1. a) For the frame element shown below and the transformation and stiffness matrices given in...

  
 

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1. a) For the frame element shown below and the transformation and stiffness matrices given in Eqs. 4.52 and 4.55, respectively, determine the stiffness matrix expression in terms of angle 0. j2 Uj1 Uj3 b) Assuming that a uniform transverse load of w is acting on the element (positive in positive local y-direction) and uniform axial load f is acting in local x-direction, determine the load vector expression due to uniform transverse and axial loads w and f in terms of 0. where the transformation matrix is 13.01 cos e sine 0 0 130 -sin 0 cos 6 0 0 1 0 cos e sin e 0-sin 0 0. [T] = (4.52) %3D 0 o ledolyodt of loo O nmolqaib leol.odol ane a cos e0 di olo 0. 1 t ginoitsup vaon ni i al oiqab Ioolg odi lo 000 000 AE AE 0. 0. L 12EI 6 ΕΙ 12EI 6EI 0. L3 L2 L3 6EI 4EI 6EI 2EI 0. L2 L2 L. [K] (4.55) xy HUR AE AE 12EI 6EI 12EI 6EI 0. L3 L2 6EI 20 2EIi- 0. L O 6EI 4EI L2 - L2 L 6200 1. a) For the frame element shown below and the transformation and stiffness matrices given in Eqs. 4.52 and 4.55, respectively, determine the stiffness matrix expression in terms of angle 0. j2 Uj1 Uj3 b) Assuming that a uniform transverse load of w is acting on the element (positive in positive local y-direction) and uniform axial load f is acting in local x-direction, determine the load vector expression due to uniform transverse and axial loads w and f in terms of 0. where the transformation matrix is 13.01 cos e sine 0 0 130 -sin 0 cos 6 0 0 1 0 cos e sin e 0-sin 0 0. [T] = (4.52) %3D 0 o ledolyodt of loo O nmolqaib leol.odol ane a cos e0 di olo 0. 1 t ginoitsup vaon ni i al oiqab Ioolg odi lo 000 000 AE AE 0. 0. L 12EI 6 ΕΙ 12EI 6EI 0. L3 L2 L3 6EI 4EI 6EI 2EI 0. L2 L2 L. [K] (4.55) xy HUR AE AE 12EI 6EI 12EI 6EI 0. L3 L2 6EI 20 2EIi- 0. L O 6EI 4EI L2 - L2 L 6200