Question 2: For the 2D plane frame shown below, evaluate the transformation matrices [T] and the nodal load vectors in l

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Question 2 For The 2d Plane Frame Shown Below Evaluate The Transformation Matrices T And The Nodal Load Vectors In L 1 (63.6 KiB) Viewed 36 times

Question 2: For the 2D plane frame shown below, evaluate the transformation matrices [T] and the nodal load vectors in local axis system (PL) of all elements. Use these matrices to evaluate the nodal load vectors in the structural/global axis system (PG) of these members. Assemble the element nodal load vectors (PG) and the load acting directly at the nodes to form the overall nodal load vectors of the structure (P). 5 kN/m 3 1.8m 45 KN 4.5 m 4 40 kN 2 7.5m The nodal displacement vector of the above frame is: (X)=[0.0 0.0 0.0 43.459 0.0 -0.31421 43.519 -0.079 0.19666 43.577 0.0 -0.31432 0.0 0.0 0.0] units are in mm and degree (convert it to radian before use). From this nodal displacement vector of the whole structure, extract the nodal displacement vector (XG) of element 3. Using transformation matrix [T] of this element, convert (XG) in terms of nodal displacement vector of the element in its local axis system (XL). Evaluate the stiffness matrix of the element in its local axis system [KL] and calculate member end forces and member end moments of the element due to joint displacements and rotations using [KL] and (XL). Superpose these values with the values of fixed end forces and moments due to the applied member load of 45 kN. Use these values to draw the axial force, shear force and bending moment diagram of this element. All members of the frame have same material (E = 200 GPa) and same cross-section which is a square section of 250 mm x 250 mm. (2) 4 3 3 3 +