Development of the 6-axis forcemoment sensor

PGElectrical · Principle of Function · Universal Gripper1044Modular RoboticsModular-Standardized interfaces for mechatronics and control for rapid and simple assembly without complicated designs-Cube geometry with diverse possibilities for creating individual solutions from the modular systemIntegrated-The control and power electronics are fully integrated in the modules for minimal space requirements and interfering contours-Single-cable technology combines data transmission and the power supply for minimal assembly and start-up costs Intelligent-Integrated high-end microcontroller for rapid data processing -Decentralized control system for digital signal processing -Universal communication interfaces for rapid incorporation in existing servo-controlled conceptsYour advantages and benefitsThe modules of the PowerCube series provide the basis for flexible combinatorics in automation. Complex systems and multiple-axis robot structures with several degrees of freedom can be achieved with minimum time and expenditure spent on design and programming.Module overviewThe innovative technology of the PowerCube modules already forms the basis of numerous applications in the fields of measuring and testing systems, laboratory automation, service robotics and flexiblerobot technology.PGServo-electric2-Finger Parallel Gripper PRServo-electric Rotary Actuators PWServo-electricRotary Pan Tilt ActuatorsPSMServo-motors with integrated position controlPDUServo-positioning motor with precision gearsPLSServo-electric Linear Axes withball-and-screw spindle drivePG·Universal Gripper1045Method of actuationThe PowerCube modules work completely independently. The master control system is only required for generating the sequential program and sending it step by step to the connected modules. Therefore, only the current sequential command is ever stored in the modules, and the subsequent command is stored in the buffer. The current, rotational speed and positioning are controlled in the module itself. Likewise, functions such as temperature and limit monitoring are performed in the module itself. Real-time capability is not absolutely essential for the master control or bus system. For the communication over Bus-System the SMP - SCHUNK Motion Protocol - is used. This enables you to create industrial bus networks,and ensures easy integration in control systems.Control version AB Hardware Control with PLC (S7)Control with PC Interface Profibus DP CAN bus / RS-232SoftwareWindows (from Windows 98) operating systemLINUX operating systemDevelopment platforms MC-Demo Operating Software PowerCube (LabView, Diadem)with Online documentation, standard softwaregsd-file, programming examples(gsd file, programming examples)on requeston requestIncluded with the ''Mechatronik DVD'' (ID 9949633): Assembly and Operating Manual with manufacturer's declaration, MCDemo software and description and gsd-file for S7 use.1234567889ᕃ24VDC / 48VDC power supply provided by the customerᕄControl system provided by the customer (see control versions A, B and C)ᕅPAE 130 TB terminal block for connecting the voltage supply, the communication and the hybrid cable (Option for easy connection)ᕆPDU servo-motorᕇLinear axis with PLS ball-and-screw spindle drive and PSM servo-motorᕈHybrid cable (single-cable technology) for connecting the PowerCube modules (voltage supply and communication). Not recommended for the use in Profibus applications ᕉPW Servo-electric Rotary Pan Tilt Actuator ᕊPG Servo-electric 2-Finger Parallel Gripper ᕋPR Servo-electric Rotary ActuatorPG· Universal Gripper1046Size 70Weight 1.4 kg Gripping force up to 200 N Stroke per finger 35 mm Workpiece weight1 kgApplication exampleDouble rotary gripper module for loading and unloading of sensitive componentsPG 70 Servo-electric 2-Finger Parallel Gripper PR 70 Servo-electric Rotary ActuatorPGUniversal Gripper1047Gripping force control in the range of 30 - 200 N for the delicate gripping of sensitive workpieces Long stroke of 70 mm for flexible workpiece handlingFully integrated control and power electronics for creating a decentralized control systemVersatile actuation optionsfor simple integration in existing servo-controlled concepts via Profibus-DP, CAN bus or RS-232Standard connecting elements and uniform servo-controlled conceptfor extensive combinatorics with other PowerCube modules (see explanation of the PowerCube system)Single-cable technology for data transmission and power supplyfor low assembly and start-up costsServo-electric 2-finger parallel gripper with highly precise gripping force control and long strokeUniversal GripperArea of applicationUniversal, ultra-flexible gripper for great part variety and sensitive components in clean working environmentsYour advantages and benefitsGeneral information on the seriesWorking principle Ball screw driveHousing materialAluminum alloy, hard-anodized Base jaw materialAluminum alloy, hard-anodized ActuationServo-electric, by brushless DC servo-motorWarranty 24 monthsScope of deliveryGuide centering sleeves and ‘’Mechatronik DVD’’ (contains an Assembly and Operating Manual with manufacturer’s declarartion and MC-Demo software withdescription)PG· Universal Gripper1048Control electronicsintegrated control and power electronics for controlling the servo-motorEncoderfor gripper positioning and position evaluationDrivebrushless DC servo-motorGear mechanismtransfers power from the servo-motor to the drive spindleSpindletransforms the rotational movement into the linear movement of the base jaw Humidity protection cap link to the customer’s systemThe brushless servo-motor drives the ball screw by means of the gear mechanism.The rotational movement is transformed into the linear movement of the base jaw by base jaws mounted on the spindles.Function descriptionThe PG gripper is electrically actuated by the fully integrated control and power electronics. In this way, the module does not require any additional external control units.A varied range of interfaces, such as Profibus-DP, CAN-Bus or RS-232 are available as methods of communication. For the communication over Bus-System the SMP - SCHUNK Motion Protocol - is used. This enables you to create industrial bus networks, and ensures easy integration in control systems.If you wish to create combined systems (e.g. a rotary gripper module), various other modules from the Mechatronik-Portfolio are at your disposal.Electrical actuationSectional diagramPGUniversal Gripper1049Gripping forceis the arithmetic total of the gripping force applied to each base jaw at distance P (see illustration), measured from the upper edge of the gripper.Finger lengthis measured from the upper edge of the gripper housing in the direction of the main axis.Repeat accuracyis defined as the spread of the limit position after 100 consecutive strokes.Workpiece weightThe recommended workpiece weight is calculated for a force-type connection with a coefficient of friction of 0.1 and a safety factor of 2 against slippage of theworkpiece on acceleration due to gravity g. Considerably heavier workpiece weights are permitted with form-fit gripping.Closing and opening timesClosing and opening times are purely the times that the base jaws or fingers are in motion. Control or PLC reaction times are not included in the above times and must be taken into consideration when determining cycle times.General information on the seriesCentering sleevesElectrical accessories PAE terminal blockPAM standardconnecting elementsAccessoriesHybrid cableFor the exact size of the required accessories, availability of this size and the designation and ID, please refer to the additional views at the end of