Yield line theory solved problems. A yield line is a line in the plane of the slab across which reinforcing bars have yielded and about which excessive deformation (plastic rotation) under constant limit moment (ultimate moment) continues to occur leading to failure. Question: Example By using the yield line theory, determine the ultimate resisting moment per linear meter (m) for an isotropic reinforced concrete two-way polygon slab shown in figure under a uniform load (q). The term ‘yield line’ (in Danish: ‘brudlinie’, literally meaning ‘line of rupture’) was coined in 1921 by Ingerslev [7] to describe lines in the slab - For a mechanism to develop, the yield line may pass through the intersection of the axes of rotation of adjacent segments Fig. The elastic moment is shown, as the load is increased, when the applied moment becomes equal to the flexural capacity YIELD LINE THEORY (EXAMPLES) Suhaimi Abu Bakar, PhD. Solution: In this case, p J 2 = r 1 3 11 = y;) 11 = p 3 y 2. Theory and Numerical Problems Earthquake Resistant Design of Structures Seismic Effects, Material Behaviour and General Principles of Earthquake Resistant Design of structures Aug 13, 2019 · In this research work, the yield line theory was used by the authors for the analytical modelling of the three-sides supported slabs. EXAMPLE 6: Using the yield line theory, determine the ultimate resisting moment per linear meter (m) for the isotropic two-way square slab supported by four concrete walls subjected to a uniformly distributed load (w). DESIGN EXAMPLES. This method is an upper bound method. Answer to Solved EXERCISE 1: a) Give TWO (2) Yield Line Theory | Chegg. Failure Theories (PDF) 4. The notes and questions for Yield Line Theory for Slabs have been prepared according to the Civil Engineering (CE) exam syllabus. Jun 1, 2000 · Johansen's yield-line analysis is generally considered as an acceptable technique used to determine the collapse load of reinforced concrete slabs. 23. ac. w. The yield analysis was proposed by Ingerslev in 1923. In general, elastic solutions are available only for restricted conditions, usually uniformly loaded rectangular slabs and slab systems. The yield line serves as an axis of rotation for the slab segment. It uses yield line theory to investigate failure mechanisms at the ultimate limit state. The angle of rotation of the panel B (and C) is then 1/2. Benefits of the yield-line method are that it will often identify additional reserves of strength when applied to the analysis of existing slabs, and to highly economic slabs when used in design. 3!, and the shear force acting at a yield line as Ta. Yield Line Theory challenges designers to use judgement and not to rely solely on computer analysis and design. Johansen [32], who published his PhD thesis on the subject in 1943. sc. It defines relevant symbols used in the analysis. 16. with the conventional yield line method. Two approaches are possible in yield line theory: 1-Energy Method: External work done by the loads during the small virtual displacement of the collapse mechanism is equated to the internal work done by the resisting moments. Given q = 20 kN/m² and negative moment is similar to positive moment, which is m. yield line method is plastic The yield line theory of analysis is a factored or ultimate load method of analysis. 4. 2. e. When using the work method various geometric parameters of a yield-line pattern can be adjusted to seek the minimum collapse load. Question: Example By using the yield line theory, determine the ultimate resisting moment per linear meter (m) for an isotropic reinforced concrete two-way slab to sustain a concentrated factored load of PkN applied as shown in figure. 6 Jul 1, 2013 · Yield Line Theory is one of the historic and trusted methods to predict the failure loads of slabs. the corresponding mechanism is the yield line. Yield line design is a well-founded method of designing reinforced concrete slabs. ' l^ virtualworkmethod, • 13 successiveapproximationmethod 26 Mar 6, 2020 · code in the virtual work met hod by simple yield line theory. This document provides an overview of yield line analysis for determining the ultimate load capacity of simply supported slabs. Micro-cracking of Concrete; Stress-strain Behavior in Multiaxial Loading (PDF) 3. It is a robust and proven design technique that challenges designers to use judgement; once grasped it is an exceedingly powerful tool. The yield line method is based on the kinematic ~Fig. 1 Dissipation in a yield line If the axes of rotation for two slab parts are not at the same depth measured from the slab surface, the relative displacement discontinuity is no longer perpendicular to the yield line. In order to compare