速计算方法，中国机械工程，2010，21 (10): 1222-122718.Ma Ruijun，Michael Short, Craig Lobsey, Alex McBratney, Brett Whelan, Budiman Minasny，Sun Guangyong. Integratedmulti-sensor hardware system for soil information measurement, Transactions of the CSAE, 2010, 26(4): 156-161（EI）19. 孙光永，李光耀，郑刚，龚志辉．拉延成形多目标序列响应面法优化设计方法．力学学报，2010, 42 (2): 245-255 (EI)20. Zhou SW, Li W, Sun GY, Li Q. A level-set procedure for the design of electromagnetic metamaterials. OpticsExpress, 2010, 18(7): 6693-6702. (SCI, EI)21. Xujing Yang, Guangyong Sun, Qing Li. A new nurbs tool path generation algorithm for precise sculpturedsurface machining. Advanced Materials Research, 2010, 97-101: 2477-2480.(EI, ISTP)22. Sun GY, Li GY, Hou SJ, Li Wei, Li Q. Crashworthiness design for functionally graded foam-filled thin-walledstructures. Materials Science and Engineering A, 2010, 527: 1911-1919.(SCI, EI)23. Sun GY, Li GY, Gong ZH, Cui XY, Li Q. Multiobjective robust optimization method for drawbead design in sheetmetal forming. Materials and Design, 2010, 32: 1917-1929.(SCI, EI)（湖南省第十三届自然科学优化论文一等奖）24. Cui XY, Liu GR, Li GY, Zhang GY, Sun GY. Analysis of elastic-plastic problems using edge-based smoothedfinite element method. International Journal of Pressure Vessels and Piping, 2009, 86(10): 711-718. (SCI, EI)25. 孙光永，李光耀，龚志辉．基于代理模型的变复杂度方法在板料成形优化中的应用，机械工程学报，2009, 45(9):201-209. (EI)26. 孙光永，李光耀，陈涛，张勇．多目标粒子群优化算法在薄板冲压成形中的应用．机械工程学报，2009, 45(5): 153-159.(EI)27. 孙光永，李光耀，钟志华，张勇．基于序列响应面法的汽车结构耐撞性多目标粒子群优化设计．机械工程学报，2009, 45(2): 224-230. (EI)28. 孙光永，李光耀，张勇，崔向阳．基于有限元的板料拉延成形质量评价准则及工艺参数优化研究．固体力学学报，2009, 30(1): 70-78. (EI)29. 孙光永，李光耀，陈涛，郑刚．基于6sigma的稳健优化设计在薄板冲压成形中的应用．机械工程学报，2008, 44(11):248-254. (EI)30. 陈涛，李光耀，孙光永．覆盖件冲压仿真参数化建模方法．中国机械工程，2008, 19(19): 2292-2296. (EI)31. 张勇，李光耀，孙光永．汽车车身耐撞性与NVH多学科设计优化研究．中国机械工程，2008, 19(14): 1760-1763.(EI)32. 张勇，李光耀，孙光永，韩旭．多学科设计优化在整车轻量化设计中的应用研究．中国机械工程，2008, 19(7): 877-881.(EI)33. Cui XY, Liu GR, Li GY, Zhao X, Nguyen TT, Sun GY. A smoothed finite element method (SFEM) for linear andgeometrically nonlinear analysis of plates and shells. CMES: Computer Modeling in Engineering & Sciences, 2008, 28(2): 109-125. (SCI, EI)34. 孙光永，李光耀，王建华，张勇，钟志华．可靠性优化设计在汽车构件耐撞性中的应用．计算机辅助设计与图形学学报，2007, 19(10): 1308-1314. (EI)35. 孙光永，李光耀，张勇，钟志华．基于鲁棒性的概率优化设计在薄壁构件耐撞性中的应用．中国机械工程，2007, 18(4):479-484. (EI)36. 郑刚，李光耀，孙光永，韩利芬．基于近似模型的拉延筋几何参数反求．中国机械工程，2006，17(19): 1988-1992.(EI)。

对ansys梁单元非常之精辟的小结关于beam类单元需要澄清几点：ansys中的梁单元主要基于两种基本的梁理论：Timoshenko(shear-deformable) and Euler-Bernoulli theory.所有较老的单元都基于Euler-Bernoulli theory，它们包括：2D/3D elastic BEAM3/42D plastic BEAM232D/3D offset tapered,unsymmetic BEAM54/443D thin-walled,plastic BEAM24Euler-Bernoulli beam 的基本特点为：使用Hermitian polynomials 作为形函数Bending moment 为线性变化Transverse shear is not taken into account.Unrestrained section warping is assumed(no warping under torsion)Elastic behavior only is assumed or limited nonlinear material capabilityANSYS 中基于Timoshenko(shear-deformable)theory的有：3D 2-node BEAM1883D 3-node BEAM189Timoshenko(shear-deformable)theory 的假设有：Bending moment 为线性(188)或二次(189)变化Transverse shear stress is constant throuth thickness （first-order shear-deformable beams）可考虑自由扭转或约束扭转可考虑plasticity and creep可用与有限应变（Finite strain)关于剪切变形（Transverse shear）Euler-Bernoulli beam :尽管shear deflection constant 能够作为一个实常数(a REAL constant) 在单元中考虑，但并没有考虑剪切变形（Transverse shear）。