the size in question. You will find more detailed information on our accessory range in the …Accessories“ catalog section.PG 70· Universal Gripper1050Technical dataFinger loadMoments and forces apply per base jaw and may occur simultaneously. M y may arise in addition to the moment generated by the gripping force itself. If the max.permitted finger weight is exceeded, it is imperative to throttle the air pressure so that the jaw movement occurs without any hitting or bouncing. Service life may bereduced.Gripping force, I.D. grippingDescriptionPG 70Mechanical gripper operating data ID 0306090Stroke per finger [mm]35.0Constant gripping force (100 % continuous duty)[N]200.0Max. gripping force [N]200.0Min. gripping force [N]30.0Weight [kg] 1.4Recommended workpiece weight [kg] 1.0Closing time [s] 1.1Opening time [s] 1.1Max. permitted finger length [mm]140.0IP class20Min. ambient temperature [°C] 5.0Max. ambient temperature [°C]55.0Repeat accuracy [mm]0.05Positioning accuracy [mm]on request Max. velocity [mm/s]82.0Max. acceleration [mm/s 2]328.0Electrical operating data for gripper Terminal voltage [V]24.0Nominal power current [A] 1.8Maximum current [A] 6.5Resolution [µm] 1.0Controller operating data Integrated electronics Yes Voltage supply [VDC]24.0Nominal power current [A]0.5Sensor system EncoderInterfaceI/O, RS 232, CAN-Bus, Profibus DPPG 70Universal Gripper1051ᕃ24 VDC power supply provided by thecustomerᕄControl (PLC or similar) provided bythe customerᕅPAE 130 TB terminal block(ID No. 0307725) for connecting the power supply, the communication and the hybrid cableᕆHybrid cable for connecting thePowerCube modulesMain viewsThe drawing shows the gripper in the basic version with closed jaws, the dimensions do not include the options described below.ᕃGripper connection ᕄFinger connectionᕓᕗM16x1.5 for cable glandActuation DescriptionID Length PowerCube Hybrid cable, coiled 03077530.3 m PowerCube Hybrid cable, coiled03077540.5 mPowerCube Hybrid cable, straight (per meter)9941120The ‘Hybrid cable’ is recommended for the use in CAN-Bus- or RS232-systems. For Profibus applications we recommend to use a separate standardized Profibus cable for the communication.You can find further cables in the …Accessories“ catalog section.Interconnecting cablePG 70· Universal Gripper1052Special lengths on requestRight-angle standard element for connecting size 70 PowerCube modulesSpecial lengths on requestConical standard element for connecting size 70 and 90 PowerCube modulesSpecial lengths on requestStraight standard element for connecting size 70 PowerCube modules Right-angle connecting elements Description ID DimensionsPAM 120030782090°/70.5x98Conical connecting elements Description ID DimensionsPAM 110030781090x90/45/70x70 mm PAM 111030781190x90/90/70x70 mmStraight connecting elements Description ID DimensionsPAM 100030780070x70/35/70x70 mm PAM 101030780170x70/70/70x70 mmMechanical accessoriesYou can find more detailed information and individual parts of the above-mentioned accessories in the …Accessories“ catalog section.。

doi:10.3971/j.issn.1000-8578.2024.23.1335Lnc-BM通过FASTK/MT-ND6轴调节线粒体呼吸功能促进胃癌进展张明月1，陈晨1，王萌2，王守宇1Lnc-BM Promotes Gastric Cancer Progression by Regulating Mitochondrial RespiratoryFunction Through FASTK/MT-ND6 AxisZHANG Mingyue1, CHEN Chen1, WANG Meng2, WANG Shouyu11. Medical School of Nanjing University, Nanjing 210093, China;2. Department of Gastrointestinal Surgery, Affiliated Drum Tower Hospital of Nanjing University MedicalSchool, Nanjing 210008, ChinaCorrespondingAuthor:WANGShouyu,E-mail:**************.cnAbstract: Objective To explore the role and molecular mechanism of Lnc-BM in the occurrence and development of gastric cancer (GC). Methods GC tissues and paired adjacent normal tissues of 36 GC patients were collected, and the expression of Lnc-BM was detected by RT-qPCR. Colony formation and CCK-8 assays were used to investigate the proliferation of GC cells. The migration and invasion properties of GC cells were investigated via Transwell assay. RNA pull-down assay was applied to confirm the interaction between FASTK and Lnc-BM. Western blot assay was used to detect FASTK protein level in Lnc-BM overexpressing or knockdown cells. Mitochondrial respiratory capacity and the related proteins expression levels were detected by Seahorse and Western blot assays, respectively. Lnc-BM stably overexpressing GC cells were constructed and then injected subcutaneously into nude mice. The tumor growth was observed. Results Lnc-BM was highly expressed in GC tissues compared with their paired adjacent normal tissues. Lnc-BM overexpression significantly promoted GC cells proliferation migration and invasion, while Lnc-BM knockdown inhibited GC cells proliferation, migration and invasion (P˂0.05). RNA pull-down experiment demonstrated that Lnc-BM can directly bind to FASTK. Western blot results indicated that overexpression of Lnc-BM increased the protein levels of FASTK, while knockdown of Lnc-BM inhibited the expression of FASTK (P˂0.05). Compared to the control group, overexpression of Lnc-BM increased the levels of mitochondria associated proteins, such as MT-ND6 and TOM20 (P˂0.05). Seahorse results indicated that overexpression of Lnc-BM enhanced mitochondrial respiratory capacity (P˂0.05). Knocking down FASTKin Lnc-BM stably overexpressing cells can reverse the increase in mitochondrial respiratory capacity caused by Lnc-BM overexpression (P˂0.05). In vivo, the results of subcutaneously implanted tumor model in nude mouse showed that Lnc-BM overexpression promoted the tumor growth (P˂0.05). Conclusion Lnc-BM promotes GC progression by regulating mitochondrial respiratory function through the FASTK/MT-ND6 axis.Key words: Gastric cancer; Lnc-BM; FASTK; MitochondrionFunding: National Natural Science Foundation of China (No. 82273157, 82073114, 81773383)Competing interests: The authors declare that they have no competing interest.摘 要：目的 探究Lnc-BM在胃癌发生发展中的作用及分子机制。

Semi-rotary drives DRVSe Festo Core RangeSolves the majority of your automation tasks With the Festo Core Range, we have selectedthe most important products and functionsfrom our broad product catalogue, and addedthe quickest delivery.Worldwide:Simply good:Fast:Quickest delivery – wherever, whenever Expected high Festo qualityEasy and fast to select The Core Range off ers you the best valuefor your automation tasks.Just lookfor thestar!Semi-rotary drives DRVS Key featuresKey features at a glance• Double-acting semi-rotary drive with vane• Lighter than other semi-rotary drives • Modern and compact design• Fixed swivel angle• Swivel angle can be adjusted withthe help of accessories• Housing protected against splashwater and dust• No metal fixed stopThe technology in detailSemi-rotary drive DRVSSize 6, 8Size 12 (40)[1] Pneumatic connection[2] Mounting thread[3] Drive shaft:Size 6 ... 16: with flat areaSize 25 ... 40: with featherkeyPosition sensor SRBSThe position sensor is used for sensingthe end positions.Sensing is magnetic and contactless.Two switching points are output.Key features:• Quick installation• Simple and reliable operation usingone pushbutton• The end positions of the swivelangle are taught in at the touch of abutton• Only one connecting cable required• Long service life thanks to sturdyand non-contacting positionsensingTechnical data:• Sensing range: 0 ... 