the results in terms of the flexural bearing capacity, the slabs were analyzed by using elastic finite element In the simple yield-line analysis problem considered in the previous section a geometrically compatible yield-line pattern was pre-defined, and all that was required was to adjust the geometry of the mechanism (i. For 5 pairs of observations the following results are obtained ∑X=15, ∑Y=25, ∑X2 =55, ∑Y2 =135, ∑XY=83 Find the equation of the lines of regression and estimate the value of X on the first line when Y=12 and value of Y on the second line if X=8. uk Provided by KhartoumSpace Oct 1, 2003 · The paper also summarizes some basic or simple yield line mechanisms that may be adopted directly to solve more complicated problems. sq . It is closely related to the plastic collapse or limit analysis of steel frames, and is an Upper Bound or Mechanism approach. Concrete Plasticity (PDF) DEPT. This video will use yield line to design slabs. Introduction; Design Criteria for Reinforced Concrete Structures (PDF) 2. Example 9. A full line represents a positive yield line caused by a sagging yield moment, so that the concrete cracks in tension on the bottom face of the slab; a broken line represents Nov 30, 2019 · Yield line method of analysis was started by Ingerslev . The angle Published: 30 November 2019 Yield Line Analysis of Reinforced Concrete Slab Carrying Concentrated Loading Anunay Jain & Veerendra Kumar Journal of The Institution of Engineers (India): Series A volume 101, pages195–206(2020)Cite this article 150 Accesses Metricsdetails Abstract Yield line analysis of reinforced concrete slab, simply supported on two sides perpendicular to the span and free Answer to QUESTION 3 (20 MARKS) Calculate the collapse load (W. Finally, a yield positive line should be represented as one crooked line, a yield negative line as two crooked lines, a free edge as a line, a simply supported edge as two lines, a clamped edge as a family of parallel lines, and a column as a circle. Oct 1, 2015 · In the early ages of last century, the yield-line method has been proposed to attempt to solve such problem. SOLUTION: 𝑊𝐸= × 1 2 × × 2 × 1 3 ×4= 2 2 3 𝑊𝐼=( +𝑣𝑒× × 1 2 + −𝑣𝑒× × 1 2)×4=16 . The assumed failure criteria is termed by a pattern of yield lines, along that the reinforcement has yielded and the location of which counts loads and boundary conditions. The advantages and disadvantages of both the equilibrium and energy Feb 1, 2020 · The Yield Lines Theory, which is one of limit state analysis based on expected failure criteria of slabs. The slab is given a unit virtual displacement at the yield line joining the two plate segments to apply the principle of virtual work. The study demonstrates and evaluates an approach in the structural analysis phase when assessing reinforced concrete slabs. The yield line theory is conducted based on the bending moment of the structural element at its collapse state. 1 An Experimental Basis for Yield-line Analysis The pioneer of yield-line theory was K. Jun 1, 2022 · The yield-line theory is an upper bound method of reinforced concrete slabs [24]. 3. Yield-line analysis removes this inconsistency. , with the aid of the rules by Jones and Wood ], and then the work method is used to obtain a solution. 2 Illustrative Examples 19 Yield line theory 653. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. . For a given slab, the ultimate load obtained by the yield-line theory may be correct or excessive. Due to different values of a parameter in the tests’ results, 10 models was crated for the first case study and 4 models for the second one. This particular example will show you step by step how to easily use yield line analysis for s more. 2 Typical Yield line patterns Fig. Both the endplate yield line patterns and the - column side yield line patterns are provided. 1 Deformation of slab with yield lines positive yield line negative yield line axis of rotation simply supported edge unsupported edge point load column support built in edge 2. 