German - English Glossary for Civil Engineering
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DEFINITIONS Beams and Stringers (B&S) Beams and Stringers Are
DEFINITIONS Beams and Stringers (B&S) Beams and stringers are primary longitudinal support members, usually rectangular pieces that are 5.0 or more in. thick, with a depth more than 2.0 in. greater than the thickness. B&S are graded primarily for use as beams, with loads applied to the narrow face. Bent. A type of pier consisting of two or more columns or column-like components connected at their top ends by a cap, strut, or other component holding them in their correct positions. Camber. The convex curvature of a beam, typically used in glulam beams. Cantilever. A horizontal member fixed at one end and free at the other. Cap. A sawn lumber or glulam component placed horizontally on an abutment or pier to distribute the live load and dead load of the superstructure. Clear Span. Inside distance between the faces of support. Connector. Synonym for fastener. Crib. A structure consisting of a foundation grillage and a framework providing compartments that are filled with gravel, stones, or other material satisfactory for supporting the structure to be placed thereon. Check. A lengthwise separation of the wood that usually extends across the rings of annual growth and commonly results from stresses set up in wood during seasoning. Creep. Time dependent deformation of a wood member under sustained load. Dead Load. The structure’s self weight. Decay. The decomposition of wood substance by fungi. Some people refer to it as “rot”. Decking. A subcategory of dimension lumber, graded primarily for use with the wide face placed flatwise. Delamination. The separation of layers in laminated wood or plywood because of failure of the adhesive, either within the adhesive itself or at the interface between the adhesive and the adhered. -
Two-Dimensional Rotational Kinematics Rigid Bodies
Rigid Bodies A rigid body is an extended object in which the Two-Dimensional Rotational distance between any two points in the object is Kinematics constant in time. Springs or human bodies are non-rigid bodies. 8.01 W10D1 Rotation and Translation Recall: Translational Motion of of Rigid Body the Center of Mass Demonstration: Motion of a thrown baton • Total momentum of system of particles sys total pV= m cm • External force and acceleration of center of mass Translational motion: external force of gravity acts on center of mass sys totaldp totaldVcm total FAext==mm = cm Rotational Motion: object rotates about center of dt dt mass 1 Main Idea: Rotation of Rigid Two-Dimensional Rotation Body Torque produces angular acceleration about center of • Fixed axis rotation: mass Disc is rotating about axis τ total = I α passing through the cm cm cm center of the disc and is perpendicular to the I plane of the disc. cm is the moment of inertial about the center of mass • Plane of motion is fixed: α is the angular acceleration about center of mass cm For straight line motion, bicycle wheel rotates about fixed direction and center of mass is translating Rotational Kinematics Fixed Axis Rotation: Angular for Fixed Axis Rotation Velocity Angle variable θ A point like particle undergoing circular motion at a non-constant speed has SI unit: [rad] dθ ω ≡≡ω kkˆˆ (1)An angular velocity vector Angular velocity dt SI unit: −1 ⎣⎡rad⋅ s ⎦⎤ (2) an angular acceleration vector dθ Vector: ω ≡ Component dt dθ ω ≡ magnitude dt ω >+0, direction kˆ direction ω < 0, direction − kˆ 2 Fixed Axis Rotation: Angular Concept Question: Angular Acceleration Speed 2 ˆˆd θ Object A sits at the outer edge (rim) of a merry-go-round, and Angular acceleration: α ≡≡α kk2 object B sits halfway between the rim and the axis of rotation. -
Beam Structures and Internal Forces
ENDS 231 Note Set 13 S2008abn Beam Structures and Internal Forces • BEAMS - Important type of structural members (floors, bridges, roofs) - Usually long, straight and rectangular - Have loads that are usually perpendicular applied at points along the length Internal Forces 2 • Internal forces are those that hold the parts of the member together for equilibrium - Truss members: F A B F F A F′ F′ B F - For any member: T´ F = internal axial force (perpendicular to cut across section) V = internal shear force T´ (parallel to cut across section) T M = internal bending moment V Support Conditions & Loading V • Most often loads are perpendicular to the beam and cause only internal shear forces and bending moments M • Knowing the internal forces and moments is necessary when R designing beam size & shape to resist those loads • Types of loads - Concentrated – single load, single moment - Distributed – loading spread over a distance, uniform or non-uniform. 1 ENDS 231 Note Set 13 S2008abn • Types of supports - Statically determinate: simply supported, cantilever, overhang L (number of unknowns < number of equilibrium equations) Propped - Statically indeterminate: continuous, fixed-roller, fixed-fixed (number of unknowns < number of equilibrium equations) L Sign Conventions for Internal Shear and Bending Moment Restrained (different from statics and truss members!) V When ∑Fy **excluding V** on the left hand side (LHS) section is positive, V will direct down and is considered POSITIVE. M When ∑M **excluding M** about the cut on the left hand side (LHS) section causes a smile which could hold water (curl upward), M will be counter clockwise (+) and is considered POSITIVE. -
