GridFrames.pdf - ����������� The degrees of freedom are as follows dn x dn y dn z df x df y df z as shown in the figure and the

# GridFrames.pdf - ����������� The...

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���� ������ The degrees of freedom are as follows, d n x ' , d n y ' , d n z ' , d f x ' , d f y ' , d f z ' as shown in the figure and the corresponding forces with d replaced with q . The local stiffness matrix connection connects q and d . q n x ' q n y ' q n z ' q f x ' q f y ' q f x ' = GJ L 0 0 - GJ L 0 0 0 12 EI L 3 6 EI L 2 0 - 12 EI L 3 6 EI L 2 0 6 EI L 2 4 EI L 0 - 6 EI L 2 2 EI L - GJ L 0 0 GJ L 0 0 0 - 12 EI L 3 - 6 EI L 2 0 12 EI L 3 - 6 EI L 2 0 6 EI L 2 2 EI L 0 - 6 EI L 2 4 EI L d n x ' d n y ' d n z ' d f x ' d f y ' d f x ' ������� [ �� _ � �� _ � � _] =  �� � �� �� - �� � �� � �� �� �� � �� � �� - �� �� � �� �� � �� � �� � �� - � �� � �� - �� � �� �� �� � �� � �� - �� �� - � �� � �� �� �� - � �� �� � �� � �� � �� - � �� � ��  ���������� [ [ ��� ��� � ]] ������������������� �� - �� �� �� � �� - �� �� � �� � �� � �� - � �� � �� - �� �� - �� �� - � �� �� �� - � �� � �� � �� - � �� � �� ������� [ λ _ λ _] = {{ λ �� �� λ �� �� �� � } { �� �� �� �� �� � } {- λ �� �� λ �� �� �� � } { �� �� �� λ �� �� λ } { �� �� �� �� �� � } { �� �� �� - λ �� �� λ }} [ λ �� λ ] // ���������� ������������������� λ λ - λ λ λ λ - λ λ The basic transformation rules are as follows: { d } = [ T ] { D } { Q } = [ T ] T { q } { q } = [ k ] { d } { Q } = [ K ] { D } , where [ K ] = [ T ] T [ k ] [ T ]

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[ K ] is obtained as �������� = ��������� [ [ λ �� λ ]] �� [ ��� ��� � ] � � [ λ �� λ ] ���������� [ ] �������������������� �� λ + � �� λ - � �� λ - � �� λ λ + �� λ λ - �� λ + � �� λ � �� λ - � �� λ λ - �� λ λ - � �� λ �� �� � �� λ - � �� λ - �� �� � �� λ - � �� λ
• Fall '19
• chandiramani

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