virtual work method of structural analysis

... of the slope-deflection method The above description outlines the introduction of the two fundamental methods ofstructural analysis, the displacement method and the force method, and their applications ... important in theunderstanding of the behavior of a structure and the development of a feel for it The force method of analysis is then extended to beam and rigid frame analysis, almost inparallel ... have a direct bearing on the design of the content of a course in structuralanalysis: the reduction of credit hours to three required hours in structural analysis inmost civil engineering curricula

Ngày tải lên: 06/07/2014, 11:20

... that is the essence of the method of joint, namely using joint equilibrium equations to find force unknowns Denote the number of all member force unknowns as M and the number of reaction forces ... in bars in the 3rd panel from the left of the truss shown.An example problem for the method of section. Solution. We shall solve this problem by the method of section with the following procedures ... each node of a plane truss: Thus the total number of equilibrium equations available is 2N, where N is the number of nodes in a truss In the present example, N=3 and 2N=6 Thus, the number of available

Ngày tải lên: 05/08/2014, 09:20

... force The principle of virtual force states that the virtual work done by an external virtual force upon a real displacement system is equal to the virtual work done by internal virtual forces, which ... external virtual force, upon the real deformation Denoting the external virtual work by δW and the internal virtual work by δU, we can express the principle of virtual force as In view of Eq.15 ... conditions and the method of solution is called the method of consistent deformations. The procedures of the method of consistent deformations are outlined below (1) Determine the degree(s) of redundancy,

Ngày tải lên: 05/08/2014, 09:20

... can see from the previous examples, the force method of analysis for frames is practical for hand calculation only for cases of one to two degrees of redundancy Although we can computerize the ... o c x 1 Trang 15The basic concept of the approximate methods is to assume the location of zero internal moments At the point of zero moment, the conditions of construction apply, i.e., additional ... configuration of the frame, we can apply either the portal method or the cantilever method The portal method is generally applicable to L roller hinge Trang 16(1) Every mid-point of a beam or

Ngày tải lên: 05/08/2014, 09:20

... the moment distribution and slope-deflection methods 2 Moment Distribution Method The moment distribution method is a unique method of structural analysis, in which solution is obtained iteratively ... concept of the displacement method for beam and frame analysis is that the state of a member is completely defined by the displacements of its nodes Once we know the nodal displacements, the rest of ... procedures of the moment distribution method: (1) Identify the node which is free to rotate In the present case, it was node b The number of “free” rotating nodes is called the degree-of-freedom (DOF)

Ngày tải lên: 05/08/2014, 09:20

... diminish the advantage of the moment distribution method. A better method for treating side-sway is the slope-deflection method, which is introduced next after the derivation of the key formulas ... by superposition of the standard model solutions as shown in the series of figures below. Beam and Frame Analysis: Displacement Method, Part I by S. T. Mau 203 Superposition of two standard models ... Frame Analysis: Displacement Method, Part I by S. T. Mau 200 A frame without side-sway and one with side-sway. Nodes b and c of both frames are free to rotate, but no translation movement of nodes

Ngày tải lên: 05/08/2014, 09:20

... Treatment of side-sway The end-nodes of a member may have translation displacements perpendicular to the axis of the member, creating a “rotation” like configuration of the member This kind of displacement ... force equilibrium of the whole structure: FBD of the whole structure. The two shear forces in the third equation can be expressed in terms of member-end moments, via the FBD of each member V a ... configuration Side-sway of a member and the member-end moments. The member-end moments given in the figure above were derived in the context of the moment distribution method We recall that while

Ngày tải lên: 05/08/2014, 09:20

... the force method and the displacement method under static loads There are other topics either within the realm of linear static analysis or beyond, that are fundamental to structural analysis ... and VbR of the beam shown and find the maximum value of each for a distributed load of intensity 10 kN/m and indefinite length of coverage Problem 1 (2) (3) Construct the influence lines of VcL, ... level of the upper chord members Problem 2.(2) 4 m 6@3 m = 18 m A G F 4 m 6@3 m = 18 m A G F Trang 191 IntroductionThe present text covers mainly the two major methods of linear structural analysis,

Ngày tải lên: 05/08/2014, 09:20

... used in any displacement method of analysis. A sample of the numerical values of the factors in these two equations is given in the table below for two configurations of rectangular sections. ... direct effect of temperature change and construction or manufacturing error is the change of shape or dimension of a structural member. For a statically determinate structure, this change of shape ... moments of the beam shown. L=10 m. Non-prismatic beam example. Solution. We choice to use the slope-deflection method. There is only one DOF, the rotation at node b: θ b . The equation of equilibrium

Ngày tải lên: 05/08/2014, 09:20

... degrees of freedom because the spatial variable, x, is continuous and represents an infinite number of points along the beam We shall pursue an approximate analysis by lumping the total mass of the ... the beam at the tip of the beam This results in a single degree of freedom (SDOF) system because we need to consider dynamic equilibrium only at the tip Dynamic equilibrium of a distributed mass ... dynamic equilibrium of this SDOF system is shown in the above figure The dynamic equilibrium equation of the lumped mass is m 2 2 dt v d where m= ρL and k is the force per unit length of lateral deflection

Ngày tải lên: 05/08/2014, 09:20

... microenvironment of ripples and wisps of wind which relate to the particular dynamics of the stock itself. Relegating to a later article the important topic of the application of Midas methods to the ... credibility of the S/R hierarchy on the basis of its manifest ability to bring a degree of order into the apparently random zigzag patterns of stock prices. One measure of the power of any scientific ... simultaneously does a good job of accommodating all of the pullbacks from the start of the move through the dip to 31 at a cumulative volume of about 3.3. (The subsequent penetrations of the TOPFINDER curve...

Ngày tải lên: 23/04/2014, 21:07

... be determined. The resulting method of analysis is simple and straightforward and is very easy to be implemented into a computer program. As a matter of fact, virtually all structural analysis computer ... truss. A complex truss is best solved by the computer version of the method of joint to be described later. A special method, called method of substitution, was developed for complex trusses in the ... given loading case. P A D E F P 31 Truss Analysis: Force Method, Part I 1. Introduction In the chapter on matrix displacement method of truss analysis, truss analysis is formulated with nodal displacement...

Ngày tải lên: 06/07/2014, 11:20

... be determined. The resulting method of analysis is simple and straightforward and is very easy to be implemented into a computer program. As a matter of fact, virtually all structural analysis computer ... and Method of Section The method of joint draws its name from the way a FBD is selected: at the joints of a truss. The key to the method of joint is the equilibrium of each joint. From each FBD, two ... 2. x y 1 2 4m 3m 2m 2m 3 3m 1 3 2 1.0 MN 0.5 MN 31 Truss Analysis: Force Method, Part I 1. Introduction In the chapter on matrix displacement method of truss analysis, truss analysis is formulated with nodal displacement...

Ngày tải lên: 05/08/2014, 09:20