270°• Repetition accuracy: š 1°• 2 switching outputs (24 V)• Switching output:PNP or NPN programmable• Switching element function:N/O contact or N/C contact,programmableFor manufacturing lithium-ion batteriesDRVS-...AccessoriesRecommended for production facilities for manufacturing lithium-ion batteries.Metals with copper, zinc or nickel as the main constituent are excluded from use.Exceptions are nickel in steels, chemically nickel-plated surfaces, printed circuitboards, cables, electrical plug connectors and coils.Your Festo contact partner can provide information about which accessories aresuitable for manufacturing lithium-ion batteries.2d Internet: /catalogue/...Subject to change – 2022/1132022/11 – Subject to changed Internet: /catalogue/...Semi-rotary drives DRVSKey features and type codesMounting options With female thread Via through-holeSize 6 (40)Size 12 (40)Centring via centring collar Size 6 (40)Type codes H- -NoteThis type of mounting is not permissible in combination withaccessories.[1]Centring collarSemi-rotary drives DRVSPeripherals overviewSize 6 and 84d Internet: /catalogue/...Subject to change – 2022/11Semi-rotary drives DRVS Peripherals overviewSize 12 (40)5 2022/11 – Subject to change d Internet: /catalogue/...6d Internet: /catalogue/...Subject to change – 2022/11Semi-rotary drives DRVSDatasheetFunction-N- Size6 (40)2532G1/82)Corrosion resistance class CRC 1 to Festo standard FN 940070 Low corrosion stress. Dry internal application or transportand storage protection. Also applies to parts behind covers, in the non-visible interior area, or parts which are covered in the application (e.g. drive trunnions).1)Note the ATEX certification of the accessories.Semi-rotary drives DRVSDatasheetMaterialsSectional view13452DRVS-6/8DRVS-12 (40)1) The axis of rotation and the centre of the drive shaft are the point of reference for the forcesH--NoteIf the semi-rotary drives DRVS are used without a stop system or the mass mo-ment of inertia is exceeded, external stops must be used. A minimum radius rel-ative to the drive shaft (r min) must be observed. The stop force must not exceedthe maximum force.7 2022/11 – Subject to change d Internet: /catalogue/...8d Internet: /catalogue/...Subject to change – 2022/11Semi-rotary drives DRVSDatasheetMass moment of inertia J as a function of swivel time t Size 6Size 8Size 12Size 16Size 25Size 32Size 4090°180°270°Semi-rotary drives DRVS Datasheet9 2022/11 – Subject to change d Internet: /catalogue/...Semi-rotary drives DRVSDatasheet10d Internet: /catalogue/...Subject to change – 2022/111) Included in the scope of delivery1) Included in the scope of deliveryq Core RangeFoot mounting DAMH Material:Galvanised steel RoHS-compliantFor sizes 6 and 8, foot mountings canonly be mounted on the front.1) For a foot mounting2) Suitable for ATEXFlange mounting DAMF Material: Galvanised steel RoHS-compliantMounting variants in combination with supply ports:• For sizes 12 ... 25, possible every 60°•For sizes 32/40, possible every 90°1) Suitable for ATEXFlange: Anodised wrought aluminium alloyScrews: galvanised steelRoHS-compliant1) Suitable for ATEXStop kit KSMMaterial:Housing: Anodised aluminium Stops: High-alloy stainless steel Free of copper and PTFE Description:For adjusting the swivel angle1) Suitable for ATEXMounting kit WSMMaterial:Bracket, magnet holder: Polyamide Rail in bracket: Aluminium Description:• For sensing the swivel angle • For mounting the proximity switch SME/SMT-10Material:Housing: Reinforced PA, nickel-plated brassRoHS-compliantDescription:• Sturdy, non-contacting and encap-sulated position sensor with long service life• For sensing the end positions• Simple and reliable operation using one pushbutton• Only one connecting cable requireda page 23Stop kit DADP-ES Material:Disc: Anodised aluminiumLever: Nickel-plated beryllium bronze Stop: DADP-12: Nickel-plated beryllium bronze,DADP-16 ... 40: Stainless steel RoHS-compliantDescription:• For adjusting the swivel angle (precision adjustment via thread)• With flexible cushioning elements for noise reductionOptimal swivel motion:For an even swivel motion it is recommended to position the stops symmetrically to the mid-position.Size 12Size 16 (40)Mounting variant 90 ... 270°Mounting variant 0 ... 130°0 ... 190°min. 90°max. 270°H- -NotePermissible mass moment of inertia d Basic driveSemi-rotary drives DRVS Accessories1) Suitable for ATEXMinimum swivel angle W1 in combination with stop kit DADP-ES and attached proximity switchesWith proximity switch SIEN-M5/SIEN-M8With proximity switch SME-10/SMT-1021 2022/11 – Subject to change d Internet: /catalogue/...Semi-rotary drives DRVSAccessories1) Packaging unit22d Internet: /catalogue/...Subject to change – 2022/11Semi-rotary drives DRVS Accessories23 2022/11 – Subject to change d Internet: /catalogue/...Festo - Your Partner in AutomationConnect with us/socialmedia 1Festo Inc.2Festo Pneumatic 3Festo Corporation 4Regional Service Center 5300 Explorer DriveMississauga, ON L4W 5G4CanadaAv. 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新《物理专业英语》范围单词篇1 、加速度acceleration2 、速度 velocity3 、角速度 angular velocity4 、角动量angular momentum5 、热量 amount of heat6 、热力学第一定律 the first law of thermodynamics7 、干涉 interference8 、反射 reflection9 、折射 refraction10 、振幅 amplitude11 、机械运动 mechanical motion12、保守场 conservative field13 、向心力 centripetal force14、保守力 conservative force15、摩擦力 friction force16 、面积area17 、体积 volume18、阿伏加德罗常数 Avogadro constant19 、绝对零度 absolute zero20 、电势能 energy of position21、重力势能 gravitational potential energy22 、重力场 the field of gravity force23 、真空中的磁场 magnetic field in a vacuum24 、电磁波 electromagnetic wave25 、电流的相互作用interaction of current1、（第3页）第四段的第3句A typical problem of mechanics consists in determining the states of a system at all the following moments of time t when we know the state of the system at a certain initial moment to and also the law governing the motion.翻译：机械运动的一个典型的问题的构成取决于一个系统在接下来的时间间隔t的状态，（因此）当我们知道了一个确切的最初的系统状态时，也可以知道运动的规律。

㊀２０２１年㊀第１期仪表技术与传感器Ｉｎｓｔｒｕｍｅｎｔ㊀Ｔｅｃｈｎｉｑｕｅ㊀ａｎｄ㊀Ｓｅｎｓｏｒ２０２１㊀Ｎｏ．１㊀收稿日期：２０２０－０１－１４一种无线式六维力传感器的研制吕志鹏，王卫英，刘思凡，马成聪（南京航空航天大学机电学院，江苏南京㊀２１００１６）㊀㊀摘要：针对旋翼系统在旋转状态下的多个维度的力和力矩信息采集的应用背景，设计了一种带有数据无线发送功能的六维力传感器㊂建立了传感器弹性体的有限元分析模型，确定了应变片的粘贴位置㊂通过合理的组桥电路设计，将六个维度的力和力矩以电压信号的方式反馈出来，并设计了相应的信号处理电路使其满足Ａ／Ｄ采集模块的范围电压㊂最后将整个硬件电路以ＰＣＢ封装在传感器内部，制成传感器样机㊂关键词：旋翼系统；无线数据发送；六维力传感器；有限元分析；组桥电路设计；传感器样机中图分类号：ＴＨ８２３㊀㊀㊀文献标识码：Ａ㊀㊀㊀文章编号：１００２－１８４１（２０２１）０１－０００４－０５ＤｅｖｅｌｏｐｍｅｎｔｏｆＷｉｒｅｌｅｓｓＳｉｘ⁃ａｘｉｓＦｏｒｃｅＳｅｎｓｏｒＬＹＵＺｈｉ⁃ｐｅｎｇ，ＷＡＮＧＷｅｉ⁃ｙｉｎｇ，ＬＩＵＳｉ⁃ｆａｎ，ＭＡＣｈｅｎｇ⁃ｃｏｎｇ（ＣｏｌｌｅｇｅｏｆＭｅｃｈａｎｉｃａｌａｎｄＥｌｅｃｔｒｉｃａｌＥｎｇｉｎｅｅｒｉｎｇ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＡｅｒｏｎａｕｔｉｃｓａｎｄＡｓｔｒｏｎａｕｔｉｃｓ，Ｎａｎｊｉｎｇ２１００１６，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ａｉｍｉｎｇａｔｔｈｅａｐｐｌｉｃａｔｉｏｎｂａｃｋｇｒｏｕｎｄｆｏｒｃｏｌｌｅｃｔｉｎｇｆｏｒｃｅａｎｄｍｏｍｅｎｔｉｎｆｏｒｍａｔｉｏｎｉｎｍｕｌｔｉｐｌｅｄｉｍｅｎｓｉｏｎｓｏｆｔｈｅｒｏ⁃ｔｏｒｓｙｓｔｅｍｉｎｔｈｅｒｏｔａｔｉｎｇｓｔａｔｅ，ａｓｉｘ⁃ａｘｉｓｆｏｒｃｅｓｅｎｓｏｒｗｉｔｈｗｉｒｅｌｅｓｓｄａｔａｔｒａｎｓｍｉｓｓｉｏｎｆｕｎｃｔｉｏｎｗａｓｄｅｓｉｇｎｅｄ．Ｔｈｅｆｉｎｉｔｅｅｌｅｍｅｎｔａ⁃ｎａｌｙｓｉｓｍｏｄｅｌｏｆｔｈｅｅｌａｓｔｉｃｂｏｄｙｏｆｔｈｅｓｅｎｓｏｒｗａｓｅｓｔａｂｌｉｓｈｅｄ，ａｎｄｔｈｅｓｔｉｃｋｉｎｇｐｏｓｉｔｉｏｎｏｆｔｈｅｓｔｒａｉｎｇａｕｇｅｗａｓｄｅｔｅｒｍｉｎｅｄ．Ｔｈｅｆｏｒｃｅｏｆｓｉｘｄｉｍｅｎｓｉｏｎｓｗａｓｆｅｄｂａｃｋｉｎｔｈｅｆｏｒｍｏｆｖｏｌｔａｇｅｓｉｇｎａｌｔｈｒｏｕｇｈｔｈｅｒｅａｓｏｎａｂｌｅｃｉｒｃｕｉｔｄｅｓｉｇｎｏｆｔｈｅｂｒｉｄｇｅａｓｓｅｍｂｌｙ，ａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｓｉｇｎａｌｐｒｏｃｅｓｓｉｎｇｃｉｒｃｕｉｔｗａｓｄｅｓｉｇｎｅｄｔｏｍｅｅｔｔｈｅｒａｎｇｅｖｏｌｔａｇｅｏｆｔｈｅＡ／Ｄａｃｑｕｉｓｉｔｉｏｎｍｏｄｕｌｅ．Ｆｉｎａｌｌｙ，ｔｈｅｅｎ⁃ｔｉｒｅｈａｒｄｗａｒｅｃｉｒｃｕｉｔｗａｓｐａｃｋａｇｅｄｉｎｓｉｄｅｔｈｅｓｅｎｓｏｒｗｉｔｈａＰＣＢｔｏｍａｋｅａｓｅｎｓｏｒｐｒｏｔｏｔｙｐｅ．Ｋｅｙｗｏｒｄｓ：ｒｏｔｏｒｓｙｓｔｅｍ；ｗｉｒｅｌｅｓｓｄａｔａｔｒａｎｓｍｉｓｓｉｏｎ；ｓｉｘ⁃ａｘｉｓｆｏｒｃｅｓｅｎｓｏｒ；ｆｉｎｉｔｅｅｌｅｍｅｎｔａｎａｌｙｓｉｓ；ｃｉｒｃｕｉｔｄｅｓｉｇｎｏｆｂｒｉｄｇｅａｓｓｅｍｂｌｙ；ｓｅｎｓｏｒｐｒｏｔｏｔｙｐｅ０㊀引言目前大多数的六维力和力矩传感器都是安装在机器人腕部，用来检测机械手抓取工件或者与外部环境接触时所承受的力和方向［１］㊂而用于与直升机旋翼轴相连，检测旋翼系统在旋转状态下作用在旋转轴上的力和力矩分量的多维力传感器并不多见㊂而如果能够得到这些力和力矩的准确信息，对于了解旋翼的动力学性能，对旋转机翼的翼型配置㊁桨叶平面形状和桨尖形状设计将提供重要的数据来源［２］㊂本文设计了一种能够和旋翼主轴共同旋转的小型的六维力传感器原理样机，可以通过法兰与旋翼的主轴相连，并且能够将所测得的六维力和力矩信息实时地以无线的方式发送出去，代替传统利用导电旋转滑环的方式传输数据㊂１㊀传感器总体结构设计本文设计的六维力传感器是基于电阻应变式测量原理，总体结构如图１所示㊂其中，传感器数据采集系统的硬件电路部分被集成在了传感器内部㊂传感器的装配体从上而下分别为顶盘㊁基座㊁弹性体㊁电路板㊁电池和底座㊂顶盘上内圈的４个通孔通过螺栓和螺母与弹性体中心凸台上的４个通孔相连接㊂弹性体轮辐外圈上的８个通孔通过沉头螺丝与基座上的８个螺纹孔相连接㊂电路板最外圈有４个通孔通过六角铜螺栓与底板上相对应的螺纹孔相连接㊂电池通过双面胶粘贴在底板上㊂图１㊀传感器三维模型剖视图㊀㊀㊀㊀㊀第１期吕志鹏等：一种无线式六维力传感器的研制５㊀㊀２㊀弹性体设计及有限元分析２．