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prob_06_07_03

# prob_06_07_03 - Problem 6.7-3 Given The sketch shows two...

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Problem 6.7-3 Given: The sketch shows two uniform beam elements connected at node 2. Prior to making the connection, d.o.f. θ z2 in element 1-2 is condensed, so that node 2 is a hinge connection. Starting with the stiffness matrix of Eq. 2.3-5, obtain the condensed 3 by 3 stiffness matrix of the left hand element. Solution: Eq. 2.3-5 k d E I z L 3 12 6 L 12 6 L 6 L 4 L 2 6 L 2 L 2 12 6 L 12 6 L 6 L 2 L 2 6 L 4 L 2 v 1 θ z1 v 2 θ z2 = Need to condense using: k rr k cr k rc k cc d r d c r r r c = The d.o.f. are already ordered such that: d d r d c = where d r v 1 θ z1 v 2 = d c θ z2 = k rr E I z L 3 12 6 L 12 6 L 4 L 2 6 L 12

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