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# mudzm8 - Muddy Card Responses Lecture M8 What were the...

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Muddy Card Responses Lecture M8 What were the three points for compatibility of displacements?. For the case of trusses, the displacements of a joint at the end of two or more bar are made up of two components: extension parallel to the axis of the bar, and a rotation that is perpendicular to the bar axis. In addition the two components of displacement must be compatible with the bars remaining joined at that joint. The compatibility PRS question: did not understand? Look at the example of the use of compatibility for the three bar truss in lecture. We will do another example at the start of the next lecture. Didn’t understand the displacement diagram. See above comment. How do we do rotations mathematically, what are they useful for? By making the assumption that we are dealing with small deflections and small displacements, the rotation can be reduced to a displacement perpendicular to the axis of the bar. This makes it easy to solve for the displacements by using trigonometry, or by drawing the displacement diagram to scale. They are useful because they allow us to calculate the deflection of the truss, which is a key component of the structural integrity that we are interested in. What will we use the new point C’ (determined from expansion/compression/rotation) for? This is the displaced location of C. By determining where C’ is, we know the deflection of the truss. We will be asked to design structures to have deflections less than a certain amount, or bar forces less than a certain level, as part of ensuring structural integrity in the design process.

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