１㊀弹性体结构设计弹性体作为传感器上粘贴应变片的承力元件，其结构设计的好坏直接决定了传感器的工作性能［３］㊂六维力传感器弹性体由整块圆盘料加工而成，如图２所示㊂图中，Ａ１Ａ２㊁Ｂ１Ｂ２㊁Ｃ１Ｃ２和Ｄ１Ｄ２为弹性梁，Ｅ１Ｅ２㊁Ｆ１Ｆ２㊁Ｇ１Ｇ２和Ｈ１Ｈ２为浮动梁，４支弹性梁通过中心凸台连接，中心凸台的上表面作为弹性体承受外载荷的受力面用来将力和力矩传递给弹性梁㊂４支浮动梁的作用是通过增大弹性体的应变输出来增加传感器的灵敏度㊂弹性体各主要几何尺寸如下：（１）弹性梁：宽４ｍｍ，高６ｍｍ，长２０ｍｍ；（２）浮动梁：宽１ｍｍ，高６ｍｍ，长２４ｍｍ；（３）中心凸台：边长２４ｍｍ，高８ｍｍ；（４）轮缘：外径８０ｍｍ，内径５６ｍｍ，高６ｍｍ㊂图２㊀弹性体结构２．２㊀弹性体有限元分析本文中采用Ａｂａｑｕｓ软件进行弹性体受力变形的有限元分析㊂弹性体的材料选择为７０７５铝合金，其材料参数如表１所示［４］㊂表１㊀弹性体材料参数材料弹性模量Ｅ／ＭＰａ泊松比μ屈服极限σｓ／ＭＰａＡＬ７０７５７２００００．３５０５㊀㊀弹性体是通过轮缘上的８个定位孔固定在基座上的，因此将８个定位孔的所有方向上的自由度全部设置为０㊂施加载荷前，在弹性体中心处设置一参考点并且与凸台的中心孔内壁表面建立耦合关系［５］㊂此外，因为弹性体结构关于坐标轴严格对称，所以只对ｘ和ｚ轴方向的力和力矩进行分析㊂其中ｘ和ｚ轴方向的作用力以集中力的方式作用在耦合参考点上；ｘ和ｚ轴方向的力矩以力偶的形式作用在耦合参考点上㊂通过Ａｂａｑｕｓ的分析和后处理技术［５］，增大变形放大系数，弹性体分别受到满量程的单维力Ｆｘ＝３００Ｎ㊁Ｆｚ＝９００Ｎ㊁Ｍｘ＝２０Ｎｍ与Ｍｚ＝２０Ｎｍ时的应变分布云图如图３所示㊂从图中可以看出，弹性体在各维度满量程的载荷下的最大米塞斯应力都没有超过材料的屈服应力，所以弹性体结构在强度方面达到了要求㊂（ａ）Ｆｘ＝３００Ｎ㊀（ｂ）Ｆｚ＝９００Ｎ（ｃ）Ｍｘ＝２０Ｎｍ㊀（ｄ）Ｍｚ＝２０Ｎｍ图３㊀弹性体受力应变分布云图为了更清楚的了解弹性梁表面节点在各单维载荷作用下的应变大小，同时也是为了给应变片的贴片位置选择提供参考［６］，运用Ａｂａｑｕｓ的路径映射技术，输出弹性梁在各单维额定载荷下的节点应变路径曲线㊂以弹性梁与中心凸台的交界处作为顶端，与浮动梁交界处作为末端，根据前面的应力㊁应变分布云图，在弹性梁发生主要变形的表面定义一条用于应变映射的节点路径，从而输出这一条路径上各节点应变的确切数值，如图４所示㊂从图中可以看出，弹性梁的应变与距离呈现递减趋势，在弹性梁与中心凸台和浮动梁的交界处由于应力集中的关系，应变路径曲线出现较大幅度的弯折㊂这部分应力集中可以通过在交界处增加圆角的方式予以减轻［７］㊂３㊀应变片布置及组桥设计传感器的弹性体上共粘贴有２４个应变片，其中每４个应变片组成一个全桥电路，共组成６个全桥电路来测量作用在传感器上的六维力和力矩㊂参考图４的应变路径曲线图和应变片自身的尺寸大小，将用来测量Ｆｘ㊁Ｆｙ和Ｆｚ的应变片贴片位置定于弹性梁表面距中心凸台边界的５ｍｍ处，用来测量Ｍｘ㊁Ｍｙ和Ｍｚ的应变片贴片位置定于弹性梁表面距中心凸台边界１２ｍｍ处㊂粘贴应变片的弹性体和应变片编号示意如图５所示㊂㊀㊀㊀㊀㊀６㊀ＩｎｓｔｒｕｍｅｎｔＴｅｃｈｎｉｑｕｅａｎｄＳｅｎｓｏｒＪａｎ．２０２１㊀（ａ）Ｆｘ＝３００Ｎ作用下沿路径各节点的应变分布图（ｂ）Ｆｚ＝９００Ｎ作用下沿路径各节点的应变分布图（ｃ）Ｍｘ＝２０Ｎｍ作用下沿路径各节点的应变分布图（ｄ）Ｍｚ＝２０Ｎｍ作用下沿路径各节点的应变分布图图４㊀节点应变沿路径分布图图５㊀应变片布置示意图其中应变片１㊁２㊁３㊁４组成一个全桥电路用来测量切向力Ｆｘ所引起的应变㊂应变片５㊁６㊁７㊁８组成一个全桥电路用来测量切向力Ｆｙ所引起的应变㊂应变片９㊁１０㊁１１㊁１２组成一个全桥电路用来测量轴向力Ｆｚ所引起的应变㊂应变片１３㊁１４㊁１５㊁１６组成一个全桥电路用来测量弯矩Ｍｙ所引起的应变㊂应变片１７㊁１８㊁１９㊁２０组成一个全桥电路用来测量弯矩Ｍｚ所引起的应变㊂应变片２１㊁２２㊁２３㊁２４组成一个全桥电路用来测量扭矩Ｍｚ所引起的应变㊂４㊀硬件电路及ＰＣＢ设计４．１㊀硬件电路总体结构设计传感器硬件系统能够实现六维力和力矩的信号采集以及通过无线模块实现测量数据的无线传输，图６是传感器硬件电路系统框图，具体可以划分为以下模块：（１）信号调理模块：将电桥输出的电压信号经由仪表放大器ＡＤ６２３电路进行放大，再将放大后的信号经过双通道通用运算放大器ＬＭ３５８电路进行电压抬升与滤波处理，处理后输入到ＳＴＭ３２微控制器的Ａ／Ｄ口进行数模转换；（２）ＳＴＭ３２微控制器模块：用来接收处理传感器采集的数据信息，包括实时的力和力矩信号数据㊁温度信号数据，并将采集的数据信息发送到无线端口；（３）无线通讯模块：将所有采集的数据信息通过ＮＲＦ２４Ｌ０１无线模块电路发送到另一块载有ＮＲＦ无线模块的ＳＴＭ开发板，并由它将接收到的数据通过串口通信方式发送到ＰＣ端进行实时的处理和显示㊂图６㊀传感器硬件电路系统框图４．２㊀信号调理模块电路设计信号调理模块电路由前置放大电路和后置电压抬升与滤波电路两部分构成，如图７所示㊂在设计放大电路时，首先对放大倍数进行估计㊂对于每一维度的应变电桥来说㊂由有限元分析结果，可以大概估计出贴片位置在满量程情况下的最大应变ε，根据全桥电路原理［８］，估算出每一维度的电桥在满载情况下的㊀㊀㊀㊀㊀第１期吕志鹏等：一种无线式六维力传感器的研制７㊀㊀输出电压㊂为了获得较好的模拟电压输出信号，将经过放大后的输出电压范围控制在－１．６５ ＋１，６５Ｖ之间，由此计算出所需的放大倍数并将其列于表２㊂（ａ）前置放大电路（ｂ）后置电压抬升与滤波电路图７㊀信号调理模块电路表２㊀放大倍数估算表力和力矩满载时电桥输出应变ε／１０－６满载时电桥输出电压／ｍＶ放大倍数Ｆｘ＝３００Ｎ１１５１．６１１．５１４３Ｆｚ＝９００Ｎ１９２６．７１９．２８６Ｍｘ＝２０Ｎｍ１３８７．７１３．８１２０Ｍｚ＝２０Ｎｍ１０５４．５１０．５１５７㊀㊀由表２可知，电压信号的放大倍数不是很大，这里直接选用仪表放大器ＡＤ６２３对电压信号进行放大㊂ＡＤ６２３是一款易于使用，可提供满摆幅输出，高性能的芯片㊂它具有低成本㊁低功耗的特点㊂此外，ＡＤ６２３的外围电路非常简单，只需外接一只反馈电阻ＲＧ就可以精确控制放大电路的增益［９］㊂此外，本设计使用的Ａ／Ｄ采集模块是微控制ＳＴＭ３２自带的，它只能够转换范围０ ＋３．３Ｖ的电压信号，所以经由放大后的电压信号，必须再进行相应的电压抬升才能满足要求㊂这里选用双通道通用运放ＬＭ３５８来搭建后置的电压抬升与滤波电路，其中，ＬＭ３５８的１通道连接外围电路用来作为反相加法器将电桥经由放大后的－１．６５ ＋１．６５Ｖ的范围电压信号反相抬升至－３．３ ０Ｖ，２通道用来作为一阶的有源滤波滤除了１００Ｈｚ以上的高频噪声并进行了反相的等比例放大，最终将电压信号调理成０ ＋３．３Ｖ的可被Ａ／Ｄ采集的范围电压㊂４．３㊀无线通信模块电路设计采用ＳＴＭ３２微控制器连接外部无线模块ＮＲＦ２４Ｌ０１实现六维力传感器实测数据的无线发送㊂ＮＲＦ２４Ｌ０１模块接口和微控制器的连接电路如图８所示㊂ＳＴＭ３２微控制器使用的是ＳＰＩ２口与ＮＲＦ２４Ｌ０１模块接口相连，ＳＴＭ３２的４个引脚ＰＧ１０㊁ＰＢ１３㊁ＰＢ１４和ＰＢ１５分别与ＮＲＦ２４Ｌ０１模块的片选线ＮＲＦ＿ＣＳ㊁时钟线ＳＰＩ＿ＳＣＫ㊁主设备数据输入线ＳＰＩ＿ＭＩＳＯ和主设备数据输出线ＳＰＩ＿ＭＯＳＩ相连㊂ＰＩ１１㊁ＰＧ１２引脚分别与无线模块的中断引脚ＮＲＦ＿ＩＲＱ㊁芯片使能引脚ＮＲＦ＿ＣＥ相连㊂图８㊀ＮＲＦ２４Ｌ０１模块接口与微控制器连接电路４．４㊀ＰＣＢ设计根据传感器信号采集的硬件连接原理图设计相应的集成电路板㊂电路板采用双层敷铜板作为印制板，双面铜皮与地线网络相连接㊂电路板形状为圆形，直径９６ｍｍ，在顶层走信号线，底层走电源线，信号线宽度为０．２５４ｍｍ，电源线与地线宽度都为０．５０８ｍｍ，通过过孔将顶层与底层的印制线相连接㊂焊有电子元器件的ＰＣＢ如图９所示㊂图９㊀含有电子元器件的电路板整个硬件电路的ＰＣＢ板制作完成后，将顶盘基座㊁弹性体㊁电路板与电池按照图１所示的三维剖视图进行装配，装配完成的实物如图１０所示㊂５㊀结束语本文设计了一种带无线数据发送功能的能够与旋翼模型共同旋转的小型六维力传感器原理样机，通过对弹性体的有限元分析，确定应变片适合的粘贴位置㊂共２４片应变片组成６路全桥电路测量六个维度的力和力矩信息，并对６路电压信号进行了相应的处㊀㊀㊀㊀㊀８㊀ＩｎｓｔｒｕｍｅｎｔＴｅｃｈｎｉｑｕｅａｎｄＳｅｎｓｏｒＪａｎ．２０２１㊀理㊂最后制成六维力传感器样机㊂（ａ）粘贴完应变片的弹性体㊀（ｂ）传感器内部（ｃ）传感器实物外观图１０　六维力传感器样机参考文献：［１］㊀郑朝阳．一种机器人腕力传感器弹性体结构设计与力学性能分析［Ｊ］．仪表技术与传感器，２０１７（１１）：１４－１６．［２］㊀陈维芹．用于直升机旋翼试验的多功能测试系统及应用［Ｊ］．测试技术学报，２００３（１）：２９－３２．［３］㊀ＭＡＪＱ，ＳＯＮＧＡＧ．Ｆａｓｔｅｓｔｉｍａｔｉｏｎｏｆｓｔｒａｉｎｓｆｏｒｃｒｏｓｓ⁃ｂｅａｍｓｓｉｘ⁃ａｘｉｓｆｏｒｃｅ／ｔｏｒｑｕｅｓｅｎｓｏｒｓｂｙｍｅｃｈａｎｉｃａｌｍｏｄｅｌｉｎｇ．［Ｊ］．Ｓｅｎｓｏｒｓ（Ｂａｓｅｌ，Ｓｗｉｔｚｅｒｌａｎｄ），２０１３，１３（５）：６６６９－６６８６．［４］㊀周建方．材料力学［Ｍ］．北京：机械工业出版社，２００２．［５］㊀孙永军．空间机械臂六维力／力矩传感器及其在线标定研究［Ｄ］．哈尔滨：哈尔滨工业大学，２０１６．［６］㊀茅晨，宋爱国，马俊青．新型六维腕力传感器［Ｊ］．南京信息工程大学学报（自然科学版），２０１１，３（５）：４０２－４０７．［７］㊀何小辉，蔡萍．一种小量程六维力／力矩传感器的设计与分析［Ｊ］．传感器与微系统，２０１２，３１（１）：２０－２２．［８］㊀周杏鹏，孙永荣，仇国富．传感器与检测技术［Ｍ］．北京：清华大学出版社，２０１０．［９］㊀余秋军，李丹，杜娟，等．基于ＡＤ６２信号处理的压力变送器设计［Ｊ］．仪表技术与传感器，２０１８（４）：２４－２７．作者简介：吕志鹏（１９９５ ），硕士研究生，主要研究方向为力传感器㊂Ｅ⁃ｍａｉｌ：８３８６３５８９５＠ｑｑ．ｃｏｍ王卫英（１９６５ ），副教授，主要研究方向为计算机辅助工程㊁仿生机械㊁柔性生产系统㊂Ｅ⁃ｍａｉｌ：ｍｅｅｗｙｗａｎｇ＠ｎｕａａ．ｅｄｕ．ｃｎ（上接第３页）［６］㊀ＫＵＲＯＳＡＷＡＫ，ＳＨＩＲＡＫＡＷＡＫ，ＫＩＫＵＣＨＩＴ．Ｄｅｖｅｌｏｐｍｅｎｔｏｆｏｐｔｉｃａｌｆｉｂｅｒｃｕｒｒｅｎｔｓｅｎｓｏｒｓａｎｄｔｈｅｉｒａｐｐｌｉｃａｔｉｏｎｓ［Ｃ］／／ＴｒａｎｓｍｉｓｓｉｏｎａｎｄＤｉｓｔｒｉｂｕｔｉｏｎＣｏｎｆｅｒｅｎｃｅａｎｄＥｘｈｉｂｉｔｉｏｎ：ＡｓｉａａｎｄＰａｃｉｆｉｃ，２００５ＩＥＥＥ／ＰＥＳ．ＩＥＥＥ，２００５：１－６．［７］㊀ＳＴＡＮＣＩＵＭ，ＧＨＩＴＡＯ，ＶＩＮＴＥＡＡ，ｅｔａｌ．Ｄｅｓｉｇｎｏｆａｃｕｒｒｅｎｔｓｅｎｓｏｒｂａｓｅｄｏｎｏｐｔｉｃａｌｆｉｂｅｒｓ［Ｃ］／／ＩｎｔｅｒｎａｔｉｏｎａｌＳｙｍｐｏｓｉｕｍｏｎＡｄｖａｎｃｅｄＴｏｐｉｃｓｉｎＥｌｅｃｔｒｉｃａｌＥｎｇｉｎｅｅｒｉｎｇ．ＩＥＥＥ，２０１５：９６１－９６４．［８］㊀张斌．小型化铯光泵原子磁力仪研究［Ｄ］．杭州：浙江大学，２０１５．［９］㊀张豪敏．铷原子激光光泵磁力仪的研究［Ｄ］．杭州：浙江大学，２０１６．［１０］㊀耿毅．激光光泵原子磁力仪的研究［Ｄ］．杭州：浙江大学，２０１４．［１１］㊀王永超．光泵磁力仪的频率采集系统的设计与实现［Ｄ］．武汉：武汉理工大学，２０１２．［１２］㊀孙伟民，刘双强，赵文辉，等．光学原子磁力仪［Ｍ］．哈尔滨：哈尔滨工程大学出版社，２０１５．［１３］㊀ＫｅｙｓｉｇｈｔＴｅｃｈｎｏｌｏｇｉｅｓ，ＫｅｙｓｉｇｈｔＢ２９６２ＡＤａｔａＳｈｅｅｔ［Ｚ］，２０１９．［１４］㊀王虹，马俊兴．实验曲线的线性度研究［Ｊ］．河南科学，２００５，２３（１）：２６－２８．作者简介：王维东（１９６７ ），博士，副教授，主要研究方向为原子磁力仪系统㊁ＡＩ嵌入式系统设计及图像视频处理等㊂Ｅ⁃ｍａｉｌ：ｗｄｗａｎｇ＠ｚｊｕ．ｅｄｕ．ｃｎ。

海口2024年11版小学6年级英语第三单元期末试卷[含答案]考试时间：100分钟（总分:120）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、填空题：The first man to swim the English Channel was _______. (马修·韦本)2、听力题：The sun is _____ (shining/raining).3、What is the largest mammal in the world?A. ElephantB. Blue WhaleC. GiraffeD. Hippo4、What is the term for the gravitational attraction that keeps planets in orbit around the sun?A. GravityB. MagnetismC. ElectromagnetismD. Nuclear Force5、填空题：The lemur has big _______ (眼睛).6、听力题：A scientific law is a statement based on repeated ______ (experiments).7、听力题：The flowers are ________ in the vase.8、听力题：The book is ___. (interesting)9、What is the capital of Egypt?A. CairoB. AlexandriaC. LuxorD. Giza答案:A10、What do we call a young female pig?A. CalfB. KidC. PigletD. Sow答案:C11、填空题：My uncle loves to __________ (探险) in nature.12、What is the name of the famous river in Egypt?A. AmazonB. NileC. MississippiD. Yangtze答案:B. Nile13、What is the name of the famous ancient city in Iran?A. PersepolisB. IsfahanC. TehranD. Shiraz答案:A. Persepolis14、Which day comes after Friday?A. SaturdayB. SundayC. MondayD. Thursday15、填空题：The dog barks ________ (大声).16、填空题：A hamster is a popular ______ (宠物).17、What do we use to read?A. BookB. SpoonC. PlateD. Cup答案:A18、听力题：Atoms are made up of protons, neutrons, and ________.19、听力题：My brother plays the ____ (keyboard) in a band.20、选择题：What do we call a person who catches fish?A. FishermanB. HunterC. FarmerD. Forager21、What is the opposite of 'happy'?A. SadB. AngryC. ExcitedD. Joyful答案:A22、What is the process of taking in oxygen and releasing carbon dioxide?A. RespirationB. PhotosynthesisC. DigestionD. Metabolism23、What is the name of the bird that cannot fly and is native to New Zealand?A. OstrichB. KiwiC. EmuD. Cassowary答案：B24、听力题：The Pacific Ring of Fire is known for its high number of ______ and earthquakes.25、听力题：The ____ makes a soft sound and is often seen in the garden.26、填空题：The __________ (历史的教育贡献) shape future leaders.27、听力题：My ______ is very outgoing and friendly.28、What do we call the science of studying space?A. BiologyB. ChemistryC. AstronomyD. Geology29、听力题：A chemical reaction that produces light and heat is called a _____ reaction.30、听力题：The Earth's surface is shaped by both ______ and erosion.31、填空题：The hamster runs on its _________. (跑轮)32、Where do fish live?A. TreesB. AirC. WaterD. Land33、填空题：I want to _______ (了解)更多关于科学。

