By William R. Spillers

ISBN-10: 0080167829

ISBN-13: 9780080167824

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**Sample text**

G. when Ft =fi+). 4. 3 to perform plastic analysis. Answer: In this exercise, the simplest plastic analysis problem is con sidered in which: 1. Loads are only allowed to act at nodes. 2. All supports are fixed. 3. The reduction of the moment capacity of a beam due to the presence of axial load is neglected. 4. e. P = λΡ(), where P is the usual joint load matrix, P0 is a matrix which represents the fixed ratios of the loads, and λ > 0 is a scalar. 5. The members are uniform between nodes. For this problem (see P.

4) can be written as FN8 = FA. 5) If Eq. 5) is to be valid for an arbitrary F, then Δ = Νδ. If it were not, there would exist a component of Δ, say Δ7 for which (Νδ)7 Φ Δ7, which would yield a contradiction to Eq. 5) by selecting the elements of F to be zero except F7 = 1. If some form other than Eq. 1) is used for the node method, it is simply necessary to use some form other than Eq. 3) for the energy. 3 THE DECOMPOSITION With numerical computation in mind, it is worthwhile to pursue the details of the system matrix, NKN, a little further.

IfW' = E and NF = P are to ho Idfor arbitrary F, it follows Proof: Since NF = P, Eq. 4) can be written as FN8 = FA. 5) If Eq. 5) is to be valid for an arbitrary F, then Δ = Νδ. If it were not, there would exist a component of Δ, say Δ7 for which (Νδ)7 Φ Δ7, which would yield a contradiction to Eq. 5) by selecting the elements of F to be zero except F7 = 1. If some form other than Eq. 1) is used for the node method, it is simply necessary to use some form other than Eq. 3) for the energy. 3 THE DECOMPOSITION With numerical computation in mind, it is worthwhile to pursue the details of the system matrix, NKN, a little further.

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