# Deflection of determinate structures

A statically indeterminate structure may be classified as: Its use is equivalent to the use of many equilibrium equations. In the example shown above, therefore, we have introduced bending moment at the base, Mb. The equation c is called the principle of virtual w ork for a particle.

Figure 3 A portal frame is statically determinate if there are only three external reactions, because there are three conditions of equilibrium for such a system. When the arbitrary constants?

The beam in figure 3 b is statically redundant to two degree. One of the key ideas of Lagrangian mechanics is that the virtual work done by th e constraint forces should be zero.

For completeness, we would also have to introduce a shear force V and an axial force N at the base of the column, but, as we shall see, there is no component of virtual displacement conjugate to these forces.

A truss having more than 2j — 3 members is statically indeterminate or redundant, the degree of indeterminacy or redundancy being equal to the number of extra members. We are familiar with real work, i.

This is a reasonable assumption, for otherwise a physical system might gain or lose energy simply by being constrained imagine a bead on a stationary hoop moving faster and faster for no apparent reason!

The degree of indeterminacy or redundancy is given by the number of extra or redundant reactions to be determined. Therefore, simply supported cantilever and overhanging beams shown in figure 2 are statically determinate structures.

It is valid irrespective of material behaviour, and hence leads to powerful applications in structural analysi s and finite element analysis. If a portal frame has more than three reactions it is statically indeterminate, the degree of indeterminacy or redundancy being equal to the number of redundant or extra reactions to be determined.

The situ ation is illustrated in Part 1 of the following figure: A more general mathematical statement of the principle of virtual work is as follows: The total virtual work i n the body may also be found by the volume integral of the product of stresses Thus, the principle of virtual wo rk for a deformable body is: Let Qi be a set of real loads acting on a given structure Let Ri be the corresponding real support reactions Let Mi, Vi, and Ni be the sectional forces bending moment, shear, and axial force introduced at the locations where the structure has been cut to allow it to undergo a virtual displacement.

Since the preceding equality is valid for arbitrary virtual displacements, it leads back to the equilibrium equations in a.Chapter 5: Indeterminate Structures – Force Method 1.

Introduction • Statically indeterminate structures are the ones where the independent reaction components, and/or internal forces cannot be beam (beam I) is stable and determinate. The deflection at the reaction point is calculated.

Consider the same determinate beam. STRUCTURAL ANALYSIS - I UNIT-I DEFLECTION OF DETERMINATE STRUCTURES 1. Why is it necessary to compute deflections in structures? Computation of deflection of structures is necessary for the following reasons. Most of the real world structures are statically determinate.

State whether the above statement is true or false. a) True b) False Deflection of centre of simply supported beam will be _____ times that of defection of centre of fixed beam.

a) 1 b) 2 c) 3 d) 4 View Answer. Force Method for Analysis of Indeterminate Structures determinate one by removing some unknown For determinate structures, the force method allows us to find internal forces (using equilibrium i.e.

based on Statics) irrespective of the material information. Material (stress -strain) relationships are. Structure is generally classified into two categories as Determinate and Indeterminate Structures or Redundant Structures for analysis of structures to find forces based on criteria discussed below.

Structure is an assemblage of a number of components like slabs, beams, columns, walls, foundations. deflections of elastic structures using both geometric and energy methods.

A geometric method uses the strain of an elastic structure to determine the deflection. Deflections Deflection Diagrams and the Elastic Curve If you have a difficult time drawing the deflected shape.

Deflection of determinate structures
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