A Simple Beam Test: Motivating High School Teachers to Develop Pre-Engineering Curricula
Session 2326 A Simple Beam Test: Motivating High School Teachers to Develop Pre-Engineering Curricula Eric E. Matsumoto, John R. Johnston, E. Edward Dammel, S.K. Ramesh California State University, Sacramento Abstract The College of Engineering and Computer Science at California State University, Sacramento has developed a daylong workshop for high school teachers interested in developing and teaching pre-engineering curricula. Recent workshop participants from nine high schools performed “hands-on” laboratory experiments that can be implemented at the high school level to introduce basic engineering principles and technology and to inspire students to study engineering. This paper describes one experiment that introduces fundamental structural engineering concepts through a simple beam test. A load is applied at the center of a beam using weights, and the resulting midspan deflection is measured. The elastic stiffness of the beam is determined and compared to published values for various beam materials and cross sectional shapes. Beams can also be tested to failure. This simple and inexpensive experiment provides a useful springboard for discussion of important engineering topics such as elastic and inelastic behavior, influence of materials and structural shapes, stiffness, strength, and failure modes. Background engineering concepts are also introduced to help high school teachers understand and implement the experiment. Participants rated the workshop highly and several teachers have already implemented workshop experiments in pre-engineering curricula. I. Introduction The College of Engineering and Computer Science at California State University, Sacramento has developed an active outreach program to attract students to the College and promote engineering education. In partnership with the Sacramento Engineering and Technology Regional Consortium1 (SETRC), the College has developed a daylong workshop for high school teachers interested in developing and teaching pre-engineering curricula. -
I-Beam Cantilever Racks Meet the Latest Addition to Our Quick Ship Line
48 HOUR QUICK SHIP Maximize storage and improve accessibility I-Beam cantilever racks Meet the latest addition to our Quick Ship line. Popular for their space-saving design, I-Beam cantilever racks can allow accessibility from both sides, allowing for faster load and unload times. Their robust construction reduces fork truck damage. Quick Ship I-beam cantilever racks offer: • 4‘ arm length, with 4” vertical adjustability • Freestanding heights of 12’ and 16’ • Structural steel construction with a 50,000 psi minimum yield • Heavy arm connector plate • Bolted base-to-column connection I-Beam Cantilever Racks can be built in either single- or double-sided configurations. How to design your cantilever rack systems 1. Determine the number and spacing of support arms. 1a The capacity of each 4’ arm is 2,600#, so you will need to make sure that you 1b use enough arms to accommodate your load. In addition, you can test for deflection by using wood blocks on the floor under the load. 1c Use enough arms under a load to prevent deflection of the load. Deflection causes undesirable side pressure on the arms. If you do not detect any deflection with two wood blocks, you may use two support arms. Note: Product should overhang the end of the rack by 1/2 of the upright centerline distance. If you notice deflection, try three supports. Add supports as necessary until deflection is eliminated. Loading without overhang is incorrect. I-Beam cantilever racks WWW.STEELKING.COM 2. Determine if Quick Ship I-Beam arm length is appropriate for your load. -
1.2 Rules for Translations