2 equilibriumequationsmethod. W 4: Using yield line theory for the isotropic slab shown in figure below, find the uniformly collapse load (Wu) assume m* = m*=m 5m So 9 m Show transcribed image text Here’s the best way to solve it. Many researchers have extended Johansen's ideas, perhaps further than he envisaged or desired. For the method of virtual works, the document outlines the key steps of drawing Yield-line theory is accepted as a method for the design of reinforced concrete structures in many codes. As for feature (b) above, the particular nature of element “S3”, especially, the way curvature is calculated, makes this possible. These two methods should give exactly the same results because they are based on the same basic assumptions for the yield line theory. Suppose, now, that we impose a unit virtual dis- placement on the yield line at f; e will suffer the same virtual displacement since ef and ab are paral- lel. However, a basic understanding of the yield line theory is assumed in the following discussion and the reader is referred to the standard texts on the subject [ 1,2]. Information about Yield Line Theory for Slabs covers topics like and Yield Line Theory for Slabs Example, for Civil Engineering (CE) 2024 Exam. (4 marks) (b) A two-way rectangular slab has two potential mode of failure as shown in FIGURE Q1(b)(i) and FIGURE Q1(b)(ii). Mohammed Abdelgadir Ahmed Alasam Supervisor: Prof. Yield line theory is a limit analysis using which we can achieve an ultimate load carrying capacity of the slabs by selecting a suitable collapse pattern which depict the actual boundary conditions. Solution: Y –5 = 0. Yield-line theory permits, within limits, an arbitrary readjustment of moments found by elastic analysis to arrive at design moments that Yield line Theory for Concrete Slabs Subjected to Axial Force - 10 - 7 Theory 7. A suitable yield line pattern is assumed according to the given loads, dimensions and edge conditions. SOLUTION: 𝑊𝐸=𝑊𝐼 There are two methods of yield line analysis of slab : (i) Virtual Work Method, and (ii) Equilibrium Method. Traditionally a hand-based method, the yield-line method is easy to apply to problems involving simple slab geometries and loading regimes. This tutorial video will explain step by step on how to determine the design moment for a rectangular slab using Yield line analysis. 12. Find important definitions, questions, notes, meanings, examples Jan 9, 2004 · This chapter contains sections titled: Introduction to Yield-Line Method Work Method Equilibrium Method Further Applications of Yield-Line Analysis Yield Lines due to Concentrated Loads S 8. Slabs equally reinforced in two normal Yield line analysis. 2. Y . Simple geometry problems could easily be solved by using traditional hand analyses Figure 8. Solve the yield-line analysis problem On solve, the software uses cutting-edge optimization techniques to automatically consider billions of potential yield-line mechanisms, identifying the critical case and associated factor of safety within seconds. W. Their intention has been Loads distributed over small areas and load combinations are discussed in Ref. Obtain a relationship between the yield stress under pure shear y and the yield stress under uni-axial stress y Solution: We know that under uni-axial stress, the material yields when the Question: - H. The ultimate load of slabs is estimated by assuming a failure mechanism which is compatible with the boundary conditions. show this link to your f compatible. A line shaft rotating at 200 rpm is to transmit 20 kW power. 1. The beam design chart in Fig. Many handbooks [27,28] and researches [18,19, 23, 29] discussed this method proposing several Q1 (a) Briefly discuss TWO (2) assumptions in yield line analysis. g. 8(X–3) = 0. 9 LIMITATIONS OF YIELD LINE THEORY The usefulness of yield line theory should be apparent from the preceding sections. I El-Niema December 2006 CORE Metadata, citation and similar papers at core. Yield line theory, on the other hand, is an efficient way of determining the collapse load of reinforced concrete slabs, and it pre-dates limit analysis. Understanding the numerical problems and solving practice and test problems will give a better understanding of the theories of yield line analysis and their applications. EXAMPLES IN YIELD LINE ANALYSIS Dr. Let the regression line X on Y be . The yield line theory is briefly reviewed below. OF BUILDING & CONSTRUCTION TECH. 2-1 shows some tyRical yield-line patterns for slabs in the collapse state under uniformly dtstributed loads. Title: PowerPoint Presentation Author: suhaimi Created Date: 9/28/2005 6:11:59 AM parameters for end-plate moment connections. In either method, a yield line pattern is assumed so that a collapse mechanism is produced. The slabs designed by yield-line theory become economical as it accounts for the reserve strength characteristics of most concrete structures. Yield Line Theory 2. The allowable shear stress for the shaft material is 42 N/mm 2. 