Lesson 1Compression MembersNew Words1. achieve achievement2. eccentricity center, 中心; ec centric 偏心的；ec centricity 偏心,偏心距3. inevitable evitable 可避免的avoidable; in evitable 不可避免的unavoidable4. truss 桁架triangular truss, roof truss, truss bridge5. bracing brace 支柱,支撑；bracing, 支撑,撑杆6. slender 细长,苗条；stout; slenderness7. buckle 压曲,屈曲；buckling load8. stocky stout9. convincingly convince, convincing, convincingly10. stub 树桩, 短而粗的东西；stub column 短柱11. curvature 曲率；curve, curvature12. detractor detract draw or take away; divert; belittle, 贬低,诽谤；13. convince14. argument dispute, debate, quarrel, reason, 论据理由15. crookedness crook 钩状物,v弯曲,crooked 弯曲的16. provision 规定,条款Phrases and Expressions1. compression member2. bending moment shear force, axial force3. call upon on 要求,请求,需要4. critical buckling load 临界屈曲荷载critical 关键的,临界的5. cross-sectional area6. radius of gyration 回转半径gyration7. slenderness ratio 长细比8. tangent modulus 切线模量9. stub column 短柱10. trial-and-error approach 试算法11. empirical formula 经验公式empirical 经验的12. residual stress 残余应力residual13. hot-rolled shape 热轧型钢hot-rolled bar14. lower bound 下限upper bound 上限16. effective length 计算长度Definition 定义Compression members are those structural elements that are subjected only to axial compressive forces: that is, the loads are applied along a longitudinal axis through the centroid of the member cross section, andthe stress can be taken as f a =P/A, where f a is considered to be uniform over the entire cross section. 受压构件是仅受轴向压力作用的构件,即：荷载是沿纵轴加在其截面形心上的,其应力可表示为…,式中,假定f a 在整个截面上均匀分布; This ideal state is never achieved in reality, however, and some eccentricity of the load is inevitable. 然而,现实中从来都不可能达到这种理想状态,因为荷载的一些偏心是不可避免的;This will result in bending, but it can usually be regarded as secondary and can be neglected if the theoretical loading condition is closely approximated. 这将导致弯曲,但通常认为它是次要的,如果理论工况是足够近似的,就可将其忽略;This cannot always be done if there is a computed bending moment, and situation of this type will be considered in Beam-Columns. 但这并非总是可行的,如有计算出的弯矩存在时,这种情形将在梁柱理论中加以考虑;The most common type of compression member occurring in buildings and bridges is the column , a vertical member whose primary function is to support vertical loads. 在建筑物和桥梁中最常见的受压构件就是柱,其主要功能就是支承竖向荷载;In many instances these members are also called upon to resist bending, and in these cases the member is a beam-column . Compression members can also be found in trusses and as components of bracing systems. 在许多情况下,它们也需要抵抗弯曲,在此情况下,将它们称为梁柱;受压构件也存在于桁架和支撑系统中;Column Theory 柱理论assume the shape indicated by the dashed line. 如果慢慢增加轴向荷载P,它最终将达到一个足够大的值使该柱变得不稳定失稳,如图中虚线所示; The member is said to have buckled, and the corresponding load is called th e critical buckling load . 这时认为构件已经屈曲,相应的荷载称为临界屈曲荷载;If the member is more stocky members and for more slender columns before they buckle, the compressive stress P/A is uniform over the cross section at any point along the length. 对这些短柱以及更细长的柱,在其屈曲前,在其长度方向上任意点处横截面上的压应力P/A 都是均匀的;As we shall see, the load at which buckling occurs is a function of slenderness , and for very slender members this load could be quite small. 我们将会看到,屈曲发生时的荷载是长细程度的函数,非常细长的构件的屈曲荷载将会很低;If the member is so slender a precise definition of slenderness will be given shortly that the stress just before buckling is below the proportional limit —that is, the member is still elastic —the critical buckling load is given by 如果构件如此细长随后将会给出细长程度的精确定义以致即将屈曲时的应力低于比例极限—即,构件仍是弹性的,临界屈曲荷载如下式给出：22L EIP cr π=where E is the modulus of elasticity of the material, I is the moment of inertia of the cross-sectional area with respect to the minor principal axis, and L is the length of the member between points of support. 式中E 为材料弹性模量,I 为关于截面副主轴的惯性矩,L 为支座间的距离;For to be valid, the member must be elastic, and its ends must be free to rotate but not translate laterally. This end condition is satisfied by hinges or pins. 要使方程成立,构件必须是弹性的,且其两端必须能自由转动,但不能侧向移动;This remarkable relationship was first formulated by Swiss mathematician Leonhard Euler and published in 1975. 此着名公式是瑞士数学家欧拉于1975年提出的;The critical load is sometimes referred to as the Euler load or the Euler buckling load. The validity of has been demonstrated convincingly by numerous tests. 因此有时将临界荷载称为欧拉荷载或欧拉临界荷载;欧拉公式的有效性正确性已由许多试验充分证实;It will be convenient to rewrite as follows: 方程可方便地写为2222222)/(r L EA L EAr L EIP cr πππ===where A is the cross-sectional area and r is the radius of gyration with respect to the axis of buckling. The ratio L/r is the slenderness ratio and is the measure of a compression member ’s slenderness, with large values corresponding to slender members. 式中A 为截面面积,r 为关于屈曲轴的回转半径,L/r 为长细比,它是对受压构件细长程度的一种度量,该值越大,构件越细长;If the critical load is divided by the cross-sectional area, the critical buckling stress is obtained: 如果将屈曲荷载除以截面面积,便可得到以下屈曲应力： 22)/(r L E A P F cr cr π==This is the compressive stress at which buckling occur about the axis corresponding to r. 这便是绕相应于r 的轴发生屈曲时的压应力;Since buckling will take place as soon as the load reaches the value by the column will become unstable about the principle axis corresponding to the largest slenderness ratio. This usually means the axis with the smaller moment of inertia. 由于一旦荷载达到式之值,柱将在与最大长细比对应的主轴方向变得不稳定失稳,通常该轴是惯性矩较小的轴;Thus, the minimum moment of inertia and radius of gyration of the cross section should be used in and . 因此,应在方程和中采用截面的最小惯性矩和最小回转半径;Early researchers soon found that Euler ’s equation did not give reliable results for stocky, or less slender, compression members. 早期的研究者很快发现对短柱或不太细长的受压构件,欧拉公式并不能给出可靠的结果,This is because of the small slendernessthe stress at which buckling occurs is greater than the proportional limit of the material, the relation between stress and strain is not linear, and the modulus of elasticity E can no longer be used. 如果屈曲发生时的应力大于材料的比例极限,应力应变关系就不再是线性的,也不能再用弹性模量E;This difficulty was initially resolved by Friedrich Engesser, who proposed in 1889 the use of a variable tangent modulus E tpl . The tangent modulus E t is defined as the slope of the tangent to the stress-strain curve for values of f between F pl and F y . 对于如图所示的应力应变曲线的材料,当应力超过比例极限时,E 并非常数,当应力处于F pl 和F y 之间时,将切线模量定义为应力应变曲线的切线的斜率,If the compressive stress at buckling, P cr /A, is in this region, it can be shown that 如果屈曲时的压应力在此范围时,可以证明22L IE P t cr π=This is identical to the Euler equation, except that E t is substituted for E. 除公式中将E 代之以E t 外,上式与欧拉公式完全相同;Effective Length 计算长度Both the Euler and tangent modulus equations are based on the following assumptions: 欧拉和切线模量方程都是基于如下假定：1. The column is perfectly straight, with no initial crooked ness. 柱完全竖直,无初始弯曲;2. The load is axial, with no eccentricity. 荷载是轴向加载,无偏心;3. The column is pinned at both ends. 柱在两端铰结;The first two conditions mean that there is no bending moment in the member before buckling. 前两假定条件意味着在屈曲前无弯矩存在;As mentioned previously, some accidental moment will be present, but in most cases it can be neglected. 如前所述,可能偶然会存在一些弯矩,但在大多数情况下都可被忽略;The requirement for pinned ends, however, is a serious limitation, and provisions must be made for other support conditions. 然而,铰结要求是一个严重的局限,必须对其它支撑条件作出规定;The pinned-end condition is one that requires that the member be restrained from lateral translation, but not rotation, at the ends. 铰结条件要求约束构件两端不发生侧移,但并不约束转动;Since it is virtually impossible to construct a frictionless pin connection, even this support condition can only be closely approximated at best. 由于实际上不可能构造无摩擦铰连接,即使这种支撑条件最多也只能是非常近似;Obviously, all columns must be free to deform axially. 显然,所有柱必须在轴向自由变形; In order to account for other end conditions, the equations for critical buckling load will be written as 为了考虑其它边界条件,将临界荷载写为如下形式22)/(r KL EAP cr π= or 22)/(r KL AE P t cr π=where KL is the effective length, and K is called the effective length factor. Values of K for different cases can be determined with the aid of the Commentary to the AISC Specification. 式中KL 为计算长度,K 称为计算长度系数,各种情况下的K 值可借助于AISC 美国钢结构学会American Institute of Steel Construction 规范的条文说明加以确定;Lesson 2Introduction to structural designNew words1. framework frame+work=frame 构架,框架; frame structure, 框架结构2. constraint vt. constrain 约束,强迫；n. constraint 约束3. collaborate vt. 