1.2. Rules for Translations www.ck12.org 1.2 Rules for Translations Here you will learn the different notation used for translations. The figure below shows a pattern of a floor tile. Write the mapping rule for the translation of the two blue floor tiles. Watch This First watch this video to learn about writing rules for translations. MEDIA Click image to the left for more content. CK-12 FoundationChapter10RulesforTranslationsA Then watch this video to see some examples. MEDIA Click image to the left for more content. CK-12 FoundationChapter10RulesforTranslationsB 18 www.ck12.org Chapter 1. Unit 1: Transformations, Congruence and Similarity Guidance In geometry, a transformation is an operation that moves, flips, or changes a shape (called the preimage) to create a new shape (called the image). A translation is a type of transformation that moves each point in a figure the same distance in the same direction. Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation. There are two types of notation to know. T x y 1. One notation looks like (3, 5). This notation tells you to add 3 to the values and add 5 to the values. 2. The second notation is a mapping rule of the form (x,y) → (x−7,y+5). This notation tells you that the x and y coordinates are translated to x − 7 and y + 5. The mapping rule notation is the most common. Example A Sarah describes a translation as point P moving from P(−2,2) to P(1,−1). -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
2-D Drawing Geometry Homogeneous Coordinates
2-D Drawing Geometry Homogeneous Coordinates The rotation of a point, straight line or an entire image on the screen, about a point other than origin, is achieved by first moving the image until the point of rotation occupies the origin, then performing rotation, then finally moving the image to its original position. The moving of an image from one place to another in a straight line is called a translation. A translation may be done by adding or subtracting to each point, the amount, by which picture is required to be shifted. Translation of point by the change of coordinate cannot be combined with other transformation by using simple matrix application. Such a combination is essential if we wish to rotate an image about a point other than origin by translation, rotation again translation. To combine these three transformations into a single transformation, homogeneous coordinates are used. In homogeneous coordinate system, two-dimensional coordinate positions (x, y) are represented by triple- coordinates. Homogeneous coordinates are generally used in design and construction applications. Here we perform translations, rotations, scaling to fit the picture into proper position 2D Transformation in Computer Graphics- In Computer graphics, Transformation is a process of modifying and re- positioning the existing graphics. • 2D Transformations take place in a two dimensional plane. • Transformations are helpful in changing the position, size, orientation, shape etc of the object. Transformation Techniques- In computer graphics, various transformation techniques are- 1. Translation 2. Rotation 3. Scaling 4. Reflection 2D Translation in Computer Graphics- In Computer graphics, 2D Translation is a process of moving an object from one position to another in a two dimensional plane. -
Roof Truss – Fact Book
Truss facts book An introduction to the history design and mechanics of prefabricated timber roof trusses. Table of contents Table of contents What is a truss?. .4 The evolution of trusses. 5 History.... .5 Today…. 6 The universal truss plate. 7 Engineered design. .7 Proven. 7 How it works. 7 Features. .7 Truss terms . 8 Truss numbering system. 10 Truss shapes. 11 Truss systems . .14 Gable end . 14 Hip. 15 Dutch hip. .16 Girder and saddle . 17 Special truss systems. 18 Cantilever. .19 Truss design. .20 Introduction. 20 Truss analysis . 20 Truss loading combination and load duration. .20 Load duration . 20 Design of truss members. .20 Webs. 20 Chords. .21 Modification factors used in design. 21 Standard and complex design. .21 Basic truss mechanics. 22 Introduction. 22 Tension. .22 Bending. 22 Truss action. .23 Deflection. .23 Design loads . 24 Live loads (from AS1170 Part 1) . 24 Top chord live loads. .24 Wind load. .25 Terrain categories . 26 Seismic loads . 26 Truss handling and erection. 27 Truss fact book | 3 What is a truss? What is a truss? A “truss” is formed when structural members are joined together in triangular configurations. The truss is one of the basic types of structural frames formed from structural members. A truss consists of a group of ties and struts designed and connected to form a structure that acts as a large span beam. The members usually form one or more triangles in a single plane and are arranged so the external loads are applied at the joints and therefore theoretically cause only axial tension or axial compression in the members. -
Determination of Mohr-Coulomb Parameters for Modelling of Concrete
