5003 Lectures - Faculty of Engineering and Applied Science

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E5003 - Ship Structures I 108 © C.G. Daley Topic 10: Problems 10.1. Solve the below by removing the reaction RB (as shown). This creates ‘cut’ problem that is a cantilever beam. 10.2. Force Method. a) Sketch 3 alternative approaches to solving this indeterminate problem using the force method. For each approach, you will need two sketches of the auxiliary systems. b) Using one of the approaches sketched in a) , solve the system to find the reaction at B (in kN)
E5003 - Ship Structures I 109 © C.G. Daley Topic 11: Indeterminate Beams – Displacement Method Cruise Ship in Adriatic Introduction In this chapter we will • introduce the displacement method used to solve structural problems • introduce the standard stiffness components for a beam in 2D and 3D ~~~~~~~~~~~~~~~~~~~~ Indeterminate Problem We start by considering the indeterminate beam as shown below. This could be described as a fixed-pinned beam or a cantilever with a pinned end. Find MA RA and RB To solve this problem with the displacement (stiffness) method we create two subproblems, each simpler than the whole problem. Rather than removing a support (removing a force or moment), we remove a movement (i.e we completely fix the structure). This becomes the problem marked * below. To the * problem, we add a second problem, the ** problem, that fixes any errors that we created with the * problem. In this case we have a moment MB* that should not exist, while we have a θB* that should not be zero. So, in the ** problem, we impose θB**, (and only a θB**) sufficiently large to cause a moment MB** that is equal and opposite to MB*.
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5003 Lectures - Faculty of Engineering and Applied Science

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