合作,通敌；collaboration, collaborative4. evaluation vt. evaluate, value; assess, assessment5. fixture vt. fix, fixture 固定设备,固定物,夹具6. partition vt. n 分割,划分, make apart; partition wall7. overlook8. crane n. 超重机,鹤9. fatigue 疲劳fatigue strength, fatigue failure10. drift 漂流,漂移,雪堆11. enumerate v. list 列举12. plumbing n. 卫生,自来水管道,plumber 管道工13. ventilation n. 通风, ventilate, ventilate a room, a well-ventilated room, vent 通风口14. accessibility n. 可达性, access, n. vt. 通道,接近；accessible 易接近的,可达到的15. code n. vt 代码,编码,规范16. administer v. 管理,执行；administrate, 管理17. metropolitan a. 大城市,of metropolis18. consolidate v. 巩固,strengthen,reinforce; consolidation19. prescription n. 规定,命令,药方；prescribe20. municipality n. 市政当局,直辖市, municipal government21. specification n. 详述,规格, 规范；specify22. mandate n. 书面命令,委托,Phrases and expressions1. functional design 功能设计2. bending moment 弯矩3. dead load4. live load5. nonstructural components 非结构构件6. force due to gravity7. gravity load8. building code9. design specifications 设计规程10. nonprofit organization 非赢利组织,弄non-government organization11. the National Building Code12. the Uniform Building Code13. the Standard Building Code14. Building Officials and Code Administrators International BOCA 国际建筑公务员与法规管理人员联合会15. AISC 美国钢结构学会American Institute of Steel Construction16. AASHTO 美国公路和运输工作者协会American Association of State Highway and Transportation Officials17. AREA 美国铁道工程协会the American Railway Engineering Association18. AISI 美国钢铁学会American Iron and Steel InstituteIntroduction to Structural DesignStructural designThe structural design of building, whether of structural steel or reinforced concrete, requires the determination of the overall proportions and dimensions of the supporting framework and the selection of the cross sections of individual members. 建筑结构设计,不论是钢结构还是钢筋混凝土结构,都需要确定其支承结构的整体比例和尺寸以及各构件的截面尺寸;In most cases the functional design, including the establishment of the number of stories and the floor plan, will have been done by an architect, and the structural engineer must work within the constraints imposed by this design. 在大多数情况下,功能设计,包括楼层层数和楼层平面的确定,将要由建筑师来完成,因而结构工程师必须在此约束条件下工作;Ideally, the engineer and architect will collaborate throughout the design process so that the project is completed in an efficient manner. 在理想状态下,工程师和建筑师将在整个设计过程中协同工作从而高效地完成设计工作;In effect, however, the design can be summed up as follows: 然而,事实上,设计过程可概括如下：The architect decides how the building should look; the engineer must make sure that it doesn’t fall down. 建筑师确定建筑物的外观,工程师必须确保其不会倒塌;Although this is an oversimplification, it affirms the first priority of the structural engineer: safety. Other important considerations include serviceability how well the structure performs in terms of appearance and deflection and economy. 尽管这样说过分简单,但它明确了工程师的第一个主要任务,即,确保安全;其它要考虑的因素包括适用性就外观和挠曲而言其工作性能如何;An economical structure requires an efficient use of materials and construction labor. Although this can usually be accomplished by a design that requires a minimum amount of material, savings can often be realized by using slightly more material if it results in a simpler, more easily constructed projects. 经济的结构要求对材料和人工的有效使用,尽管这通常都能通过要求最少材料来取得,但通过采用稍多的材料,但能使建筑物更简单和更容易建造常常会实现节约的目的;LoadsThe forces the act on a structure are called loads. They belong to one of two broad categories, dead load and live load. 作用在结构物上的各种力称为荷载,它们属于一两种广义类型,恒载和活载;Dead loads are those that are permanent, including the weight of the structure itself, which is sometimes called the self-weight. 恒载是那些永久荷载,包括结构自身的重量,有时也称为自重;Other dead loads in a buildinginclude the weight of nonstructural components such as floor coverings, suspended ceilings with light fixtures, and partitions. 其它建筑物恒载包括非结构构件的重量,如楼面面层、带有灯具的吊顶以及隔墙;All of the loads mentioned thus far are forces due to gravity and are referred to as gravity loads. 至此所提的各种荷载都是由重力所引起,因而称为重力荷载;Live loads, which can also be gravity loads, are those that are not as permanent as dead loads. 活载也可以是重力荷载,它们是那些不如恒载那样永久的荷载;This type may or may not be acting on the structure as any given time, and the location may not be fixed. 这类荷载可能也可能不总是作用在结构物上,且作用位置也可能不是固定的;Examples of live load include furniture, equipment, and occupants of buildings. 活荷载包括家具、设置和建筑物的居住者;In general, the magnitude of a live load is not as well defined as that of a dead load, and it usually must be estimated. In many cases, a given structural member must be investigated for various positions of the live load so that a potential failure situation is not overlooked. 通常,活荷载的大小不如恒载那样确定,常常必须估计;在许多情况下,必须研究活荷载作用在一给定的结构构件的各个位置以便不会漏掉每个可能的破坏情形;Building codesBuilding must be designed and constructed according to the provisions of a building codes, which is a legal document containing requirements related to such things as structural safety, fire safety, plumbing, ventilation, and accessibility to the physically disabled. 建筑物必须根据各种建筑规范的条款设计和建造,规范是一种法律文件,包含各种要求,如建筑安全、防火安全、上下水、通风和体残人的可达性等;A building code has the force of law and is administered by a governmental entity such as a city, a county, or, for some large metropolitan areas, a consolidated government. 建筑规范具有法律效力,由政府部位发布,如城市、县、对于大的城区,如联合政府;Building codes do not give design provisions, but they do specify the design requirements and constraints that must be satisfied. 建筑规范并不给出设计规定,但却规定设计必须满足的各种要求和约束条款;Of particular importance to the structural engineer is the prescription of minimum live loads for buildings. 对结构工程师特别重要的是建筑物的最小活荷载规定;Although the engineer is encouraged to investigate the actual loading conditions and attempt to determine realistic values, the structure must be able to support these specified minimum loads. 尽管鼓励工程师研究实际荷载工况以确定真实的荷载值,结构必须能支承这些规定的最小荷载;Design specificationsIn contrast to building codes, design specifications give more specific guidance for the design of structural members and their connections. 与建筑规范不同,设计规程给出结构构件及其连接的更具体的指南;They present the guidelines and criteria that enable a structural engineer to achieve the objectives mandated by a building code. 它们给出各种方针和标准,使结构工程师能建筑规范所规定的目标;Design specifications represent what is considered to be good engineering practice based on their latest research. 根据其最新研究,设计规程结出认为是好的工程作法;They are periodically revised and updated by supplements or by completely new editions. 它们通过补充或通过发布新版本得到定期修订和更新;As with model building codes, design specifications are written in a legal format by nonprofit organizations. 如同一般建筑规范,设计规程由非赢利组织编写;They have no legal standing on their own, but by presenting design criteria and limits in the form of legal mandates and prohibitions, they can easily be adopted, by reference, as part of a building code. 尽管它们本身并无法律地位,但却以法令和禁令的形式给出设计准则和限制,以参考文献的形式,它们可容易地被录入,并作为建筑规范的一部分;Lesson 3New words1. col`loidal 胶状的,胶体的,`colloid 胶体2. sieve n,v. 筛,过筛,过滤3. sample . 样品,取样specimen4. mesh 网孔,网格,分网格5. `cumulative a. 积累的；cumulate, cumulation6. grading n. 级配,等级；grade7. sedimentation n. 沉淀; sediment8. suspension n. 悬浮；suspend ~bridge cable-stayed bridge9. agitate v. 搅动,混合；disturb10. hydro meter n. 液体比重计11. viscosity n. 黏性；viscoidal12. flaky n. 薄片状的,of flake13. pipette n. 吸液管14. ir recoverable a.不可恢复的ir retrievable15. con cave a. 凹的；con vex凸的16. permeability n. 渗透性; permeate, permeable seep seepagePhrases and expressions1. frost susceptibility 霜冻敏感性2. sieving method 筛分法3. semi-logarithmic curve 半对数曲线4. grading curve 级配曲线5. wet sieving 湿法筛分6. dispersing agent 分散剂7. Stoke’s law 斯托克定律8. unit weight 重度9. coefficient of grading 级配系数10. sedimentation method 沉降法11. particle-size distribution 粒径分布Text Particle Size Analysis 粒径分析The range of particle sizes encountered in soils is very wide: from around 200mm down to the colloidal size of some clays of less than . 