crystals Article Determination of Mohr-Coulomb Parameters for Modelling of Concrete Selimir Lelovic 1,* and Dejan Vasovic 2,* 1 Faculty of Civil Engineering, University of Belgrade, 11000 Belgrade, Serbia 2 Faculty of Architecture, University of Belgrade, 11000 Belgrade, Serbia * Correspondence: [email protected] (S.L.); [email protected] (D.V.) Received: 23 July 2020; Accepted: 7 September 2020; Published: 13 September 2020 Abstract: Cohesion is defined as the shear strength of material when compressive stress is zero. This article presents a new method for the experimental determination of cohesion at pre-set angles of shear deformation. Specially designed moulds are created to force deformation (close to τ-axis) at fixed pre-set values of angle with respect to normal stress σ. Testing is performed on series of concrete blocks of different strengths. From the compressive side, cohesion is determined from the extrapolation of the linear Mohr–Coulomb (MC) model, as the intercept on the shear stress axis. From the tensile stress side (from the left), cohesion is obtained using the Brazilian test results: BT first, indirect tensile strength of material σt is measured, then Mohr circle diagram values are calculated and cohesion is determined as the value of shear stress τBT on the Mohr circle where normal stress (σ)t = 0. A hypothesis is made that cohesion is the common point between two tests. In the numerical part, a theory of ultimate load is applied to model Brazilian test using the angle of shear friction from the MC model. Matching experimental and numerical results confirm that the proposed procedure is applicable in numerical analysis. -
Translation and Reflection; Geometry
Translation and Reflection Reporting Category Geometry Topic Translating and reflecting polygons on the coordinate plane Primary SOL 7.8 The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. Materials Graph paper or individual whiteboard with the coordinate plane Tracing paper or patty paper Translation Activity Sheet (attached) Reflection Activity Sheets (attached) Vocabulary polygon, vertical, horizontal, negative, positive, x-axis, y-axis, ordered pair, origin, coordinate plane (earlier grades) translation, reflection (7.8) Student/Teacher Actions (what students and teachers should be doing to facilitate learning) 1. Introduce the lesson by discussing moves on a checkerboard. Note that a move is made by sliding the game piece to a new position. Explain that the move does not affect the size or shape of the game piece. Use this to lead into a discussion on translations. Review horizontal and vertical moves. Review moving in a positive or negative direction on the coordinate plane. 2. Distribute copies of the Translation Activity Sheet, and have students graph the trapezoid. Guide students in completing the sheet. Emphasize the use of the prime notation for the translated figure. 3. Introduce reflection by discussing mirror images. 4. Distribute copies of the Reflection Activity Sheet, and have students graph the trapezoid. Guide students in completing the sheet. Emphasize the use of the prime notation for the translated figure. 5. Give students additional practice. Individual whiteboards could be used for this practice. Assessment Questions o How does translating a figure affect the size, shape, and position of that figure? o How does rotating a figure affect the size, shape, and position of that figure? o What are the differences between a translated polygon and a reflected polygon? Journal/Writing Prompts o Describe what a scalene triangle looks like after being reflected over the y-axis. -
Reinforced Concrete Cantilever Beam Analysis and Design (ACI 318-14)
Reinforced Concrete Cantilever Beam Analysis and Design (ACI 318-14) Reinforced Concrete Cantilever Beam Analysis and Design (ACI 318-14) Cantilever beams consist of one span with fixed support at one end and the other end is free. There are numerous typical and practical applications of cantilever beams in buildings, bridges, industrial and special structures. This example will demonstrate the analysis and design of the rectangular reinforced concrete cantilever beam shown below using ACI 318-14 provisions. Steps of the structural analysis, flexural design, shear design, and deflection checks will be presented. The results of hand calculations are then compared with the reference results and numerical analysis results obtained from the spBeam engineering software program by StructurePoint. Figure 1 – Rectangular Reinforced Concrete Cantilever Beam Version: June-23-2021 Contents 1. Preliminary Member Sizing ..................................................................................................................................... 2 2. Load and Load combination ..................................................................................................................................... 2 3. Structural Analysis ................................................................................................................................................... 3 4. Flexural Design .......................................................................................................................................................