5-2 may of course be used for slab design, but since practical slabs are Aug 1, 2013 · The energy dissipated by a yield line due to a virtual rotation can be calculated by projecting the yield line into other directions, usually the global horizontal and vertical axes in the slab plane [3], [5]. The application of yield line mechanism analysis is included, covering steel plates, open-section members, closed-section members, void-filled members, welded connections and bolted connections. Aug 1, 2013 · A new lower bound finite element method for slab analysis is presented as a practical substitute to full, non-linear, finite element methods that require expert knowledge and long running times. Johansen [2, 3] extended the work of Ingerslev, and yield line method of analysis was established as a viable method of analysis based on theory of plasticity. 333 m uni-axial stress loading yield occurs when the applied stress (say 11), reaches the value 11 = p 3 y. 2-Equilibrium Method: Equilibrium of the segments or parts of slab into which the slab is divided by the yield lines. the distance x ) to determine the critical case. Simple design leads to simple details that are fast to detail and fast to fix. Dec 24, 2003 · The paper also summarizes some basic or simple yield line mechanisms that may be adopted directly to solve more complicated problems. ” As shown in this paper, many of the classical solutions of yield line analysis correspond to incorrect yield patterns. The application of yield line mechanism analysis is included For practical purposes, the ultimate moment of resistance [1] of reinforced concrete slabs may be determined by the methods explained in Chapter 4 for beams. com Feb 1, 2021 · The fundamentals of the yield-line method as they apply to the design of reinforced concrete slabs are reviewed and design procedures suitable for routine office use are presented. The document then discusses two methods for performing the analysis - the method of virtual works and the method of segment equilibrium. 1 YIELD LINE THEORY There are two approaches to the calculation of the ultimate load-carrying capacity of a reinforced concrete slab involving yield line theory. Johansen. 19. VIRTUAL WORK METHOD. 8X+2. 33. Portions of the original theory, such as the virtual work equation and the yield criterion, have been incorporated into the elastic and inelastic theory of yield-line elements. 12. Jan 15, 2003 · If yield lines are “incorrect,” or not possible, yield line analysis can only be performed, in general, by means of “skew moment method. E. Dec 1, 2018 · In this paper, different types of reinforced concrete slabs system of different support conditions have been analyzed using yield line theory to determine the maximum resisting moment, the result When carrying out a yield-line analysis by hand, usually a yield-line pattern is postulated by hand [e. Mathematical analysis of all cases that are adopted by method three of the ACI 1963 C ode is. Solution We=P×1=P Wi= We=Wi P=11. Nielson carried out yield line analysis for orthogonally reinforced slabs supplementing Johansen’s work [2, 3]. Determine the diameter of the shaft Yield Line Method Applied to Slabs with Different Supports Thesis Submitted in Partial Fulfilment of requirements for the degree of M. A simply supported uniformly loaded reinforced concrete slab shown in Fig(2-2) with é< é Õ. in Structural Engineering By: Eng. 1 Introduction Yield line analysis is an analysis approach for determining the ultimate load capacity of reinforced concrete slabs and was pioneered by K. EXAMPLE 13: by using the yield line theory, determine the moment (m) for the simply supported two-way reinforced concrete slab shown in the figure below which is subjected to a uniformly distributed load (w) kPa. The method presented here, yield line theory, was developed in the early 1960s by the Danish engineer, K. Current initiatives such as Egan[4 Jun 1, 2000 · Johansen's yield-line analysis is generally considered as an acceptable technique used to determine the collapse load of reinforced concrete slabs. Once grasped, Yield Line Theory is exceedingly easy to put into practice and everyone in the procurement chain benefits. there will be a yield line ad along the built-in edge. Johansen in the 1940s. 2 Yield-line Theory 8. MOHAMMED ZUHEAR ALMULALI EXAMPLE 22: For the fixed two-way slab shown below, using the yield line theory determine the ultimate resisting moment per linear meter (m) if the slab was subjected to a concentrated load of P kN. Many guidelines have been provided to find the most possible failure mechanism and the lowest upper solution. Download scientific diagram | Yield Line patterns for two-way rectangular slabs of all 9 cases of method 3 of the ACI 1963 Code from publication: Implication of Yield Lines Theory in Method Three ^rld 73 ^^,cj (1^11 ^f/3 tableopcontents synopsis 1 introduction. For each yield line parameter, either the derivation is given or details about how the yield line parameter was obtained from one of the other derived yield line parameters is described. ghkdzudlufdrtfjvorpkfwrijoeqogvuedibqfmwbinotf