在各种土中所遇到的粒径范围很大,大到200mm小到小于的一些粘土胶粒;Although natural soils are mixtures of various-sized particles, it is common tofind a predominance occurring within a relatively narrow band of sizes. 尽管天然土都是由各种粒径的颗粒组成,但通常可发现其主要组成颗粒出现在一个比较小的粒径范围内;When the width of this size band is very narrow the soil will be termed poorly-graded, if it is wide the soil is said to be well-graded. 当这一粒径范围非常小时,称这种土级配较差,而当其较大时,称这种土级配良好;A number of engineering properties, . permeability, frost susceptibility, compressibility, are related directly or indirectly to particle-size characteristics. 土的许多工程特性,如渗透性、霜冻敏感性、可压缩性等都直接或间接的与土的级配特性有关;shows the British Standard range of percentage of particle sizes. 图为粒径百分数的英国标准范围;The particle-size analysis of a soil is carried out by determining the weight percentage falling within bands of size represented by these divisions and sub-divisions. 通过确定落入由这些粒径分组和子组所代表的粒径范围的重量百分比,对土进行粒径分析;In the case of a coarse soil, from which fine-grained particles have been removed or wereabsent, the usual process is a sieve analysis. 对于粗粒土,它里面的细粒土被除去或本身就无细颗粒,常用的方法就是筛分法;A representative sample of the soil is split systematically down to a convenient sub-sample size and then oven-dried. 此法是将要分析土的一代表样本系统地分为方便的子样本,然后烘干;This sample is then passed through a nest of standard test sieves arranged in descending order of mesh size. 再使烘干的土样通过一组筛孔尺寸由大至小放置的标准试验筛;Where the soil sample contains fine-grained particles, a wet sieving procedure is first carried out to remove these and to determine the combined clay/silt fraction percentage. 在土样中含有细土粒的场合,首先用湿筛分法将其除去,并确定粘粒/粉粒总共所占的分数;A suitable-sized sub-sample is first oven-dried and then sieved to separate the coarsestparticles >20mm. 将一适量的分土样烘干,并过筛分开最粗的颗粒>20mm的颗粒The sub-sample is then immersed in water containing a dispersing agent and allowed to stand before being washed through a 63mmicron mesh sieve. 然后将土样浸入含有分散剂的水中,并在将其用63微米筛过筛前搁置起来并将其搁置一会,再用63micron的筛子过筛;The retained fraction is again oven-dried and passed through a nest of sieves. 将筛中保留的部分烘干,并用一组筛子过筛;After weighing the fractions retained on each sieve and calculating the cumulative percentage passing each sieve, the grading curve is drawn. 称量落在每个筛中土重,并计算出通过每个的累计百分数后,就可描出级配曲线;The combined clay/silt fraction is determined from the weight difference and expressed as a percentage of the total sub-sample weight. The coarsest fraction >20mm can also be sieved and the results used to complete the grading curve. 由重量差确定粘粒/粉粒的总重,并将其表示为子土样总重的百分数;最粗的部分即粒径>20mm的部分也可被过筛,并用其结果完成级配曲线的绘制;A further sub-division of particle-size distribution in the fine-grained fraction is not possible by the sieving method. 不能用筛分法对细粒部分的粒径分布作进一步分组;A processof sedimentation is normally carried out for this purpose. 通常必须用沉降法实现此目的; A small sub-sample of soil is first treated with a dispersing agent and then washed through a63m sieve. 首先将一小子土样用分散剂进行处理,然后洗过63的筛子;The soil/water suspension is then made up to 500 ml,agitated vigorously for a short while and then allowed to settle.再从中取出500ml的土/水悬浮液,充分搅拌一会后让其沉降;The procedure is based on Stoke’s law, which states that the velocity at which a spherical particle will sink due to gravity ina suspension is given by: 此方法是基于斯托克思定律,即在重力作用下球形颗粒在某一悬浮液中下降的速度为Where d=diameter of particle 颗粒直径=unit weight of the grain of particle 颗粒重度s=unit weight of the suspension fluid usually water 悬浮液w的重度通过为水的重度=vescosity of the suspension fluid 悬浮液的黏度Usually h=100mm, 通常h=100mm, giving 由此给出Samples taken at a depth of 100mm, at an elapsed time of t,will not, therefore, include particles of greater size than thediameter d given by 因此在,在深度100mm处,t 时间后所取的悬浮液中将不会有粒径大于式所给出的土粒; but the proportions of particles smaller than d in the suspension willremain unchanged. 但悬浮液中小于d的颗粒所占的比例仍保持不变;The procedure using a hydrometer consists of measuring the suspension density at a depth of 100mm at a series of elapsed-time intervals. 用液体比重计的方法包括以一系列时间间隔在深度100mm处测定悬浮液的比重;The percentage-finer values corresponding to particular diameter . particle sizes are obtained from the density readings, and thus a grading curve for the fine-grained fraction may be drawn. 通过比重读数得到小于某一特定粒径的颗粒的百分数,从而可画出细粒部分的级配曲线;Grading CharacteristicsThe grading curve is a graphical representation of the particle-size distribution and is therefore useful in itself as a means of describing the soil. 级配曲线是粒径分布的一种图形表达,因而可用来作为描述土的手段;For this reason it is always a good idea to include copies of grading curves in laboratory and other similar reports. 因此,人们总是认为在实验室报告或其它报告里附上几份级配曲线是一种好做法; It should also be remembered that the primary object is to provide a descriptive term for the type of soil. 还应牢记的是我们的主要目的是提供对土的类型的描述性术语;This iseasily done using the type of chart by estimating the range of sizes included in the most representative fraction of the soil. 这可容易地通过采用这种级配曲线做到,因为用它能估计出土中最有代表性的成分的粒径范围;For example, the steep curve may be taken to represent a poorly-graded medium sand, indicating a narrow range of sizes. 例如,陡峭的曲线可用来表示级配差的中砂,并表示其粒径范围比较小;A further quantitative analysis of grading curves may be carried out using certain geometric values known as grading characteristics. 通过采用某些称为级配特征的几何值,可进一步对级配曲线进行定量的分析;First of all, three points are located on the grading curve to give the following characteristic sizes: 首先,定出级配曲线上的三个点以给出以下特征粒径：D10=maximum size of the smallest 10 percent of the sample; 只有10%土样通过的最大粒径；D30= maximum size of the smallest 30 percent of the sample; 只有30%土样通过的最大粒径；D60= maximum size of the smallest 60 percent of the sample；只有60%土样通过的最大粒径；From these characteristic sizes, the following grading characteristics are defined: 根据这些特征粒径,定义出如下级配特征：Effective size 有效粒径Uniformity coefficient 均匀系数Coefficient of gradation 级配系数Lesson 4New Words1.u ndergo ndu vt. 经历, 遭受, 忍受; experience2.e vaporation ivprein n.蒸发作用evaporate vapor3.a ttribute tribju:t vt.把…归因于, 把…归咎于,加于, 归结于;ascribe, impute, credit, assign, refer4.s hrinkageshrink rinkid n.收10.distribution distribju:nn.分配, 分发distribute distributor11. upwind pwindadj.逆风的adv.逆风地windward; leeward 12.diminish diminiv.使减少, 使变小diminishment; decrease13.creep kri:p n. 徐变;14.slippage slip缩shrink5.c apillary kpilri adj. 毛细作用的tensioncapillarity6.e vaporate ivpreitv.使蒸发, 消失7.p aste peist n.糊, 粘土团cement paste 8.a mbient mbint adj. 周围的,包围着的surrounding ambient air9.s pecimen spesimin n. 标本, 样品, 样本, 待试验物; sampleslipid n.滑动, 滑移, 滑程slip15.humidityhju:miditin.湿气, 潮湿, 湿度; humidrelative humidity 16.aug`ment: ment v.增加, 增大n.增加; increase, enlarge augmentation17.sustained ssteindadj.持续不变的, 相同的; sustainable development18.fatigue fti:n.疲乏, 疲劳, vt.使疲劳, vi.疲劳strengthPhrases and Expressions1.m oisture content 含8.s ustained load 永久水量,含湿度; water content2.c ement paste 水泥浆mortar3.c apillary tension 毛细管张力,微张力4.g radation of aggregate 骨料级配coarse fine crushed stone, gravel5.T he British Code PC100英国混凝土规范PC100; nowaday BS81106.c oefficient of thermal expansion of concrete 混凝土热膨胀系数7. The Code 英国标准规范荷载,长期荷载9.p ermanent plastic strain 永久的塑性应变stress10.crystal lattice晶格, 晶格11.cement gel 水泥凝胶体12.water-cement ratio 水灰比13.expansion joint 伸缩缝14.stability of the structure 结构的稳定性structural stability15. fatigue strength ofconcrete 混凝土的疲劳强度Text Volume Changes of ConcreteConcrete undergoes volume changes during hardening. 混凝土在硬结过程中会经历体积变化;If it loses moisture by evaporation, it shrinks, but if the concrete hardens in water, it expands. 如果蒸发失去水分,混凝土会收缩；但如果在水中硬结,它便膨胀;The causes of the volume changes in concrete can be attributed to changes in moisture content, chemical reaction of the cement with water, variation in temperature, and applied loads. 混凝土体积变化的原因可归结为含水量的变化、水泥与水的水化反应、温度变化和所施加的荷载;ShrinkageThe change in the volume of drying concrete is not equal to the volume of water removed. The evaporation of free water causes little or no shrinkage. 