Moment distribution method examples1/10/2024 ![]() ![]() When the unit load is at point A and B, C y = 0ġ3.3 Influence Lines for Statically Indeterminate Beams by Kinematic Method When the unit load is at point C, C y = 1 When the unit load is at point B and C, A y = 0 When the unit load is at point A, A y = 1 For instance, to determine the ordinate of the influence line at point 1, place the unit load at point 1 and the value of the redundant when the unit load is at point 1 and solve as follows: Now that B y is known, the values of the ordinate of the influence lines for other reactions can be obtained using statics. ![]() When the unit load is at different points along the beam, the ordinate of the influence line for the redundant at B y can be computed using the compatibility equation: Cantilever beam.ĭraw the influence lines for the reactions at the supports A, B, and C of the indeterminate beam shown in Figure 13.3. Δ BB = deflection at B due to the unit value of the redundant (i.e., B y = 1). Δ BX = deflection at B due to the unit load at any arbitrary point on the primary structure at a distance x from the fixed support. The redundant B y at the prop can be determined using the following compatibility equation: Then, compute the deflections at these points on the beam using any method. The next step is to apply a unit load at various distances x from the fixed support and at the position where the redundant was removed. Considering the reaction at the prop as the redundant and removing it from the system provides the primary structure. Thus, the propped cantilever has one reaction more than the three equations of equilibrium. For the propped cantilever, the degree of indeterminacy is one, as the beam has four reactions (three at the fixed end and one at the prop). To construct the influence line for the reaction at the prop of the cantilever beam shown in Figure 13.1, first determine the degree of indeterminacy of the structure. The analysis and constructions of the influence lines using the equilibrium and kinematic methods are discussed in this chapter. The distinguishing feature between the graphs of the influence lines for determinate and indeterminate structures is that the former contains straight lines while the later consists of curves. ![]() The procedures for finding influence lines for indeterminate structures by these methods are similar to those outlined in chapter nine for determinate structures. The influence lines for statically indeterminate structures are obtained by the static equilibrium method or by the kinematic method, as was the case for determinate structures. Influence Lines for Statically Indeterminate Structures ![]()
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