Structures w m jenkins bsc, phd, ceng, fice, fistructe emeritus professor of civil engineering, school of engineering, the hatfield polytechnic contents 3. To show the performance of the methods of analysis of the hyperstatic structures, selected beams, gantries and reticular structures are selected and subjected to a comparative study by the different methods of analysis of the hyperstatic structures. Deflections using energy methods conservation of energy. Chapter 2 basis for the analysis of indeterminate structures. Aims determine the slope and deflection by using unit load method expected outcomes. It has to satisfy the fundamental criteria of strength, stiffness, economy, durability and compatibility, for its existence. Chapter 16 analysis of statically indeterminate structures. Hence, the unit load method for finding deflection will be discussed briefly for a determinate structure. Determinate and indeterminate structures and their differences. Equilibrium conditions are fully adequate to analyze the structure. In strain energy method, an imaginary load p is applied at the point where the deflection is desired to be determined. It s hould be noted that the results of analysis are. Brief explanation of equilibrium equations and how to determine if a structure is statically determinate, indeterminate, or unstable. Analysis of statically determinate trusses theory of structures asst.
Deflection method previously we have discussed forceflexibility methods of analysis of statically indeterminate structures. To find a deflection apply virtual force p at that point and in that direction. Sometimes referred as the unitload method generally provides of obtaining the displacement and slope at a specific point on structure i. The requirements of force and moment equilibrium make up a second set. Analysis of statically determinate structures the most common type of structure an engineer will analyze lies in a plane subject to a force system in the same plane. Hibbeler, 7th edition, prentice hall structural analysis, hibbeler, 7th edition, prentice hall. To compute a component of deflection by the method of virtual work, the designer applies a force to structure at the point and in the direction of the desired displacement. For determinate structures, the force method allows us to find internal forces using equilibrium i. Classify each of the beams shown below as statically determinate or statically indeterminate. Material stress strain relationships are needed only to calculate deflections. Analysis of statically indeterminate structures by the displacement method. Draw fbd and count number of redundancies each redundancy gives rise to the need for a compatibility equation.
Kinematically indeterminate structures versus statically indeterminate structures. Once the structural model is defined, the unknowns. Conditions of equilibrium are not adequate to fully analyze the structure. The beams are subjected to external loadings that are assumed to. Determine the slope and deflection by using moment area method expected outcomes. Compute deflections in trusses using unitload method due to fabrication errors. Deflection analysis of statically determinate beams, trusses and frames. Difference between determinate and indeterminate structures. If the deflection of a structure is more than the permissible, the structure will not look aesthetic and will cause psychological upsetting of the occupants. Determinate structures extra conditions like compatibility of displacements are not required to.
Common types of trusses a truss is one of the major types of engineering structures which provides a practical and economical solution for many engineering constructions, especially in the design of bridges and buildings that. Table 21 supports for coplanar structures 3 f 4 f 1. In force method,theunknown redundant forces are determined first by solving the structures compatibility equations. Bending moment or shear force at any section is independent of the material property of the structure. Pdf deflection of determinate structures researchgate. Solve the problem using the same procedure as a statically determinate problem to determine the reaction. Determinate, indeterminate and unstable structures duration. The deflection or slope at any point on a structure as a result of a number of forces, including the reactions, is equal to.
Thus, the material covered in existing textbooks on structural analysis contains. Methods of analysis two different methods are available. For the case of indeterminate structures this may be stated as. Knowledge on theory of deflection in beams is used in analyzing for magnitudes of deflection resulting from a given loads. Thus slopedeflection method is a displacement method. Force flexibility method for determinate structures, the force method allows us to find internal forces using equilibrium i. Also draw the axial force, shear force and bending moment diagram of the member ab, assuming the horizontal reactions at support a and d are equal. Force method for analysis of indeterminate structures. The force system created by the virtual loads is called. It is generally classified into two categories as determinate and indeterminate structures or redundant structures.
Able to analyze determinate beam deflection and slope by unit load. Using a general approach, this book supports the student to enable mastery of the methods of analysis of isostatic and hyperstatic structures. In the afternoon, you are to answer 60 questions, and structural analysis is about 10% of the test content or about 6 questions. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Page 1 m9 truss deflections and statically indeterminate. Slopedeflection method in this method it is assumed that all deformations. Computation of deflection of structures is necessary for the following reasons.
In the figure above, the beams number 1 and 2 are statically determinate structures due to the following reasons. Analysis of statically indeterminate structures by the. Draw the afd, sfd and bmd of the beam bcd in the frame abcde loaded as shown below. If statically indeterminate, report the number of degrees of indeterminacy. Civl 3121 analysis of statically determinant structures 112. Determinate structures a pin connection confines deflection. Combinely these slopes and deflections are known as displacements. It is no different from that used with the force method. Why is it necessary to compute deflections in structures. Pdf this book has been written for the 3rd year undergraduate students of civil engineering who are learning about calculating deflection of.
Gate material ies master structural analysis study. The slopedeflection method was originally developed by heinrich manderla and otto mohr for computing secondary stresses in trusses. Structural analysis iii chapter 2 basis for indeterminate structures 3 dr. Any structure is designed for the stress resultants of bending moment, shear force, deflection, torsional stresses, and axial stresses. Civil engineeringstructural analysis 53 important mcq pdf. P is equated to zero in the final step and the deflection is obtained. Able to analyze determinate beam deflection and slope by unit load method references mechanics of materials, r. Maney in 1915 for analyzing rigid jointed structures. Introduction slopedeflection method is the second of the two classical methods presented in this course. L a word about constitutive relations you are familiar with one such constitutive relationship, namely that between the. All bars have cross sectional area a, youngs modulus e. Structural analysis of statically determinate beams, trusses and frames.
Equations for the calculations of the deflections of trusses and beams using the. Deflection of statically indeterminate structures 343 the right hand term in equation 4 may also be interpreted in the sense of equation 3. Statically determinate structures a statically determinate structure is the one in which reactions and internal forces can be determined solely from freebody diagrams and equations of equilibrium. Able to analyze determinate beam deflection and slope by moment area method. However, for indeterminate structures, statics equilibrium alone is not sufficient to conduct. The force is called the dummy loador the virtual load. Deflections using energy methods purdue university. Slope deflection method is useful to analyse indeterminate structures like continuous beams and plane frames. Analysis of indeterminate structure by slope deflection. No statically determinate structures statically indeterminate structures. Determine the slope and deflection by using unit load method.
Conditions of equilibrium are sufficient to analyze the structure. Most structures in the real world are statically indeterminate. The basic assumption used in the slopedeflection method is that a typical member can flex but the shear and axial deformation are negligible. In subject of solid and structural mechanics taught at second and third level of study in the degree course in mechanical engineering, students are. Force method for analysis of indeterminate structures number of. Placement of the live loads to maximize the desired response function is obtained from the qualitative ild. Statically indeterminate explanation structural analysis. Analysis of statically determinate structures analysis of statically determinate structures in general, it. Chapter 16 analysis of statically indeterminate structures statically indeterminate structures occur more frequently in practice than those that are statically determinate and are generally more economical in that they are stiffer and stronger. Uniformly distributed live loads are placed over the. Structure is an assemblage of a number of components like slabs, beams, columns, walls, foundations and so on, which remains in equilibrium. M9 truss deflections and statically indeterminate trusses truss deflection example calculate deflection of loading point e in pinjointed truss shown below.
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