混凝土干燥时的体积变化量不等于它所失去的水的体积;自由水的蒸发基本不产生收缩;As concrete continues to dry, water evaporates and the volume of the restrained cement paste changes, causing concrete to shrink, probably dueto the capillary tension that develops in the water remaining in concrete. 随着混凝土的不断变干,水分蒸发,受约束水泥浆的体积也变化,导致了混凝土的收缩,这多半是由于残留在混凝土中的水的毛细张力所致; Emptying of the capillaries causes a loss of water without shrinkage. But once the absorbed water is removed, shrinkage occurs. 毛细管变空导致无收缩的水分丢失,但一旦失去吸收的水分,收缩便发生;Many factors influence the shrinkage of concrete caused by the variations in moisture conditions. 许多因素都会影响因水分环境发生变化而产生的混凝土收缩;and water content. The more cement or water content in the concrete mix, the greater the shrinkage. 水灰比：水灰比越大,收缩越大；and fineness of cement. High-early-strength and low-heat cements show more shrinkage than normal portland cement. The finer the cement, the greater is the expansion under moist conditions. 水泥的成分和细度：早强和低热水泥的收缩大于普通水泥,水泥越细,其在潮湿环境中的膨胀越大;, amount, and gradation of aggregate. The smaller the size of aggregate particles, the greater is the shrinkage. The greater the aggregate content, the smaller is the shrinkage. 骨料的类型、含量及其级配：骨料的粒径越小,收缩越大；骨料含量越大,收缩则越小;conditions, moisture, and temperature. Concrete specimens subjected to moist conditions undergo an expansion of 200to300×10-6,but if they are left to dry in air, they shrink. High temperature speeds the evaporation of water and, consequently, increases shrinkage. 外部条件,水分与温度：潮湿环境下的混凝土试件的膨胀量为200to300×10-6,但如果让其在空气中干燥,它们将收缩;高温加速了水分的蒸发,因此也加快了收缩;. Admixtures that increase the water requirement of concrete increase the shrinkage value. 添加剂：使用水量增加的外加剂也增加了收缩值;and shape of specimen. As shrinkage takes place in a reinforced concrete member, tension。

XXX工业大学2017 ～2018 学年第二学期期末考试试卷学院_________________ 班级__________ 姓名__________ 学号___________ 《理论力学》课程试卷B（附参考答案和评分标准）Instructor: Lin Zongxi题号 1 2 3 4 5 6 总得分题分20 15 15 15 15 20得分1．Choose the correct answers with proper justification (10×2=20, 20%)1 2 3 4 5 6 7 8 9 10C B A B B A C CD C(1) Which one of the following is a scalar quantity? .A) Force B) Position C) Mass D) Velocity(2) If a particle starts from rest and accelerates according to the graph shown, the particle’svelocity at t = 20 s is ____ ______.A) 200 m/sB) 100 m/sC) 0D) 20 m/s(3) A particle has an initial velocity of 3 m/s to the left at s0 = 0 m. Determine its position whent= 3 s if the acceleration is 2 m/s2 to the right. .A) 0 m B) 6.0 m C) 18.0 m D) 9.0 m(4) The directions of the tangential acceleration and velocity are always .A) perpendicular to each other. B) collinear.C) in the same direction. D) in opposite directions.(5) Calculate the impulse due to the force F. .A) 20 kg·m/sB) 10 kg·m/sC) 5 N·sD) 15 N·s(6) As shown in the right figure, two blocks are interconnected by a cable. Which of thefollowing is correct? .A) v A= - v BB) (v x)A= - (v x)BC) (v y)A= - (v y)BD) All of the above.(7) If a particle moves in the x-y plane, its angular momentum vector is in the .A) x direction. B) y direction. C) z direction. D) x-y direction.(8) If the position, s, is given as a function of angular position, θ, by s=10 sin2θ, the velocity, v,is . (Noting that θ=ωt, ω is the angular velocity at time t).A) 20 cos 2θB) 20 sin 2θC) 20 ω cos 2θD) 20 ω sin 2θ(9) If v A=10 m/s, determine the angular acceleration,α, of the rod whenθ=30︒. .A) 0 rad/s2B) -50.2 rad/s2C) -112 rad/s2D) -173 rad/s2(10) A slender rod (mass =M) is at rest. If a bullet (mass = m) is fired with a velocity of v b, theangular momentum of the bullet about A just before impact is .A) 0.5 m v b2B) m v bC) 0.5 m v bD) zeroDetermine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis.Solution:Using the vector analysis, we have the x- and y-components of forces 6kN and 2kN as()()()()o1o1o2o26kN cos603kN6kN sin6033 5.196kN2kN cos452 1.414kN2kN sin452 1.414kNxyxyFFFF=-=-=========(4%)Hence, the force vectors are obtained as1112223 5.1961.414 1.414x yx yF FF F=+=-+=+=+F i j i jF i j i j(4%)According to the vector addition rule, the resultant force is expressed in the vector form()()1212121.586 6.61R x x y yRx RyF F F FF F=+=+++=+=-+F F F i ji j i j(3%)So, the magnitude and direction of the resultant force are obtained as()()()()2222o1.586 6.61 6.80kN6.61arccos arccos103.496.80R Rx RyRyRF F FFFθ=+=-+=⎛⎫⎛⎫===⎪ ⎪⎝⎭⎝⎭(4%)Determine the magnitude of the moment of the 200N force about the x axis. Solve the problem using both a scalar and a vector analysis.Solution:(1) Scalar analysis.The x, y and z-components of the force F can be expressed as()()()ooocos200N cos120100Ncos200N cos60100Ncos200N cos45173.2NxyzF FF FF Fαβγ===-======(3%)Thus, the magnitude of the moment of the force F about the x axis is obtained as()()()()23100N0.25m173.2N0.3m17.43N mx y zM F d F d=-+=-+=(4%)(2) Vector analysis.First, we establish a position vector from origin O to point A on the force line of action:0.30.25OA A==+r r j k(2%)And the vector of force F is100100173.2x y zF F F=++=-++F i j k i j k(2%)Hence, the moment of force F about point O yields00.30.2517.432530100100173.2O==-+-i j kM i j k(2%)And the magnitude ofOM about the x-axis is obtained as()17.432530N m17.43N mx OM==-+=i M i i j k(2%)The overhanging beam is supported by a pin at A and the two-force strut BC. Determine the horizontal and vertical components of reaction at A and the reaction at B on the beam.Solution:(1) Free-body diagram (6%)We draw a free-body diagram for the overhanging beam as below:(2) Equations of equilibrium (6%)Consider the counterclockwise moment of the force positive. According to the free-body diagram, we have x- and y-component equations and moment about point A of equilibrium as follows()()()()()()()20,02.51.50,600N800N02.51.50,600N1m2m800N4m900N m02.5x Ax By Ay BA BF F FF F FM F=-==+--==-+--=∑∑∑After solving, we have (3%)3133.33N,950N,3916.67NAx Ay BF F F==-=The negetive sign indicates that the direction sence is oppisite to that shown in the free-body diagram.A 50-lb bar is rotating downward at 2 rad/s. The spring has an un-stretched length of 2 ft and a spring constant of 12 lb/ft. Determine the angle (measured down from the horizontal) to which the bar rotates before it stops its initial downward movement. (The acceleration of gravity g=32.2 ft/s2).(1%) Solution:Potential Energy:Let’s put the datum in line with the rod when θ= 0. Then, at position 1, the gravitational potential energy is zero and the elastic potential energy will beV1 = ½ k (s1)2= ½ (12) (4 - 2)2(2%)Gravitational potential energy at position 2: - (50) (3 sin θ) (2%)Elastic potential energy at position 2: (2%)½ (12) {4 + (6 sin θ) - 2}2 . So, V2 = - (50) (3sin θ) + ½ (12) {4 + (6 sin θ) - 2}2Kinetic Energy:At position 1 (when θ = 0), the rod has a rotational motion about point A.T1 = ½ I A (w2 ) = ½{1/3 (50/32.2) 62} (22 ) (2%)At position 2, the rod momentarily has no translation or rotation since the rod comes to rest. Therefore, T2 = 0. (2%)Now, substitute into the conservation of energy equation.T1 + V1 = T2 +V2 (2%)½{1/3 (50/32.2) 62}( 22 ) + ½ (12) (4 - 2)2= 0.0 - (50)(3 sin θ) + ½(12){4 + (6 sin θ) - 2}2 Solving for sin θ yields (2%)sin θ = 0.4295. Thus, θ= 25.4 deg.6. (20%)The disk is rotating with ω =3 rad/s, α = 8 rad/s 2 at this instant. Determine the acceleration at point B , and the angular velocity and acceleration of link AB .(5%)Solution:Draw the kinematic diagram and then apply the relative-acceleration equation:2//B A AB B A AB B A ω=+⨯-a a αr r (4%)where()()()()222o o /o o o o0.2*3 1.8m/s0.2*8 1.6m/s 0.4cos300.4sin 30,01.6 1.80.4cos300.4sin 301.60.4sin 30 1.80.4cos30n A t A B A AB AB AB B AB ABABa αωααα====↓=-===-+⨯-=++-+a a r i j αk i i j k i j i j(5%)Equating the i and j components, we haveo o 1.60.4sin300 1.80.4cos30B AB AB a αα=+=-+ (2%)After solving, we have222.61m/s 5.2rad/s (counterclockwise)B AB a α=→= (4%)。