The procedure for applying the Muller-Breslau principle is as follows:Remove the constraint at the point of interest for the function of interest. This means if the influence line for a reaction is asked for simply start by pretending the beam is no longer attached to the reaction in question and is free to rotate about the other support. If the influence line for a moment is desired, pretend the point in question is a hinge and the subsequent two sides can rotate about their supports. If the influence line for shear is desired, again pretend the point in question is a shear release, again where both sides can rotate about their supports.Consider the remaining portion of the beam to have infinite rigidity, so it is a straight line free to rotate about the support.Lastly rotate whatever is free to rotate in its positive direction, but only enough to create a deflection of 1 unit total. This means if the moment IL is in question and an imaginary hinge is splitting the beam in two pieces, the two angles created between each rotated side and the original beam must add to equal 1. Similarly if the shear IL is in question the two sides will have opposite directions of rotation. So at the shear release the right side will typically be rotated upwards and the left side will be rotated downward, as this is the sign convention for shear. The total displacement between the two sides of the shear release must equal 1.
Posted on: Sat, 08 Jun 2013 02:25:37 +0000
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